Hindawi Publishing CorporationJournal of Industrial EngineeringVolume 2013 Article ID 987172 10 pageshttpdxdoiorg1011552013987172

Research ArticleModid trinistic Modl for Rrs upplChain inManufacturing

R N Mahapatra1 B B Biswal2 and P K Parida3

1 Department of Mechanical Engineering Institute of Technical Education and Research SOA University Bhubaneswar 751030 India2Department of Industrial Design National Institute of Technology Rourkela 769008 India3Department of Mechanical Engineering National Institute of Technology Rourkela 769008 India

Correspondence should be addressed to B B Biswal bibhutibiswalgmailcom

Received 30 August 2012 Revised 9 December 2012 Accepted 10 December 2012

Academic Editor Wen Chiung Lee

Copyright copy 2013 R N Mahapatra et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Technology is becoming pervasive across all facets of our lives today Technology innovation leading to development of newproducts and enhancement of features in existing products is happening at a faster pace than ever It is becoming difficult forthe customers to keep up with the deluge of new technology is trend has resulted in gross increase in use of new materials anddecreased customersrsquo interest in relatively older products is paper deals with a novel model in which the stationary demandis fullled by remanufactured products along with newly manufactured products e current model is based on the assumptionthat the returned items from the customers can be remanufactured at a xed rate e remanufactured products are assumed to beas good as the new ones in terms of features quality and worth A methodology is used for the calculation of optimum level forthe newly manufactured items and the optimum level of the remanufactured products simultaneously e model is formulateddepending on the relationship between different parameters An interpretive-modelling-based approach has been employed tomodel the reverse logistics variables typically found in supply chains (SCs) For simplicity of calculation a deterministic approachis implemented for the proposed model

1 Introduction

Gradual increase in the demand of goods has resulted in thereduction of nonrenewable resources with a high percentageof land ll of waste is has shied the modus operandi ofsupply chain largely focusing on recovery options for theend of life products and products returned from variousstages Reverse logistics is the process of moving goods fromtheir typical nal destination for the purpose of capturingvalue or proper disposal It is a process whereby supplychains can become more environments friendly throughrecycling and reusing thereby reducing the amount of virginmaterials used It is observed that all the sales transactionscarried in many product-based supply chains are not nalwith the payment recovery at the point of sales ere isa need to cope up with returns of the product due torecalls warranty claims service returns recovery at the end-of-use disposal at the end-of-life and so forth us the

reverse distribution which is from consumer to producer hasgained tremendous importance in the recent years Reverselogistics stands for all the operations related to reuse ofproducts coming back from customers excess inventory ofproducts andmaterials including collection disassembly andprocessing of used products product parts andor materialsis concept is complicated by the following typical gureson critical thinking

(i) 50 of customers with bad return experience will notbuy from the brand again

(ii) In 60 of the cases the cost increase to process areturned product can be higher than value of product

(iii) Data for returned products are not available or are notused for improving revenue growth and protability

(iv) Liability from noncompliance on waste regulations

2 Journal of Industrial Engineering

ese facts and gures make most of the successfulcompanies focus on their core competenciesmdashdelightingcustomers through stellar forward supply chain Howeverthey experience a persistent lack of control over their reverselogistic processes leading to high cost poor customer servicereduced asset recovery low protability loss of shareholdervalue and decreased competitiveness Organizations andcommunities are forced to consider recovery alternativessuch as reuse repair recycle refurbish remanufacture andcannibalize rather than discarding of the products aer endof life e different product recovery options are shown inFigure 1e product recovery processes aim tominimize theamount of waste sent to landll sites by recovering materialsand parts from old or obsolete products Product recoveryincludes collection disassembly cleaning sorting repairingreconditioning reassembling and testing Brennan et al [1]

Product recovery and reuse of products and materials isnot a new story Waste paper recycling metal scrap brokersand deposit systems for so drink bottles are all examplesthat are in practice since long In all these cases the recoveryof the used products is found to be economically moreattractive than the disposal Out of the different recoveryoptions this paper emphasizes on the remanufacturing ofreturned products that come back to the chain from vari-ous points A model is developed which operates both ondirect manufacturing as well as remanufacturing In themathematical model care has been taken to optimize theinventory level of direct manufacturing as well as that ofthe remanufacturing e primary aim of the work is to thereutilize the resources and therefore it focuses on integrationof the upstreamanddownstreamchains A generalizedmodelfor remanufacturing is shown in Figure 2 is model is acombination of direct manufacturing and remanufacturing

e present study focuses on the deterministic approachof optimizing the reverse supply chain related to inventorycontrol Basically themodel considers some of the parametersas known and constant ones for simplicity of calculationand tries to optimize the return quantities using differenttechniques

2 RelatedWork

A supply chain is a network of facilities and distributionoptions that executes the functions of procurement of mate-rials conversion of these materials into intermediate andnished products and the distribution of these nishedproducts to customers Supply chains exist in both serviceandmanufacturing organizations although the complicationof the chain may vary greatly from industry to industry andorganization to organization e literature review for thesake of clear understanding of this paper is divided into twodistinct divisions forward supply chain and reverse supplychain with specic orientation towards inventory control

3 Forward Supply Chain

Much has been said in the past and research is still goingon the effectiveness of the forward supply chain Accordingto Frankel [2] more emphasis should be given on the key

components (supplier manufacturing and customer) andfactors responsible for successful collaboration of supplychain to make the forward supply chain effective e factorsconsidered for this purpose are willingness to innovate andchange understanding otherrsquos business laying down com-mongoals and objectives choosing appropriatemeasures andincentives and sharing of information

e ability of supply chain members to successfullydesign and execute solutions that facilitate inventory arrivingon time (in the proper condition at the proper location andto the proper customerconsumer) is critical to developingefficient supply chains Arshinder et al [3] has stressedupon the coordination between various members of thesupply chain Supply chains are generally complex and arecharacterized by numerous activities spread over multiplefunctions which differ from organizations to organizationserefore it becomes a challenge for effectively coordinatingthe supply chain In the paper the coordination mechanismis elaborately discussed with the gaps in the coordinationprocess An empirical case study has been conducted andthe difficulty in SC coordination is expressed through a shbone diagram e authors conclude that the Supply chaincoordination (SCC) problems could be due to the conictingobjectives that leads to a short time relationships with SCmembers hence the environment and expectations changesfrequently with addition of new members Hence the SCmembersmust work towards a unied system and coordinatewith each other Silver [4] investigated and presented atutorial overview of inventory management In this paperthe author tried to categorize the inventory problems andassociated models based on dimensions He concluded thatthere exists a continuing gap between theory and practiceof SC pertinent to inventory management and suggested anumber of research topics that will bridge the gap Alfares[5] has presented a model of an inventory system withstock-dependent demand in which the holding cost is astep function of storage time Two types of holding costvariation in terms of storage time have been consideredese are retroactive increase and incremental increaseSimple optimization algorithms have been developed andnumerical examples have been solved From the analysis heconcluded that both the optimal order quantity and the cycletime decrease when the holding cost increases

An extensive study shows that while some researchersare emphasizing on the effectiveness of the SC with keycomponents and factors others are interested on SSC Someresearch work focuses on the cost reduction by optimizingthe order quantity From the above discussion it is clearthat SC effectiveness depends on a wide range of decisionse decision to be most effective depends on the type oforganization and the business environment

4 Reverse Supply Chain

Reverse supply chain is all about coordination and controlphysical pickup and delivery of the material parts andproducts from the eld to reuse repair recycle refurbishremanufacture cannibalize and subsequent returns to the

Journal of Industrial Engineering 3

Partsfabrication

Modulessubassembly

Productassembly

Distribution UsersRawmaterial

Landll

Recycle Cannibalize Remanufacture Refurbish Repair Reuse

F 1 Product recovery options

Material ow

Manufacturermaterial inventory

Supplier materialinventory

Manufacturerproduct inventory

Retailerproductinventory

ird party usedproduct

inventory Manufacturer used productinventory

Consumer Manufacturing

Remanufacturing

Product ow Used product ow

F 2 A generalized model for remanufacturing

eld where appropriate further action can be taken to includethem again in the mainstream of the supply chain

41 Repair and Recycle Dobos and Richter [6] has analyzeda production-recycling system His analysis consists of twotypes of models e rst model is related to minimiza-tion of the EOQ related costs and the second one is thegeneralization of the rst model with linear waste disposalrecycling production and buyback costs According to theauthor the pure strategy (either production or recycling) isoptimal when compared with the mixed strategy If thesepure strategies are not technologically feasible and someused products do not return or even more as the sold oneswill come back and some of them are not recycled thenthe option is to adopt the mixed strategy with some upperbound on the buyback rate Oh and Hwang [7] considered arecycling system where the supplier receives a xed portionof recyclable material from customers Like used cans andcrashed bottles recyclable materials become rawmaterials ofnew ones In order to meet the demand he also purchasesadditional raw material from outside He did nd out the

optimal solution by consideringcomparing the total coste order quantity production setup and the productionlot are optimized based on minimization of the total costKoh et al [8] obtained the economic order quantity (EOQ)for newly produced products and the optimal inventorylevel of recoverable items to start the recovery processsimultaneously in a joint EOQ and EPQ model Accordingto the relationship with the parameters a numerical modelis proposed with one setup for recovery (or one order fornew products) and many order for new products (or manysetups for recovery) e system was modeled under foursituations and a solution procedure is established to ndout the optimal control parameters A more clear study iscarried out by Mabini et al [9] in the eld of repairableinventory e authors considered two different situationsand the approach is similar to EOQ model formulation erst one is the single-item with a xed and known scrappingrate and ample repair capacitye second one is themodiedform of the rst which account for multiple items that share acommon and limited repair capacity From the above studyone can get important relationships between serviceable

4 Journal of Industrial Engineering

and nonserviceable inventory levels between replenishmentquantities and the specied service level or among multipleitems competing for a limited repair capacity Richter [10]modeled a situation where some share of the used products iscollected and later repaired the other products are disposedoutside according to certain waste disposal rate is modelis extended to the case of variable setup numbers n and m forproduction and repair within some collection time intervalRichter [11] studied an EOQ model in which the stationarydemand can be satised by newly made products and byrepaired productsismodel assumes that the used productsare collected and later repaired at some rate and the otherproducts might be disposed outside according to some wastedisposal rateis model extends previous studies to the caseof variable setup numbers n and m for production and repairwithin some variable collection time interval

42 Remanufacturing Teunter and Vlachos [12] studied asingle item hybrid production system with manufacturingand remanufacturing It is assumed that remanufacturing isprotable and when there are more demands than returnsTeunter and Vander Laan [13] provided a DCF (discountedcash ow) inventory model with disposal and remanufactur-ing It is of common use to add the discount rate times thecapital tied up in a product to the out-of-pocket holding costratee author suggest that one should be very careful whileapplying the average cost approach for more complex modelswith remanufacturing and disposal as no set of holdingcost rate will lead to DCF optimal Richter and Sombrutzki[14] discussed the reverse WagnerWhitinrsquos dynamic pro-duction planning and inventory control model and some ofits extensions e model can efficiently deal with severalcombinations of reverse and original models e restrictionof the proposed model is that if the quantity of used productsdoes not match the demand of remanufactured goods themodel fails erefore the design of appropriate algorithmsseems to be another important research direction Chunget al [15] analyzed an inventory system with traditionalforward-oriented material ow as well as a reverse materialow supply chain In the reverse material ow the usedproducts are returned remanufactured and shipped to theretailer for resale A multi-echelon inventory system withremanufacturing capability is proposed e authors triedto maximize the joint prots of the supplier the manufac-turer the third-party recycle dealer and the retailer undercontractual design e analytical results of this study showa substantial prot increase using the integrated approach

e objective of the present work is to provide anapproachable model which in future may replace the existingmodel with uniform demand rate nite production rateand with shortages allowed is particular study is directedtowards stabilizing the diversied opinions in the eld ofreturned item inventory In most of the cases the modelsare deterministic e approach here is a different from themodels discussed earlier in the sense that the returned iteminventory is being used as a substitute to stock out conditionse primary concern of this work is environmental benetswhere use of return items will decrease the depletion rate

of resources Successful implementation of the method canreduce the inventory cost of nished goods An exampleproblem has been discussed to illustrate the capability of themodel

5 The Conventional Inventory Model

Considering a manufacturing scenario the conventionalmodel of inventory shown (in Figure 3) has a nite produc-tion rate In thismodel the inventory is zero at the beginninge nished product inventory increases at a constant rate(119870119870 119870 119870119870119870 for time 1198791198791 until it reaches a level 119868119868119898119898 ere is noreplenishment during time 1198791198792 Inventory decreases (as it isshipped out or used internally) at a constant rate 119870119870 till itbecomes zero Shortage starts lling up at a constant rate119870119870 during time 1198791198793 (as there is no manufacturing) until thisbacklog reaches a level 119878119878max At the beginning of time 1198791198794manufacturing starts and backlog is lled at a constant rate119870119870 119870 119870119870 till the backlog becomes zero at the end of period 1198791198794is completes the cycle

6 TheModel Variables

119902119902 = manufactured quantity during the cycle119870119870 = rate of pro-duction (unitsyear) 119870119870 = rate of consumption (unitsyear)1198621198621 = holding cost during the time interval 119879119879 (Rsunityear)1198621198622 = shortage cost during time interval 119879119879 (Rsunityear) 1198621198623= setup cost per setupe total time is given by

119879119879 119879 1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 (1)

e total cost per unit time can be computed as follows

Total cost 119879 119862119862

119879 10076521007652121198621198621 times 119868119868119898119898 times 100764910076491198791198791 + 119879119879210076651007665 +

121198621198622 times 119878119878

times 100764910076491198791198793 + 119879119879410076651007665 + 119862119862310076681007668 100764910076491198791198791 + 1198791198792 + 1198791198793 + 1198791198794100766510076651198701(2)

It can be shown that

119868119868119898119898 119879 119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 119878119878119878

1198791198791 + 1198791198792 119879119868119868119898119898

119870119870 119870 119870119870+119868119868119898119898119870119870

⟹ 1198791198791 + 1198791198792 119879 119868119868119898119898 100765210076521

119870119870 119870 119870119870+111987011987010076681007668

⟹ 1198791198791 + 1198791198792 119879 10076841007684119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 11987811987810077001007700 10076521007652

1119870119870 119870 119870119870

+111987011987010076681007668 119878

(3)

also

1198791198793 + 1198791198794 119879119878119878

119870119870 119870 119870119870+119878119878119870119870

(4)

⟹1198791198793 + 1198791198794 119879 119878119878 100765210076521

119870119870 119870 119870119870+111987011987010076681007668 (5)

Journal of Industrial Engineering 5

Quantity

Time

Costs

Other considerations

bull Holding cost

bull Procurement cost

bull Shortage cost

bull Demand rate

bull Consumption rate

F 3 A model with uniform demand rate nite production rate and shortages allowed

Hence

1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 =119902119902119877119877 (6)

Now substituting (1198791198791 +1198791198792) (1198791198793 +1198791198794) 1198791198791 +1198791198792 +1198791198793 +1198791198794 and119868119868119898119898 in (2) for total cost and using 120597120597120597120597120597120597120597119902119902 = 120597 we get

119902119902optimal = 1003532100353221205971205973 times1205971205971 + 12059712059731205971205971 times 1205971205972

times 10035301003530119870119870 times 119877119877119870119870 119870 119877119877

(7)

However this model is bound to have stock outs whichmay lead to disturbance in the committed delivery scheduleand hence customer dissatisfaction Further the model usesvirgin raw materials for production which calls for moreinvestment on acquiring thematerials as well as its processingrequirements

7 The ProposedModel

is model as shown in Figure 4 can be a substitute for theinventory models where stock outs are allowede stock outpart for the existing model is replaced by the products fromremanufacturinge total cycle time is taken as ldquo119905119905rdquoere aretwo cycles operating at the same time (one is remanufacturingcycle which is shown at the bottom and the second one isthe direct manufacturing with remanufactured items whichis shown on the top)

In the remanufacturing cycle the products having poten-tial to be remanufactured are collected back at a rate 119891119891 119891119889119889 where 119891119891 is the fraction of return and 119889119889 is the demandrate e value of ldquo119891119891rdquo may vary between 0 and 1 whereasthat of ldquo119889119889rdquo depends on the market demand e rate ofremanufacturing needs to be decided in such a manner

T 1e values of 119878119878 119868119868119898119898 and total cost with variation of fractionreturned

119891119891 119878119878 119868119868119898119898 TC01 176 615 728802 277 555 692303 344 517 668404 393 491 651505 429 472 638806 457 458 629007 480 447 621108 500 437 614709 516 430 6093

that it reaches the maximum level ldquo119878119878rdquo at the end of thecycle time ldquo119905119905rdquo e whole lot of remanufactured products istransferred to the direct manufacturing cycle at this pointof time for satisfying the market demand An inventorylevel of the remanufactured products becomes zero the nextremanufacturing cycle begins

In the proposed model the cycle of direct manufacturingis supplemented with remanufactured items During the timeldquo1199051199051rdquo all the remanufactured products are consumed andthe nished product inventory comes down to zero At thebeginning of time ldquo1199051199052rdquo direct manufacturing starts with a rateldquo119901119901rdquo and at the same time the market demands are satisedwith a rate ldquo119889119889rdquo e inventory level of nished products risesat a rate (119901119901 119870 119889119889) and attains a value ldquo119868119868119898119898rdquo at the end ofperiod ldquo1199051199052rdquo At the beginning of the period ldquo1199051199053rdquo the directmanufacturing is stopped and market demand is satisedfrom the stock of inventory of nished products At the endof the period ldquo1199051199053rdquo the stock level comes down to zero By this

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

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2 Journal of Industrial Engineering

ese facts and gures make most of the successfulcompanies focus on their core competenciesmdashdelightingcustomers through stellar forward supply chain Howeverthey experience a persistent lack of control over their reverselogistic processes leading to high cost poor customer servicereduced asset recovery low protability loss of shareholdervalue and decreased competitiveness Organizations andcommunities are forced to consider recovery alternativessuch as reuse repair recycle refurbish remanufacture andcannibalize rather than discarding of the products aer endof life e different product recovery options are shown inFigure 1e product recovery processes aim tominimize theamount of waste sent to landll sites by recovering materialsand parts from old or obsolete products Product recoveryincludes collection disassembly cleaning sorting repairingreconditioning reassembling and testing Brennan et al [1]

Product recovery and reuse of products and materials isnot a new story Waste paper recycling metal scrap brokersand deposit systems for so drink bottles are all examplesthat are in practice since long In all these cases the recoveryof the used products is found to be economically moreattractive than the disposal Out of the different recoveryoptions this paper emphasizes on the remanufacturing ofreturned products that come back to the chain from vari-ous points A model is developed which operates both ondirect manufacturing as well as remanufacturing In themathematical model care has been taken to optimize theinventory level of direct manufacturing as well as that ofthe remanufacturing e primary aim of the work is to thereutilize the resources and therefore it focuses on integrationof the upstreamanddownstreamchains A generalizedmodelfor remanufacturing is shown in Figure 2 is model is acombination of direct manufacturing and remanufacturing

e present study focuses on the deterministic approachof optimizing the reverse supply chain related to inventorycontrol Basically themodel considers some of the parametersas known and constant ones for simplicity of calculationand tries to optimize the return quantities using differenttechniques

2 RelatedWork

A supply chain is a network of facilities and distributionoptions that executes the functions of procurement of mate-rials conversion of these materials into intermediate andnished products and the distribution of these nishedproducts to customers Supply chains exist in both serviceandmanufacturing organizations although the complicationof the chain may vary greatly from industry to industry andorganization to organization e literature review for thesake of clear understanding of this paper is divided into twodistinct divisions forward supply chain and reverse supplychain with specic orientation towards inventory control

3 Forward Supply Chain

Much has been said in the past and research is still goingon the effectiveness of the forward supply chain Accordingto Frankel [2] more emphasis should be given on the key

components (supplier manufacturing and customer) andfactors responsible for successful collaboration of supplychain to make the forward supply chain effective e factorsconsidered for this purpose are willingness to innovate andchange understanding otherrsquos business laying down com-mongoals and objectives choosing appropriatemeasures andincentives and sharing of information

e ability of supply chain members to successfullydesign and execute solutions that facilitate inventory arrivingon time (in the proper condition at the proper location andto the proper customerconsumer) is critical to developingefficient supply chains Arshinder et al [3] has stressedupon the coordination between various members of thesupply chain Supply chains are generally complex and arecharacterized by numerous activities spread over multiplefunctions which differ from organizations to organizationserefore it becomes a challenge for effectively coordinatingthe supply chain In the paper the coordination mechanismis elaborately discussed with the gaps in the coordinationprocess An empirical case study has been conducted andthe difficulty in SC coordination is expressed through a shbone diagram e authors conclude that the Supply chaincoordination (SCC) problems could be due to the conictingobjectives that leads to a short time relationships with SCmembers hence the environment and expectations changesfrequently with addition of new members Hence the SCmembersmust work towards a unied system and coordinatewith each other Silver [4] investigated and presented atutorial overview of inventory management In this paperthe author tried to categorize the inventory problems andassociated models based on dimensions He concluded thatthere exists a continuing gap between theory and practiceof SC pertinent to inventory management and suggested anumber of research topics that will bridge the gap Alfares[5] has presented a model of an inventory system withstock-dependent demand in which the holding cost is astep function of storage time Two types of holding costvariation in terms of storage time have been consideredese are retroactive increase and incremental increaseSimple optimization algorithms have been developed andnumerical examples have been solved From the analysis heconcluded that both the optimal order quantity and the cycletime decrease when the holding cost increases

An extensive study shows that while some researchersare emphasizing on the effectiveness of the SC with keycomponents and factors others are interested on SSC Someresearch work focuses on the cost reduction by optimizingthe order quantity From the above discussion it is clearthat SC effectiveness depends on a wide range of decisionse decision to be most effective depends on the type oforganization and the business environment

4 Reverse Supply Chain

Reverse supply chain is all about coordination and controlphysical pickup and delivery of the material parts andproducts from the eld to reuse repair recycle refurbishremanufacture cannibalize and subsequent returns to the

Journal of Industrial Engineering 3

Partsfabrication

Modulessubassembly

Productassembly

Distribution UsersRawmaterial

Landll

Recycle Cannibalize Remanufacture Refurbish Repair Reuse

F 1 Product recovery options

Material ow

Manufacturermaterial inventory

Supplier materialinventory

Manufacturerproduct inventory

Retailerproductinventory

ird party usedproduct

inventory Manufacturer used productinventory

Consumer Manufacturing

Remanufacturing

Product ow Used product ow

F 2 A generalized model for remanufacturing

eld where appropriate further action can be taken to includethem again in the mainstream of the supply chain

41 Repair and Recycle Dobos and Richter [6] has analyzeda production-recycling system His analysis consists of twotypes of models e rst model is related to minimiza-tion of the EOQ related costs and the second one is thegeneralization of the rst model with linear waste disposalrecycling production and buyback costs According to theauthor the pure strategy (either production or recycling) isoptimal when compared with the mixed strategy If thesepure strategies are not technologically feasible and someused products do not return or even more as the sold oneswill come back and some of them are not recycled thenthe option is to adopt the mixed strategy with some upperbound on the buyback rate Oh and Hwang [7] considered arecycling system where the supplier receives a xed portionof recyclable material from customers Like used cans andcrashed bottles recyclable materials become rawmaterials ofnew ones In order to meet the demand he also purchasesadditional raw material from outside He did nd out the

optimal solution by consideringcomparing the total coste order quantity production setup and the productionlot are optimized based on minimization of the total costKoh et al [8] obtained the economic order quantity (EOQ)for newly produced products and the optimal inventorylevel of recoverable items to start the recovery processsimultaneously in a joint EOQ and EPQ model Accordingto the relationship with the parameters a numerical modelis proposed with one setup for recovery (or one order fornew products) and many order for new products (or manysetups for recovery) e system was modeled under foursituations and a solution procedure is established to ndout the optimal control parameters A more clear study iscarried out by Mabini et al [9] in the eld of repairableinventory e authors considered two different situationsand the approach is similar to EOQ model formulation erst one is the single-item with a xed and known scrappingrate and ample repair capacitye second one is themodiedform of the rst which account for multiple items that share acommon and limited repair capacity From the above studyone can get important relationships between serviceable

4 Journal of Industrial Engineering

and nonserviceable inventory levels between replenishmentquantities and the specied service level or among multipleitems competing for a limited repair capacity Richter [10]modeled a situation where some share of the used products iscollected and later repaired the other products are disposedoutside according to certain waste disposal rate is modelis extended to the case of variable setup numbers n and m forproduction and repair within some collection time intervalRichter [11] studied an EOQ model in which the stationarydemand can be satised by newly made products and byrepaired productsismodel assumes that the used productsare collected and later repaired at some rate and the otherproducts might be disposed outside according to some wastedisposal rateis model extends previous studies to the caseof variable setup numbers n and m for production and repairwithin some variable collection time interval

42 Remanufacturing Teunter and Vlachos [12] studied asingle item hybrid production system with manufacturingand remanufacturing It is assumed that remanufacturing isprotable and when there are more demands than returnsTeunter and Vander Laan [13] provided a DCF (discountedcash ow) inventory model with disposal and remanufactur-ing It is of common use to add the discount rate times thecapital tied up in a product to the out-of-pocket holding costratee author suggest that one should be very careful whileapplying the average cost approach for more complex modelswith remanufacturing and disposal as no set of holdingcost rate will lead to DCF optimal Richter and Sombrutzki[14] discussed the reverse WagnerWhitinrsquos dynamic pro-duction planning and inventory control model and some ofits extensions e model can efficiently deal with severalcombinations of reverse and original models e restrictionof the proposed model is that if the quantity of used productsdoes not match the demand of remanufactured goods themodel fails erefore the design of appropriate algorithmsseems to be another important research direction Chunget al [15] analyzed an inventory system with traditionalforward-oriented material ow as well as a reverse materialow supply chain In the reverse material ow the usedproducts are returned remanufactured and shipped to theretailer for resale A multi-echelon inventory system withremanufacturing capability is proposed e authors triedto maximize the joint prots of the supplier the manufac-turer the third-party recycle dealer and the retailer undercontractual design e analytical results of this study showa substantial prot increase using the integrated approach

e objective of the present work is to provide anapproachable model which in future may replace the existingmodel with uniform demand rate nite production rateand with shortages allowed is particular study is directedtowards stabilizing the diversied opinions in the eld ofreturned item inventory In most of the cases the modelsare deterministic e approach here is a different from themodels discussed earlier in the sense that the returned iteminventory is being used as a substitute to stock out conditionse primary concern of this work is environmental benetswhere use of return items will decrease the depletion rate

of resources Successful implementation of the method canreduce the inventory cost of nished goods An exampleproblem has been discussed to illustrate the capability of themodel

5 The Conventional Inventory Model

Considering a manufacturing scenario the conventionalmodel of inventory shown (in Figure 3) has a nite produc-tion rate In thismodel the inventory is zero at the beginninge nished product inventory increases at a constant rate(119870119870 119870 119870119870119870 for time 1198791198791 until it reaches a level 119868119868119898119898 ere is noreplenishment during time 1198791198792 Inventory decreases (as it isshipped out or used internally) at a constant rate 119870119870 till itbecomes zero Shortage starts lling up at a constant rate119870119870 during time 1198791198793 (as there is no manufacturing) until thisbacklog reaches a level 119878119878max At the beginning of time 1198791198794manufacturing starts and backlog is lled at a constant rate119870119870 119870 119870119870 till the backlog becomes zero at the end of period 1198791198794is completes the cycle

6 TheModel Variables

119902119902 = manufactured quantity during the cycle119870119870 = rate of pro-duction (unitsyear) 119870119870 = rate of consumption (unitsyear)1198621198621 = holding cost during the time interval 119879119879 (Rsunityear)1198621198622 = shortage cost during time interval 119879119879 (Rsunityear) 1198621198623= setup cost per setupe total time is given by

119879119879 119879 1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 (1)

e total cost per unit time can be computed as follows

Total cost 119879 119862119862

119879 10076521007652121198621198621 times 119868119868119898119898 times 100764910076491198791198791 + 119879119879210076651007665 +

121198621198622 times 119878119878

times 100764910076491198791198793 + 119879119879410076651007665 + 119862119862310076681007668 100764910076491198791198791 + 1198791198792 + 1198791198793 + 1198791198794100766510076651198701(2)

It can be shown that

119868119868119898119898 119879 119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 119878119878119878

1198791198791 + 1198791198792 119879119868119868119898119898

119870119870 119870 119870119870+119868119868119898119898119870119870

⟹ 1198791198791 + 1198791198792 119879 119868119868119898119898 100765210076521

119870119870 119870 119870119870+111987011987010076681007668

⟹ 1198791198791 + 1198791198792 119879 10076841007684119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 11987811987810077001007700 10076521007652

1119870119870 119870 119870119870

+111987011987010076681007668 119878

(3)

also

1198791198793 + 1198791198794 119879119878119878

119870119870 119870 119870119870+119878119878119870119870

(4)

⟹1198791198793 + 1198791198794 119879 119878119878 100765210076521

119870119870 119870 119870119870+111987011987010076681007668 (5)

Journal of Industrial Engineering 5

Quantity

Time

Costs

Other considerations

bull Holding cost

bull Procurement cost

bull Shortage cost

bull Demand rate

bull Consumption rate

F 3 A model with uniform demand rate nite production rate and shortages allowed

Hence

1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 =119902119902119877119877 (6)

Now substituting (1198791198791 +1198791198792) (1198791198793 +1198791198794) 1198791198791 +1198791198792 +1198791198793 +1198791198794 and119868119868119898119898 in (2) for total cost and using 120597120597120597120597120597120597120597119902119902 = 120597 we get

119902119902optimal = 1003532100353221205971205973 times1205971205971 + 12059712059731205971205971 times 1205971205972

times 10035301003530119870119870 times 119877119877119870119870 119870 119877119877

(7)

However this model is bound to have stock outs whichmay lead to disturbance in the committed delivery scheduleand hence customer dissatisfaction Further the model usesvirgin raw materials for production which calls for moreinvestment on acquiring thematerials as well as its processingrequirements

7 The ProposedModel

is model as shown in Figure 4 can be a substitute for theinventory models where stock outs are allowede stock outpart for the existing model is replaced by the products fromremanufacturinge total cycle time is taken as ldquo119905119905rdquoere aretwo cycles operating at the same time (one is remanufacturingcycle which is shown at the bottom and the second one isthe direct manufacturing with remanufactured items whichis shown on the top)

In the remanufacturing cycle the products having poten-tial to be remanufactured are collected back at a rate 119891119891 119891119889119889 where 119891119891 is the fraction of return and 119889119889 is the demandrate e value of ldquo119891119891rdquo may vary between 0 and 1 whereasthat of ldquo119889119889rdquo depends on the market demand e rate ofremanufacturing needs to be decided in such a manner

T 1e values of 119878119878 119868119868119898119898 and total cost with variation of fractionreturned

119891119891 119878119878 119868119868119898119898 TC01 176 615 728802 277 555 692303 344 517 668404 393 491 651505 429 472 638806 457 458 629007 480 447 621108 500 437 614709 516 430 6093

that it reaches the maximum level ldquo119878119878rdquo at the end of thecycle time ldquo119905119905rdquo e whole lot of remanufactured products istransferred to the direct manufacturing cycle at this pointof time for satisfying the market demand An inventorylevel of the remanufactured products becomes zero the nextremanufacturing cycle begins

In the proposed model the cycle of direct manufacturingis supplemented with remanufactured items During the timeldquo1199051199051rdquo all the remanufactured products are consumed andthe nished product inventory comes down to zero At thebeginning of time ldquo1199051199052rdquo direct manufacturing starts with a rateldquo119901119901rdquo and at the same time the market demands are satisedwith a rate ldquo119889119889rdquo e inventory level of nished products risesat a rate (119901119901 119870 119889119889) and attains a value ldquo119868119868119898119898rdquo at the end ofperiod ldquo1199051199052rdquo At the beginning of the period ldquo1199051199053rdquo the directmanufacturing is stopped and market demand is satisedfrom the stock of inventory of nished products At the endof the period ldquo1199051199053rdquo the stock level comes down to zero By this

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

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International Journal of

Journal of Industrial Engineering 3

Partsfabrication

Modulessubassembly

Productassembly

Distribution UsersRawmaterial

Landll

Recycle Cannibalize Remanufacture Refurbish Repair Reuse

F 1 Product recovery options

Material ow

Manufacturermaterial inventory

Supplier materialinventory

Manufacturerproduct inventory

Retailerproductinventory

ird party usedproduct

inventory Manufacturer used productinventory

Consumer Manufacturing

Remanufacturing

Product ow Used product ow

F 2 A generalized model for remanufacturing

eld where appropriate further action can be taken to includethem again in the mainstream of the supply chain

41 Repair and Recycle Dobos and Richter [6] has analyzeda production-recycling system His analysis consists of twotypes of models e rst model is related to minimiza-tion of the EOQ related costs and the second one is thegeneralization of the rst model with linear waste disposalrecycling production and buyback costs According to theauthor the pure strategy (either production or recycling) isoptimal when compared with the mixed strategy If thesepure strategies are not technologically feasible and someused products do not return or even more as the sold oneswill come back and some of them are not recycled thenthe option is to adopt the mixed strategy with some upperbound on the buyback rate Oh and Hwang [7] considered arecycling system where the supplier receives a xed portionof recyclable material from customers Like used cans andcrashed bottles recyclable materials become rawmaterials ofnew ones In order to meet the demand he also purchasesadditional raw material from outside He did nd out the

optimal solution by consideringcomparing the total coste order quantity production setup and the productionlot are optimized based on minimization of the total costKoh et al [8] obtained the economic order quantity (EOQ)for newly produced products and the optimal inventorylevel of recoverable items to start the recovery processsimultaneously in a joint EOQ and EPQ model Accordingto the relationship with the parameters a numerical modelis proposed with one setup for recovery (or one order fornew products) and many order for new products (or manysetups for recovery) e system was modeled under foursituations and a solution procedure is established to ndout the optimal control parameters A more clear study iscarried out by Mabini et al [9] in the eld of repairableinventory e authors considered two different situationsand the approach is similar to EOQ model formulation erst one is the single-item with a xed and known scrappingrate and ample repair capacitye second one is themodiedform of the rst which account for multiple items that share acommon and limited repair capacity From the above studyone can get important relationships between serviceable

4 Journal of Industrial Engineering

and nonserviceable inventory levels between replenishmentquantities and the specied service level or among multipleitems competing for a limited repair capacity Richter [10]modeled a situation where some share of the used products iscollected and later repaired the other products are disposedoutside according to certain waste disposal rate is modelis extended to the case of variable setup numbers n and m forproduction and repair within some collection time intervalRichter [11] studied an EOQ model in which the stationarydemand can be satised by newly made products and byrepaired productsismodel assumes that the used productsare collected and later repaired at some rate and the otherproducts might be disposed outside according to some wastedisposal rateis model extends previous studies to the caseof variable setup numbers n and m for production and repairwithin some variable collection time interval

42 Remanufacturing Teunter and Vlachos [12] studied asingle item hybrid production system with manufacturingand remanufacturing It is assumed that remanufacturing isprotable and when there are more demands than returnsTeunter and Vander Laan [13] provided a DCF (discountedcash ow) inventory model with disposal and remanufactur-ing It is of common use to add the discount rate times thecapital tied up in a product to the out-of-pocket holding costratee author suggest that one should be very careful whileapplying the average cost approach for more complex modelswith remanufacturing and disposal as no set of holdingcost rate will lead to DCF optimal Richter and Sombrutzki[14] discussed the reverse WagnerWhitinrsquos dynamic pro-duction planning and inventory control model and some ofits extensions e model can efficiently deal with severalcombinations of reverse and original models e restrictionof the proposed model is that if the quantity of used productsdoes not match the demand of remanufactured goods themodel fails erefore the design of appropriate algorithmsseems to be another important research direction Chunget al [15] analyzed an inventory system with traditionalforward-oriented material ow as well as a reverse materialow supply chain In the reverse material ow the usedproducts are returned remanufactured and shipped to theretailer for resale A multi-echelon inventory system withremanufacturing capability is proposed e authors triedto maximize the joint prots of the supplier the manufac-turer the third-party recycle dealer and the retailer undercontractual design e analytical results of this study showa substantial prot increase using the integrated approach

e objective of the present work is to provide anapproachable model which in future may replace the existingmodel with uniform demand rate nite production rateand with shortages allowed is particular study is directedtowards stabilizing the diversied opinions in the eld ofreturned item inventory In most of the cases the modelsare deterministic e approach here is a different from themodels discussed earlier in the sense that the returned iteminventory is being used as a substitute to stock out conditionse primary concern of this work is environmental benetswhere use of return items will decrease the depletion rate

of resources Successful implementation of the method canreduce the inventory cost of nished goods An exampleproblem has been discussed to illustrate the capability of themodel

5 The Conventional Inventory Model

Considering a manufacturing scenario the conventionalmodel of inventory shown (in Figure 3) has a nite produc-tion rate In thismodel the inventory is zero at the beginninge nished product inventory increases at a constant rate(119870119870 119870 119870119870119870 for time 1198791198791 until it reaches a level 119868119868119898119898 ere is noreplenishment during time 1198791198792 Inventory decreases (as it isshipped out or used internally) at a constant rate 119870119870 till itbecomes zero Shortage starts lling up at a constant rate119870119870 during time 1198791198793 (as there is no manufacturing) until thisbacklog reaches a level 119878119878max At the beginning of time 1198791198794manufacturing starts and backlog is lled at a constant rate119870119870 119870 119870119870 till the backlog becomes zero at the end of period 1198791198794is completes the cycle

6 TheModel Variables

119902119902 = manufactured quantity during the cycle119870119870 = rate of pro-duction (unitsyear) 119870119870 = rate of consumption (unitsyear)1198621198621 = holding cost during the time interval 119879119879 (Rsunityear)1198621198622 = shortage cost during time interval 119879119879 (Rsunityear) 1198621198623= setup cost per setupe total time is given by

119879119879 119879 1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 (1)

e total cost per unit time can be computed as follows

Total cost 119879 119862119862

119879 10076521007652121198621198621 times 119868119868119898119898 times 100764910076491198791198791 + 119879119879210076651007665 +

121198621198622 times 119878119878

times 100764910076491198791198793 + 119879119879410076651007665 + 119862119862310076681007668 100764910076491198791198791 + 1198791198792 + 1198791198793 + 1198791198794100766510076651198701(2)

It can be shown that

119868119868119898119898 119879 119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 119878119878119878

1198791198791 + 1198791198792 119879119868119868119898119898

119870119870 119870 119870119870+119868119868119898119898119870119870

⟹ 1198791198791 + 1198791198792 119879 119868119868119898119898 100765210076521

119870119870 119870 119870119870+111987011987010076681007668

⟹ 1198791198791 + 1198791198792 119879 10076841007684119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 11987811987810077001007700 10076521007652

1119870119870 119870 119870119870

+111987011987010076681007668 119878

(3)

also

1198791198793 + 1198791198794 119879119878119878

119870119870 119870 119870119870+119878119878119870119870

(4)

⟹1198791198793 + 1198791198794 119879 119878119878 100765210076521

119870119870 119870 119870119870+111987011987010076681007668 (5)

Journal of Industrial Engineering 5

Quantity

Time

Costs

Other considerations

bull Holding cost

bull Procurement cost

bull Shortage cost

bull Demand rate

bull Consumption rate

F 3 A model with uniform demand rate nite production rate and shortages allowed

Hence

1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 =119902119902119877119877 (6)

Now substituting (1198791198791 +1198791198792) (1198791198793 +1198791198794) 1198791198791 +1198791198792 +1198791198793 +1198791198794 and119868119868119898119898 in (2) for total cost and using 120597120597120597120597120597120597120597119902119902 = 120597 we get

119902119902optimal = 1003532100353221205971205973 times1205971205971 + 12059712059731205971205971 times 1205971205972

times 10035301003530119870119870 times 119877119877119870119870 119870 119877119877

(7)

However this model is bound to have stock outs whichmay lead to disturbance in the committed delivery scheduleand hence customer dissatisfaction Further the model usesvirgin raw materials for production which calls for moreinvestment on acquiring thematerials as well as its processingrequirements

7 The ProposedModel

is model as shown in Figure 4 can be a substitute for theinventory models where stock outs are allowede stock outpart for the existing model is replaced by the products fromremanufacturinge total cycle time is taken as ldquo119905119905rdquoere aretwo cycles operating at the same time (one is remanufacturingcycle which is shown at the bottom and the second one isthe direct manufacturing with remanufactured items whichis shown on the top)

In the remanufacturing cycle the products having poten-tial to be remanufactured are collected back at a rate 119891119891 119891119889119889 where 119891119891 is the fraction of return and 119889119889 is the demandrate e value of ldquo119891119891rdquo may vary between 0 and 1 whereasthat of ldquo119889119889rdquo depends on the market demand e rate ofremanufacturing needs to be decided in such a manner

T 1e values of 119878119878 119868119868119898119898 and total cost with variation of fractionreturned

119891119891 119878119878 119868119868119898119898 TC01 176 615 728802 277 555 692303 344 517 668404 393 491 651505 429 472 638806 457 458 629007 480 447 621108 500 437 614709 516 430 6093

that it reaches the maximum level ldquo119878119878rdquo at the end of thecycle time ldquo119905119905rdquo e whole lot of remanufactured products istransferred to the direct manufacturing cycle at this pointof time for satisfying the market demand An inventorylevel of the remanufactured products becomes zero the nextremanufacturing cycle begins

In the proposed model the cycle of direct manufacturingis supplemented with remanufactured items During the timeldquo1199051199051rdquo all the remanufactured products are consumed andthe nished product inventory comes down to zero At thebeginning of time ldquo1199051199052rdquo direct manufacturing starts with a rateldquo119901119901rdquo and at the same time the market demands are satisedwith a rate ldquo119889119889rdquo e inventory level of nished products risesat a rate (119901119901 119870 119889119889) and attains a value ldquo119868119868119898119898rdquo at the end ofperiod ldquo1199051199052rdquo At the beginning of the period ldquo1199051199053rdquo the directmanufacturing is stopped and market demand is satisedfrom the stock of inventory of nished products At the endof the period ldquo1199051199053rdquo the stock level comes down to zero By this

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

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4 Journal of Industrial Engineering

and nonserviceable inventory levels between replenishmentquantities and the specied service level or among multipleitems competing for a limited repair capacity Richter [10]modeled a situation where some share of the used products iscollected and later repaired the other products are disposedoutside according to certain waste disposal rate is modelis extended to the case of variable setup numbers n and m forproduction and repair within some collection time intervalRichter [11] studied an EOQ model in which the stationarydemand can be satised by newly made products and byrepaired productsismodel assumes that the used productsare collected and later repaired at some rate and the otherproducts might be disposed outside according to some wastedisposal rateis model extends previous studies to the caseof variable setup numbers n and m for production and repairwithin some variable collection time interval

42 Remanufacturing Teunter and Vlachos [12] studied asingle item hybrid production system with manufacturingand remanufacturing It is assumed that remanufacturing isprotable and when there are more demands than returnsTeunter and Vander Laan [13] provided a DCF (discountedcash ow) inventory model with disposal and remanufactur-ing It is of common use to add the discount rate times thecapital tied up in a product to the out-of-pocket holding costratee author suggest that one should be very careful whileapplying the average cost approach for more complex modelswith remanufacturing and disposal as no set of holdingcost rate will lead to DCF optimal Richter and Sombrutzki[14] discussed the reverse WagnerWhitinrsquos dynamic pro-duction planning and inventory control model and some ofits extensions e model can efficiently deal with severalcombinations of reverse and original models e restrictionof the proposed model is that if the quantity of used productsdoes not match the demand of remanufactured goods themodel fails erefore the design of appropriate algorithmsseems to be another important research direction Chunget al [15] analyzed an inventory system with traditionalforward-oriented material ow as well as a reverse materialow supply chain In the reverse material ow the usedproducts are returned remanufactured and shipped to theretailer for resale A multi-echelon inventory system withremanufacturing capability is proposed e authors triedto maximize the joint prots of the supplier the manufac-turer the third-party recycle dealer and the retailer undercontractual design e analytical results of this study showa substantial prot increase using the integrated approach

e objective of the present work is to provide anapproachable model which in future may replace the existingmodel with uniform demand rate nite production rateand with shortages allowed is particular study is directedtowards stabilizing the diversied opinions in the eld ofreturned item inventory In most of the cases the modelsare deterministic e approach here is a different from themodels discussed earlier in the sense that the returned iteminventory is being used as a substitute to stock out conditionse primary concern of this work is environmental benetswhere use of return items will decrease the depletion rate

of resources Successful implementation of the method canreduce the inventory cost of nished goods An exampleproblem has been discussed to illustrate the capability of themodel

5 The Conventional Inventory Model

Considering a manufacturing scenario the conventionalmodel of inventory shown (in Figure 3) has a nite produc-tion rate In thismodel the inventory is zero at the beginninge nished product inventory increases at a constant rate(119870119870 119870 119870119870119870 for time 1198791198791 until it reaches a level 119868119868119898119898 ere is noreplenishment during time 1198791198792 Inventory decreases (as it isshipped out or used internally) at a constant rate 119870119870 till itbecomes zero Shortage starts lling up at a constant rate119870119870 during time 1198791198793 (as there is no manufacturing) until thisbacklog reaches a level 119878119878max At the beginning of time 1198791198794manufacturing starts and backlog is lled at a constant rate119870119870 119870 119870119870 till the backlog becomes zero at the end of period 1198791198794is completes the cycle

6 TheModel Variables

119902119902 = manufactured quantity during the cycle119870119870 = rate of pro-duction (unitsyear) 119870119870 = rate of consumption (unitsyear)1198621198621 = holding cost during the time interval 119879119879 (Rsunityear)1198621198622 = shortage cost during time interval 119879119879 (Rsunityear) 1198621198623= setup cost per setupe total time is given by

119879119879 119879 1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 (1)

e total cost per unit time can be computed as follows

Total cost 119879 119862119862

119879 10076521007652121198621198621 times 119868119868119898119898 times 100764910076491198791198791 + 119879119879210076651007665 +

121198621198622 times 119878119878

times 100764910076491198791198793 + 119879119879410076651007665 + 119862119862310076681007668 100764910076491198791198791 + 1198791198792 + 1198791198793 + 1198791198794100766510076651198701(2)

It can be shown that

119868119868119898119898 119879 119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 119878119878119878

1198791198791 + 1198791198792 119879119868119868119898119898

119870119870 119870 119870119870+119868119868119898119898119870119870

⟹ 1198791198791 + 1198791198792 119879 119868119868119898119898 100765210076521

119870119870 119870 119870119870+111987011987010076681007668

⟹ 1198791198791 + 1198791198792 119879 10076841007684119902119902 100765210076521 11987011987011987011987011987010076681007668 119870 11987811987810077001007700 10076521007652

1119870119870 119870 119870119870

+111987011987010076681007668 119878

(3)

also

1198791198793 + 1198791198794 119879119878119878

119870119870 119870 119870119870+119878119878119870119870

(4)

⟹1198791198793 + 1198791198794 119879 119878119878 100765210076521

119870119870 119870 119870119870+111987011987010076681007668 (5)

Journal of Industrial Engineering 5

Quantity

Time

Costs

Other considerations

bull Holding cost

bull Procurement cost

bull Shortage cost

bull Demand rate

bull Consumption rate

F 3 A model with uniform demand rate nite production rate and shortages allowed

Hence

1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 =119902119902119877119877 (6)

Now substituting (1198791198791 +1198791198792) (1198791198793 +1198791198794) 1198791198791 +1198791198792 +1198791198793 +1198791198794 and119868119868119898119898 in (2) for total cost and using 120597120597120597120597120597120597120597119902119902 = 120597 we get

119902119902optimal = 1003532100353221205971205973 times1205971205971 + 12059712059731205971205971 times 1205971205972

times 10035301003530119870119870 times 119877119877119870119870 119870 119877119877

(7)

However this model is bound to have stock outs whichmay lead to disturbance in the committed delivery scheduleand hence customer dissatisfaction Further the model usesvirgin raw materials for production which calls for moreinvestment on acquiring thematerials as well as its processingrequirements

7 The ProposedModel

is model as shown in Figure 4 can be a substitute for theinventory models where stock outs are allowede stock outpart for the existing model is replaced by the products fromremanufacturinge total cycle time is taken as ldquo119905119905rdquoere aretwo cycles operating at the same time (one is remanufacturingcycle which is shown at the bottom and the second one isthe direct manufacturing with remanufactured items whichis shown on the top)

In the remanufacturing cycle the products having poten-tial to be remanufactured are collected back at a rate 119891119891 119891119889119889 where 119891119891 is the fraction of return and 119889119889 is the demandrate e value of ldquo119891119891rdquo may vary between 0 and 1 whereasthat of ldquo119889119889rdquo depends on the market demand e rate ofremanufacturing needs to be decided in such a manner

T 1e values of 119878119878 119868119868119898119898 and total cost with variation of fractionreturned

119891119891 119878119878 119868119868119898119898 TC01 176 615 728802 277 555 692303 344 517 668404 393 491 651505 429 472 638806 457 458 629007 480 447 621108 500 437 614709 516 430 6093

that it reaches the maximum level ldquo119878119878rdquo at the end of thecycle time ldquo119905119905rdquo e whole lot of remanufactured products istransferred to the direct manufacturing cycle at this pointof time for satisfying the market demand An inventorylevel of the remanufactured products becomes zero the nextremanufacturing cycle begins

In the proposed model the cycle of direct manufacturingis supplemented with remanufactured items During the timeldquo1199051199051rdquo all the remanufactured products are consumed andthe nished product inventory comes down to zero At thebeginning of time ldquo1199051199052rdquo direct manufacturing starts with a rateldquo119901119901rdquo and at the same time the market demands are satisedwith a rate ldquo119889119889rdquo e inventory level of nished products risesat a rate (119901119901 119870 119889119889) and attains a value ldquo119868119868119898119898rdquo at the end ofperiod ldquo1199051199052rdquo At the beginning of the period ldquo1199051199053rdquo the directmanufacturing is stopped and market demand is satisedfrom the stock of inventory of nished products At the endof the period ldquo1199051199053rdquo the stock level comes down to zero By this

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 5

Quantity

Time

Costs

Other considerations

bull Holding cost

bull Procurement cost

bull Shortage cost

bull Demand rate

bull Consumption rate

F 3 A model with uniform demand rate nite production rate and shortages allowed

Hence

1198791198791 + 1198791198792 + 1198791198793 + 1198791198794 =119902119902119877119877 (6)

Now substituting (1198791198791 +1198791198792) (1198791198793 +1198791198794) 1198791198791 +1198791198792 +1198791198793 +1198791198794 and119868119868119898119898 in (2) for total cost and using 120597120597120597120597120597120597120597119902119902 = 120597 we get

119902119902optimal = 1003532100353221205971205973 times1205971205971 + 12059712059731205971205971 times 1205971205972

times 10035301003530119870119870 times 119877119877119870119870 119870 119877119877

(7)

However this model is bound to have stock outs whichmay lead to disturbance in the committed delivery scheduleand hence customer dissatisfaction Further the model usesvirgin raw materials for production which calls for moreinvestment on acquiring thematerials as well as its processingrequirements

7 The ProposedModel

is model as shown in Figure 4 can be a substitute for theinventory models where stock outs are allowede stock outpart for the existing model is replaced by the products fromremanufacturinge total cycle time is taken as ldquo119905119905rdquoere aretwo cycles operating at the same time (one is remanufacturingcycle which is shown at the bottom and the second one isthe direct manufacturing with remanufactured items whichis shown on the top)

In the remanufacturing cycle the products having poten-tial to be remanufactured are collected back at a rate 119891119891 119891119889119889 where 119891119891 is the fraction of return and 119889119889 is the demandrate e value of ldquo119891119891rdquo may vary between 0 and 1 whereasthat of ldquo119889119889rdquo depends on the market demand e rate ofremanufacturing needs to be decided in such a manner

T 1e values of 119878119878 119868119868119898119898 and total cost with variation of fractionreturned

119891119891 119878119878 119868119868119898119898 TC01 176 615 728802 277 555 692303 344 517 668404 393 491 651505 429 472 638806 457 458 629007 480 447 621108 500 437 614709 516 430 6093

that it reaches the maximum level ldquo119878119878rdquo at the end of thecycle time ldquo119905119905rdquo e whole lot of remanufactured products istransferred to the direct manufacturing cycle at this pointof time for satisfying the market demand An inventorylevel of the remanufactured products becomes zero the nextremanufacturing cycle begins

In the proposed model the cycle of direct manufacturingis supplemented with remanufactured items During the timeldquo1199051199051rdquo all the remanufactured products are consumed andthe nished product inventory comes down to zero At thebeginning of time ldquo1199051199052rdquo direct manufacturing starts with a rateldquo119901119901rdquo and at the same time the market demands are satisedwith a rate ldquo119889119889rdquo e inventory level of nished products risesat a rate (119901119901 119870 119889119889) and attains a value ldquo119868119868119898119898rdquo at the end ofperiod ldquo1199051199052rdquo At the beginning of the period ldquo1199051199053rdquo the directmanufacturing is stopped and market demand is satisedfrom the stock of inventory of nished products At the endof the period ldquo1199051199053rdquo the stock level comes down to zero By this

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Industrial Engineering

time the stock of nished products in the remanufacturedcycle are carried over to the cycle of direct manufacturingwith remanufactured items and process continues

e silver line on the proposed model is that thedisadvantages associated in the conventional model (wherestock outs are allowed) are completely eliminated As themodel uses remanufacturing of recovered products there isa decrease in the total cost and there will be an increase inthe productivity Since returned items are remanufacturedto ll out for raw material inventories there is a substantialenvironmental benet as it controls the depletion rate ofresources to a great magnitude Additionally the possibilityof loss of goodwill from the customers resulting from stockouts is completely eliminated in the proposed model eprimary concern is environmental benets where the use ofreturn items will decrease the depletion rate of resourcesSuccessfully implementing the method can reduce the costof nished goods is helps in reduction of the raw materialsupplies

8 The Variables for the ProposedModel

e following are the variables used for the model119863119863 = annual demand for the item 119889119889 = the demand

rateconsumption rate for the item 119901119901 = the rate of produc-tionprocurement of the nished product in direct manu-facturing 119891119891 = fraction of the demand rate that is used forremanufacturing 1198621198621 = holding cost for the nished goodsin direct manufacturing as well as in remanufacturing 1198621198622= holding cost for the goods in remanufacturing cycle 1198621198620= order costset up cost for direct manufacturing 1198621198621

0 =order costset up cost for remanufacturing 119868119868119898119898 = maximumlevel of the nished products in direct manufacturing 119878119878 =maximum level of the nished products in remanufacturing 119905119905= cycle time 1199051199051 = time in which remanufactured products areconsumed 1199051199052 = time during which inventory buildup takesplace in direct manufacturing 1199051199053 = time in which inventorylevel for direct manufacturing comes to zero

e model on mathematical analysis gives out thefollowing parameters

(a) Holding cost for nished goods inventory

= 1198621198621 times (Area OAB) + 1198621198621 times (Area BCD)

= 1198621198621 times121198781198781199051199051 + 1198621198621 times

12119868119868119898119898 times 100764910076491199051199051 + 119905119905210076651007665

=119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

2

⟹ Holding cost for nished goods inventory ∶

= 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734

(b) Holding cost for remanufactured ∶

goods inventory = 12times 1198911198911198891198891199051199052 times 1198621198622

(c) Number of set ups = 11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

rArr set up cost for nished goods inventory

= 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(d) Set up cost for remanufactured

goods inventory = 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

(8)

erefore the annual total cost of inventory

(TC) = 10077181007718119862119862111987811987811990511990512

+1198621198621119868119868119898119898 100764910076491199051199051 + 119905119905210076651007665

210077341007734 +

12times 1198911198911198891198891199051199052 times 1198621198622

+ 1198621198620 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665+ 1198621198621

0 times119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665

(9)

e following parameters can be derived from the model

119878119878 = 1198891198891199051199051

119878119878 = 119891119891119889119889119905119905 ⟹ 119905119905 =119878119878119891119891119889119889

(10)

From (10)

119891119891 119891 119905119905 = 1199051199051 (11)

1199051199052 =119868119868119898119898

10076491007649119901119901 119901 11988911988910076651007665 (12)

119868119868119898119898 = 1198891198891199051199053 (13)

From (12) and (13)

1198891198891199051199053 = 10076491007649119901119901 119901 11988911988910076651007665 1199051199052 ⟹ 119889119889100764910076491199051199052 + 119905119905310076651007665 = 1199011199011199051199052

⟹ 100764910076491199051199052 + 119905119905310076651007665 =119901119901119889119889times 1199051199052

(14)

Substituting these values in (9) for total cost we have

TC =11986211986211198781198781198911198911199051199052

+11986211986211198681198681198981198981199011199011199051199052

2119889119889+1198621198622119891119891119889119889119905119905

2

2+ 1198621198620 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

+ 11986211986210 times

11986311986310076491007649119868119868119898119898 + 11987811987810076651007665

⟹ TC =1198621198621119878119878

2

2119889119889+

11986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

times 1198681198682119898119898 +1198621198622119878119878

2

2119891119891119889119889

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

⟹ TC =1198781198782

1198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 +1198621198621119901119901

2119889119889 10076491007649119901119901 119901 11988911988910076651007665times 1198681198682119898119898

+119863119863

10076491007649119868119868119898119898 + 11987811987810076651007665100765010076501198621198620 + 119862119862

1010076661007666

(15)

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 7

Dir

ect

man

ufa

ctu

rin

g

wit

h r

eman

ufa

ctu

red

item

sR

e-m

anu

fact

uri

ng

F 4 e proposed model with remanufacturing

Dir

ect

man

ufa

ctu

rin

g w

ith

re

man

ufa

ctu

red

it

ems

Safety stock

ROL

Re-

man

ufa

ctu

rin

g

F 5 e inventory model considering safety stock

Equation (15) clearly shows that the total cost is a function of1198621198621 119878119878 119889119889 119901119901 1198681198681198981198981198621198622 1198911198911198631198631198621198620 and119862119862

10 Out of these1198621198621 119889119889 1199011199011198621198622

1198911198911198631198631198621198620 and11986211986210 are constants and are assumed to be known

e values of 119878119878 and 119868119868119898119898 can be found by minimizing the totalcost function erefore using

120597120597TC120597120597119868119868119898119898

= 0120597120597TC120597120597119878119878

= 0 (16)

we can get the maimum levels of nished products throughdirect manufacturing (119868119868119898119898) and that through the remanufac-turing (119878119878)

Considering 120597120597120597120597119862119862120597120597120597119868119868119898119898 = 0 we have

211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

119901119863119863 100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

⟹211986811986811989811989811986211986211199011199012119889119889 10076491007649119901119901 119901 11988911988910076651007665

=21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669

⟹ 119868119868119898119898 =2119878119878 10076491007649119901119901 119901 11988911988910076651007665

11986211986211199011199011007653100765311986211986212

+11986211986222119891119891

10076691007669

(17)

Now using 120597120597TC120597120597120597119878119878 = 0 we can have

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 119901119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652= 0

rArr21198781198781198891198891007653100765311986211986212

+11986211986222119891119891

10076691007669 =119863119863100765010076501198621198620 + 119862119862

1010076661007666

10076491007649119868119868119898119898 + 119878119878100766510076652

(18)

Substituting the value of 119868119868119898119898 from (17) in (18) we get

21198781198781198891198891007653100765311986211986212+11986211986222119891119891

10076691007669=119863119863100765010076501198621198620+119862119862

1010076661007666

10077131007713100764910076492119878119878 1007649100764911990111990111990111988911988910076651007665 120597119862119862111990111990110076651007665 1007649100764911986211986211205972+1198621198622120597211989111989110076651007665+119878119878100772910077292

(19)

Simplifying the above equation we can have

119878119878 = 10077191007719119863119863100765010076501198621198620 + 119862119862

1010076661007666 times 4119862119862

21119901119901

21198911198913119889119889

100771310077132 10076491007649119901119901 119901 11988911988910076651007665 100764910076491198621198621119891119891 + 119862119862210076651007665 + 21198621198621119901119901119891119891100772910077292 times 100764910076491198621198621119891119891 + 119862119862210076651007665

1007735100773511205973

(20)

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Industrial Engineering

9 Use of Safety Stock to Avoid the Stock out dueto Change in the Demand

It is of great importance to consider the stock out condition inthe directmanufacturing part of the cycle due to the variationof the demand rateemodel considering the stock is shownin Figure 5 It is shown as a dotted line indicating higherdemand in the triangle AOB Because of the higher demandthe zero stock condition will occur at 119883119883 instead of 119861119861 (referFigure 5) erefore the need of a safety stock is essential tocope up with this kind of situation e safety stock can becalculated by using the concept of service level We set theservice level to a very high value (more than 90) whichmeans that out of 100 times we face such situation we shallbe able to supply the items from the stock at least 90 times

e safety stocks can be determined as

Safety Stock = 119911119911119911119911119871119871 (21)

where 119885119885 = number of standard deviations for a speciedservice level which can be directly used from the normaldistribution table (eg service level 95 means that 119885119885 =165) and 119911119911119871119871 = the standard deviation during the lead timeperiod

119911119911119871119871 can be calculated as the square root of the sum of thevariances for each day during the lead time period

119911119911119871119871 = 1003534100353411987111987110055761005576119894119894=1119911119911119889119889119894119894 (22)

where119889119889119894119894 is the standard deviation for each day during the leadtime period

It is to be remembered here that while calculating thetotal cost has two components e rst one is the variablecomponent of the total cost that is related to the Figure 4 andthe second one is the xed component of the total cost that isrelated to the safety stock shown in Figure 5

10 Example Problem

onsidering the pertinent data available from a rm thefollowing values are taken for consideration

e annual demand for the product (119863119863) 24000 unitse set up cost (1198621198620) per set up for direct manufactur-ing Rs100e set up cost (1198621198621

0) per set up for remanufacturingRs60e holding cost for the nished goods in direct man-ufacturing with remanufactured items (1198621198621) Rs10 perunit per yeare holding cost for the goods in remanufacturingcycle Rs6 per unit per yeare fraction return for remanufacturing (119891119891) withinthe range of 01 to 09

Using these values in (17) and (20) with a range of valuesfor fraction return of used goods for remanufacturing the

0 02 04 06 08 1 12 140

100

200

300

400

500

600

700

800

F 6 Variation of remanufactured quantity and raw materialinventory with fraction of demand

0200

400600

800

0200

400600800

Qu

anti

ty o

f re

man

ufa

ctu

red

minus 1500

minus 1000

minus 500

0

500

1000

F 7 e variation of quantities for direct manufacturing andremanufacturing with change in fraction of demand return

associated values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo can be calculated and usingthe values of ldquo119868119868119898119898rdquo and ldquo119878119878rdquo along with the given values in (15)the total costs is computed as shown in Table 1

11 Results and Analysis

e results obtained from the calculations are shown in Table1 e inter-relationship between the various parameters isshown in Figures 6 7 and 8 Looking at the values of thetotal cost it is evident that the total cost decreases withthe increase in the fraction return for remanufacturing (119891119891)Figure 6 shows the variation of 119868119868119898119898 and S with the fraction ofdemand returned for remanufacturing e variation 119878119878 with119891119891 shows that the rate of increase in 119878119878 119878119878119878119878119878 decreases withincrease in the 119891119891 value e variation of 119868119868119898119898 shows that therate of decrease in 119868119868119898119898 119878119878119868119868119898119898119878 decreases with increase in the 119891119891value e values of 119868119868119898119898 and 119878119878 almost agree at 119891119891 = 06

Figure 7 shows the variation of remanufactured quantityand the maximum level of the inventory in direct manufac-turing with change in the fraction of demand return e

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 9

0 02 04 06 08 1 12 146000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

F 8 e variation of total cost with fraction of demand

exponential nature of the curve shows the decrease in thevalues of these parameters at both the ends that is at themaximum values of the parameters and the minimum valuesof the parameters is indicates the optimal level of theparameters that can be chosen for better return on investmentand the increased productivity

Figure 8 shows the variation of total cost with fractionof demand e exponential nature of the curve shows thedecrease in the total cost decreases at a decreased rate withincrease in the ldquo119891119891rdquo value

e major factor in the proposed model is the fractionreturn for remanufacturing is factor varies depending onthe type of industry the type of product and therefore it isvery difficult to quantify All the returned items cannot beremanufactured Remanufacturing depends on the conditionof the returned item as shown in Figure 1 So the major limi-tation is 100 remanufacturing is not attainable ereforeone needs to set the values of 119868119868119898119898 and 119878119878 depending on thetype of industry and closely analyzing its return percentagefor remanufacturing

12 Conclusions

Decreasing prot margins in global markets with overcapac-ity together with increased returns that will be expensive tohandle if products and business processes have not beendesigned to accommodate them will lead to huge lossesCompanies will realize that they need a lifecycle approachto products that is an approach that integrates all productreturns (commercial returns warranty returns repairs end-of-use returns and end-of-life returns) into the businessmodel for the product

Once the reverse supply chain becomes the dominantfactor in modern manufacturing the productivity as a wholewill nd an increasing trend e input resources to theproduction system can be brought with less cost in the formof returned items for remanufacturing is will increasethe productivity as the cost of input resources will decreasee scope and application of reverse supply chain is actually

too vast to be discussed here because of the limitations ofspaceis paper has only explored the remanufacturing partwith certain assumptions in order to making the readersunderstand the activities under reverse supply chain epurpose of this paper is to make the readers familiar withthe eld of reverse supply chain with remanufacturing ediscussed model has taken care of the remanufacturingaspect of reverse supply chain with the development ofa mathematical model e method for determination ofoptimum quantity for the remanufactured products and thedirectly manufactured products are illustrated with the helpof a simple numerical example

e readers are requested to study this carefully and usethis model for further analysis is can be taken as a basemodel to explore and develop a probabilistic model in theeld of reverse supply chain with remanufacturing Readerscan add different dimensions of reverse supply chain such asrecycling to this model and check its feasibility

References

[1] L Brennan S M Gupta and K N Taleb ldquoOperations planningissues in an assemblydisassembly environmentrdquo InternationalJournal of Operations amp Production Management vol 14 no 9pp 57ndash67 1994

[2] R Frankel ldquoe role and relevance of refocused inventorysupply chainmanagement solutionsrdquoBusiness Horizons vol 49no 4 pp 275ndash286 2006

[3] Arshinder A Kanda and S G Deshmukh ldquoSupply chaincoordination perspectives empirical studies and researchdirectionsrdquo International Journal of Production Economics vol115 no 2 pp 316ndash335 2008

[4] E A Silver ldquoInventory management an overview Canadianpublications practical applications and suggestions for futureresearchrdquo INFOR vol 46 no 1 pp 15ndash28 2008

[5] H K Alfares ldquoInventory model with stock-level dependentdemand rate and variable holding costrdquo International Journalof Production Economics vol 108 no 1-2 pp 259ndash265 2007

[6] I Dobos and K Richter ldquoAn extended productionrecyclingmodel with stationary demand and return ratesrdquo InternationalJournal of Production Economics vol 90 no 3 pp 311ndash3232004

[7] Y H Oh and H Hwang ldquoDeterministic inventory model forrecycling systemrdquo Journal of Intelligent Manufacturing vol 17no 4 pp 423ndash428 2006

[8] S G Koh H Hwang K I Sohn and C S Ko ldquoAn optimalordering and recovery policy for reusable itemsrdquoComputers andIndustrial Engineering vol 43 no 1-2 pp 59ndash73 2002

[9] M C Mabini L M Pintelon and L F Gelders ldquoEOQ type for-mulations for controlling repairable inventoriesrdquo InternationalJournal of Production Economics vol 28 no 1 pp 21ndash33 1992

[10] K Richter ldquoe EOQ repair and waste disposal model withvariable setup numbersrdquo European Journal of OperationalResearch vol 95 no 2 pp 313ndash324 1996

[11] K Richter ldquoe extended EOQ repair and waste disposalmodelrdquo International Journal of Production Economics vol 45no 1ndash3 pp 443ndash447 1996

[12] R H Teunter and D Vlachos ldquoOn the necessity of a disposaloption for returned items that can be remanufacturedrdquo Inter-national Journal of Production Economics vol 75 no 3 pp257ndash266 2002

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Industrial Engineering

[13] R Teunter and E Van der Laan ldquoOn the non-optimality of theaverage cost approach for inventorymodels with remanufactur-ingrdquo International Journal of Production Economics vol 79 no1 pp 67ndash73 2002

[14] K Richter and M Sombrutzki ldquoRemanufacturing planningfor the reverse WagnerWhitin modelsrdquo European Journal ofOperational Research vol 121 no 2 pp 304ndash315 2000

[15] S L Chung H M Wee and P C Yang ldquoOptimal policy for aclosed-loop supply chain inventory system with remanufactur-ingrdquoMathematical and ComputerModelling vol 48 no 5-6 pp867ndash881 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of