Inventory Optimization of Fresh Agricultural Products Supply...

Research ArticleInventory Optimization of Fresh Agricultural Products SupplyChain Based on Agricultural Superdocking

Lixin Shen 1 Fucheng Li1 Congcong Li1 Yumin Wang1 Xueqi Qian2 Tao Feng 3

and Cong Wang1

1Dalian Maritime University Dalian China2Beijing Jiaotong University Beijing China3Eindhoven University of Technology Eindhoven Netherlands

Correspondence should be addressed to Lixin Shen shenlixindlmueducn

Received 14 July 2019 Revised 3 December 2019 Accepted 18 December 2019 Published 24 January 2020

Academic Editor Eneko Osaba

Copyright copy 2020 Lixin Shen et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e ldquoagricultural superdockingrdquo mode which has been strong supported by the government has become the main way for freshagricultural products to enter the market in China Based on the analysis of fresh agricultural products supply chain inventorymanagement under the ldquoagricultural superdockingrdquo mode this paper constructs an integrated inventory model for fresh ag-ricultural products of ldquofarmersrsquo professional cooperatives + distribution centers + supermarketsrdquo Considering multiple membersat each echelon of a supply chain a model that maximizes the overall profit of the supply chain is proposed +e model assumesthat the market demand of fresh agricultural products is affected by freshness and sales prices and the distribution center isresponsible for not only storage processing and distribution but also coordinating the production and supply information offarmersrsquo professional cooperatives and the order sales information of supermarkets An improved genetic algorithm is developedto solve the nonlinear optimization problem Results of a case study show that the optimal supply and replenishment strategyunder the given supply chain distribution process are obtained

1 Introduction

Fresh agricultural products are indispensable necessities inpeoplersquos daily life Since 2013 the annual growth rate of freshproducts market in China has remained above 6 and themarket scale of fresh products reached 191 trillion yuan in2018 Fresh agricultural products have the characteristics ofstrong perishability large circulation loss high timelinessand difficult transportation +e traditional multiechelonsupply chain mode of ldquoproducers of agricultural pro-ducts +multiechelon processing enterprises (wholesalemarkets) + retail enterprisesrdquo has many circulation linkswhich involve large losses and the phenomenon of in-creasing price cannot meet the demand for fresh agriculturalproducts ldquoAgricultural superdockingrdquo comes to be a newsupply chain mode in the way that it omits many inter-mediate links and can circulate quickly At present manycompanies have adopted the ldquoagricultural superdockingrdquo

mode of fresh products supply chain such as WalmartHema Fresh China Resources Vanguard and CarrefourWith the strong support of Chinese governments theldquoagricultural superdockingrdquo mode has gradually become themain way for fresh agricultural products to enter the market

+e ldquoagricultural superdockingrdquomode in the paper refersto the ldquofarmersrsquo professional cooperatives + distributioncenters + supermarketsrdquo mode which is the main ldquoagricul-tural superdockingrdquo mode adopted by developing countriesincluding China Here distribution centers mainly refer tothird-party logistics service providers who are responsiblefor the collaborative management production supply andorder sales as well as storage and distribution of fresh ag-ricultural products In this way farmersrsquo professional co-operatives and supermarkets can focus more on their ownproduction and sales +is paper studies the collaborativeinventory management among three-echelon entities underthis mode also known as integrated inventory management

HindawiJournal of Advanced TransportationVolume 2020 Article ID 2724164 13 pageshttpsdoiorg10115520202724164

In general the demand and supply of fresh agriculturalproducts fluctuate considerably with climatic variationsseasonal changes and various social factors [1] thus eachmember in the supply chain should not hold high inventoryToo high or too low inventory will increase procurement costsor lead to lost opportunity costs +erefore it is necessary tooptimize the integrated inventory of the ldquoagriculturalsuperdockingrdquo mode+e goal of inventory optimization is todetermine a reasonable inventory level or replenishmentquantity reduce inventory costs and improve overall benefit+is paper establishes an integrated inventory model of freshagricultural products based on ldquofarmersrsquo professional coop-eratives + distribution centers + supermarketsrdquo mode Withan objective tomaximize the overall profit of the supply chainthe integrated inventory optimization model of fresh agri-cultural products supply chain based on the ldquoagriculturalsuperdockingrdquomode is established and examined by adjustingthe replenishment and supply strategies between variouslevels of the supply chain

2 Literature Review

ldquoAgricultural superdockingrdquo has become an important modeof fresh agricultural products supply chain In recent yearsrelated research on the ldquoagricultural superdockingrdquo modemainly includes the following aspects (1) analysis of de-velopment status and problems In practice the ldquoagriculturalsuperdockingrdquo supply chain has gradually formed multiplemodes Li [2] summarized five types of the ldquoagriculturalsuperdockingrdquo mode ldquofarmersrsquo professional coopera-tives + supermarketsrdquo mode ldquofarmersrsquo professional coop-eratives + distribution centers + supermarketsrdquo modeldquoagricultural product bases + leading enterprises of agri-cultural products + supermarketsrdquo mode direct sales modeand joint direct mining mode +e ldquoagricultural super-dockingrdquo mode in China is mainly the ldquofarmersrsquo professionalcooperatives + distribution centers + supermarketsrdquo mode[3] Guo and Xu [4] studied the stability of farmer coop-eratives in the ldquoagricultural superdockingrdquomode and itsdeterminants +e research found that the requirements ofsupermarkets for agricultural products the effects of gov-ernment policies the capacity of cooperatives and the levelof the regional economy are the most important factors thataffect the stability of the ldquoagricultural superdockingrdquo rela-tionship In the process of ldquoagricultural superdockingrdquo Yanget al [5] established a multiagent simulation model of theldquoagricultural superdockingrdquo order default problem based onthe development of ldquoagricultural superdockingrdquo in NingxiaHui Autonomous Region +e study found that the defaultrate is mainly related to agricultural products prices agri-cultural products qualification rates information trans-mission mechanisms and policy support

Zheng et al [6] constructed the profit function of therevenue sharing contract for two-stage fresh products supplychain and improved revenue sharing contract +e resultsshowed that the improved revenue sharing contract canpromote the information sharing of the fresh products supplychain so that the profit function of the farmersrsquo professionalcooperatives and supermarkets will reach the level of Pareto

optimal Yang [7] studied the unequal rights in the ldquoagri-cultural superdockingrdquo mode from the perspective of con-tribution degree and alliance position Based on the modifiedShapley value method that considers the weight power indexand the average tree solution (A-T solution) that limits thealliance structure the profit distribution strategy concerningunequal rights is given Based on the traditional Shapley profitallocation method Yao and Ran [8] proposed a modifiedprofit allocation method considering risk factors of agricul-tural supply chain participants Li and Wang [3] used therevenue sharing contract to coordinate the ldquoagriculturalsuperdockingrdquo supply chain and the optimal decision-making behavior of eachmember in the coordinationmode isobtained By adjusting the value of the revenue sharing factorthe revenue of the farmersrsquo cooperative and supermarket canachieve Pareto improvement

Chen et al [9] studied the relationship between channelopportunistic behavior and farmersrsquo psychological contractunder the ldquoagricultural superdockingrdquo mode +e studyfound that in the channel relationship the farmersrsquotransactional psychological contract will promote the gen-eration of opportunistic behavior and the relational psy-chological contract will inhibit the generation of channelopportunistic behavior Fan and Zhang [10] made an em-pirical analysis on the production and circulation data ofagricultural products in Langfang Hebei province It isconfirmed that under the guidance of the market and policythe circulation of fresh agricultural products is graduallymoving towards intensification and making full use of thepolicy advantages to develop intensive circulation will be themost advantageous way to distribute fresh agriculturalproducts

Inventory management research includes research onsingle entity two-echelon supply chain and three-echelonsupply chain Wang [11] studied the inventory of single-variety fruit in fresh supermarkets According to the per-ishability and discontinuous demand of fresh fruit a fruitinventory control model of fresh food supermarket chainswas constructed under the conditions of optimal order cycleand optimal price Wang et al [12] established a replen-ishment pricing model in which the deterioration rate obeysthe three-parameter Weibull distribution under a randomenvironment+e direct method is used to solve the retailerrsquosoptimal inventory strategy and commodity price when theprofit is largest Tang et al [13] integrated the decision-making behavior of strategic consumers constructed single-stage and two-stage pricing and inventory decision modelsof retailers and analyzed the influencing mechanism of freshagricultural productrsquos value residual rate on consumerrsquosbehavior retailerrsquos optimal pricing optimal inventory leveland profit Shen et al [14] took small and medium enter-prises in India as an example to study supplier inventorymanagement +e amount to purchase in the harvest seasonas well as how much to retrieve for each selling periodstrongly impact the profit for a wholesaler +erefore Liuet al [15] analyzed the optimal purchase and inventoryretrieval quantities for perishable seasonal agriculturalproducts considering the costs of storage underage andoverage prospects of future prices and demands and

2 Journal of Advanced Transportation

product deterioration Banerjee and Agrawal [16] analyzedthe retailerrsquos inventory management strategy and establisheda model of perishable inventory +e model considers thatthe demand for perishables is affected by sales prices andfreshness Janssen et al [17] proposed a microperiodic in-ventory replenishment policy for quickly perishable goodsunder stochastic demand which can be used for perishableitems when waste reduction is aimed for

Aiming at the two-echelon cold chain system which iscomposed of distribution centers and retailers Wanget al[18] introduced freshness efforts and time factors tocharacterize the quantity and quality loss of fresh agricul-tural products Considering that the demand is affected byprice and freshness taking the maximum average profit ofthe supply chain as the objective function an integrated two-echelon cold chain inventory model is established to analyzethe best freshness input inventory and pricing Mou et al[19] considered the combined effects of freshness and priceon customer demand and the impact of freshness attenu-ation on the deterioration rate and constructed a deterio-ration rate function that is jointly affected by the freshnessand time of fresh agricultural products +e decentralizeddecision-making inventory model and the integrated deci-sion-inventory model of the two-echelon cold chain systemreveal the impact of freshness and price fluctuations on thecold chain inventory strategy and system profit Chen andXiao [20] established a gamemodel for a two-echelon supplychain with one supplier and multiple competing retailers+ey studied the pricing decision and the replenishmentpolicy for each member under both a decentralized channeland a centralized channel Shin et al [1] proposed a two-stage dynamic inventory model for perishables which aimsto minimize the difference between supply and demandunder constraints of market consistency and perishability

Furthermore Fan [21] established an integrated modelwhich contains a manufacturer a distribution center andmultiple retailers +e introduction of preservation costs inthe integrated model combines product freshness level andfresh investment +e optimal replenishment policy whenthe integrated inventory profit is the largest is obtained bysolving the model Jiang [22] established an integrated coldchain inventory model which contains multiple manufac-turers a distribution center and multiple retailers in a finitehorizon +e model considered the value-added service ofthe distribution center and the deterioration rate obeys thethree-parameter Weibull distribution Dai et al [23] ana-lyzed a supply chain with one supplier multiple middlemenand a retailer and proposed a multiechelon inventory modelconsidering the different needs of the three entities +e goalof the model is to minimize the average inventory cost ofeach entity Xu and Feng [24] analyzed the inventory cost ofthe three-echelon inventory system of fresh agriculturalproducts which contains one manufacturer multiple dis-tributors and multiple retailers and then proposed a sim-ulation-based optimization model of the multiecheloninventory system of fresh agricultural products +e effect ofcommodity prices and freshness on demand is not con-sidered in the model Tsai and Chen [25] proposed a sim-ulation-based solution framework for tackling the

multiobjective inventory optimization problem +e goal isto find appropriate settings of reorder point and orderquantity to minimize the expected values of the total in-ventory cost the average inventory level and the expectedvalue of inventory shortage frequency Ma et al [26]regarded quantity loss and quality loss as functions offreshness efforts and demand as a function of freshnessprice and other random variables +e paper studied thecoordination of three-echelon fresh product inventory un-der asymmetric information

In summary existing literature on the two-echelonsupply chain for a single entity is well elaborated Howeverin terms of the three-echelon inventory management re-search no research addressed on the three-echelon inven-tory management issue aiming at a fresh agriculturalproducts supply chain consisting of multiple farmer coop-eratives multiple distribution centers and multiple super-markets In addition most research assumes thatmiddlemen are responsible only for the storage and dis-tribution of fresh agricultural products and without afunction of coordinating production supply and sales in-formation +us when optimizing the level of inventory thein-depth analysis of influential factors of market demandrate is insufficient

In case of the research of inventory optimization algo-rithms Fan [21] established an optimization model for athree-echelon cold chain system consisting of a manufac-turer a distribution center and multiple retailers Consid-ering the complexity and nonlinearity of the inventorymodel a genetic algorithm is used to solve the model toobtain the optimal replenishment strategy when the inte-grated inventory profit is maximized Zhao and Wang [27]verified the feasibility and effectiveness of the simulation-based genetic algorithm optimization method for inventorycontrol under order uncertainty +e simulation-based ge-netic algorithm method can realize the comprehensiveoptimization of customer satisfaction of the hybrid supplychain by modifying the inventory control parameters infinite genetic evolution generations In addition Mousaviet al [28] proposed a modified particle swarm optimizationfor solving the integrated location and inventory controlproblems in a two-echelon supply chain network Xu andFeng [24] proposed a simulation-based optimization modelof a multiechelon inventory system of fresh agriculturalproducts using the FlexSim simulation software and theimproved particle swarm optimization algorithm Particleswarm optimization algorithm is an effective tool for solvingnonlinear continuous optimization problems combinatorialoptimization problems and mixed-integer nonlinear opti-mization problems It has the advantages of simple imple-mentation and fast convergence speed

In summary through the research on literatures of in-ventory management and inventory optimization algo-rithms it is found that there is no research on multiagentinventory management of the three-echelon supply chainunder the ldquoagricultural superdockingrdquo mode +erefore thispaper constructs an integrated inventory model of freshagricultural products supply chain based on the ldquoagriculturalsuperdockingrdquo mode which has multiple members at each

Journal of Advanced Transportation 3

echelon of the supply chain +e model assumes that themarket demand rate is affected by the freshness and the salesprice A distribution center is responsible for storageprocessing and distribution and coordinates the productionand supply information of farmersrsquo professional coopera-tives and the order sales information of supermarkets Dueto the complexity of the members and echelons of the in-tegrated inventory optimization model the concavity andconvexity of the objective function cannot be judged bydirect derivation +us we use a genetic algorithm to solvethe problem At the same time the genetic algorithm isimproved by adding adaptive crossover operators andadopting the elite retention strategy Further a catastrophestep is added to prevent the genetic algorithm from pre-mature maturity falling into a local optimal value Finallythe validity of the model is proved through a case study

3 Model Formulation and Assumptions

+is paper intends to optimize the integrated inventory level ofdistribution centers represented by third-party logistics serviceproviders in the context of ldquoagricultural superdockingrdquo andanalyze the inventory management strategy when multiplesupply chain members participate in transportation anddistribution of fresh agricultural products +ree stakeholdersare taken into account in this three-stage supply chain whichare farmersrsquo professional cooperatives distribution centersand supermarket Farmersrsquo professional cooperatives sell freshagricultural products to distribution centers while distributioncenters sell them to supermarkets at a price which is higherthan their purchase price In this regard the supermarketsreceive the products from distribution centers formarket saleswhich end the operation process of the supply chain +edistribution centers are mainly responsible for the processingof fresh agricultural products purchased from farmersrsquo pro-fessional cooperatives and the logistics and distribution of thewhole supply chain Farmersrsquo professional cooperatives andsupermarkets are only responsible for their respective pro-duction and sales tasks and pay the corresponding logisticsand distribution costs

In order to build the model of this three-stage supplychain model for fresh agricultural products a few as-sumptions are made as follows

(1) Each farmersrsquo professional cooperative provides onetype of fresh agricultural product

(2) Each supermarket orders at least one type of freshagricultural product and the demand rate of freshagricultural products in supermarkets is dependenton the selling price and the degree of freshness of theproducts

(3) Without considering lead-time and out-of-stock thereplenishment process is completed instantaneously

(4) +e unit time productivity of farmersrsquo professionalcooperatives is constant within a limited period oftime

(5) Each distribution center must supply products tosupermarkets and there are no distribution centers

without supply to any supermarkets after the re-plenishment from farmersrsquo professionalcooperatives

(6) +e distribution service is provided by the distri-bution center and farmersrsquo professional cooperativesand supermarkets pay the corresponding distribu-tion costs to the distribution center

In a supply chain system of fresh agricultural productswe assume that the supply chain is composed of M farmersrsquoprofessional cooperatives K distribution centers and Nsupermarkets To make the model formulation simplifiedthe symbols used in the models are listed as follows

W a finite time interval defined to study the optimalreplenishment strategyn the total number of supermarkets for the ith su-permarket i 1 2 n

K the total number of distribution centers for the kth

distribution center k 1 2 Km the total number of farmersrsquo professional cooper-atives for the jth farmersrsquo professional cooperativej 1 2 m (note because the model assumes thateach farmersrsquo professional cooperative only providesone type of fresh agricultural product the varieties offresh agricultural products are also m)ajk the number of times the farmersrsquo professionalcooperative j supplies the distribution center k within alimited period of time wxjk time interval of supplyTjk during the limited period of time W the length ofthe supply interval that a farmersrsquo professional coop-erative j supplies to the distribution center kTjk Aajk 0lexjk le ajkbjki the number of times that the distribution center k

supplies product j to supermarket i during the supplyinterval Tjk +e length of the period of the supplyinterval tjki Tjkbjki 0le zjki le bjkiεj productivity of fresh agricultural products of thefarmersrsquo professional cooperative jIjk(t) Ijk during the supply interval xjk the inventorylevel at time t and the total stock of the entire supplyinterval when the product is supplied from farmersrsquoprofessional cooperative j to the distribution center kII

zjki

jki (t) IIzjki

jki during the supply interval zjki the in-ventory level at time t and the total stock of the entiresupply interval of the product j in the distributioncenter k (supply to the supermarket i)IIIjki(t) IIIjki during the replenishment interval theinventory level at time t and the total stock of the entiresupply interval of product j in supermarket i (re-plenishment from the distribution center k)

gjki gjk single replenishment quantity of product j

from distribution center k to supermarket i Singlereplenishment quantity of product j of distributioncenter k


gzjki

jki the initial inventory of product j (supply to su-permarket i) in the distribution center k in the supplyinterval zjkixjki the total market demand of the product j in thesupermarket i (replenishment from distribution center k)within the replenishment intervalPj unit production costs of farmersrsquo professional co-operative jPji unit selling price of product j in supermarket iP1jk P2jk P3jk unit purchase price sale price andprocessing cost of the product j in distribution center kC1jk C2jk distribution cost rate and price rate of unitproduct j in distribution center kfj djk sji unit inventory cost of fresh agriculturalproducts of farmersrsquo agricultural cooperative j dis-tribution center k and supermarket iθ1 θ2 θ3 quantitative change coefficient of fresh ag-ricultural products of farmersrsquo agricultural cooperativedistribution center and supermarketyjk dummy variable of whether distribution center k

sends orders to farmersrsquo agricultural cooperative jyjk 1 if yes and 0 otherwiseyki dummy variable of whether supermarket i sendsorders to distribution center k yjk 1 if yes and 0otherwiseDji(t) demand rate function of fresh agriculturalproduct j in supermarket iU total profits-the sum of profits of all farmersrsquo ag-ricultural cooperatives distribution centers andsupermarketsdgk sgi revenue sharing coefficient of distributioncenter k and supermarket idzk szi wholesale price discount rate of distributioncenter k and supermarket i

+e demand rate of fresh agricultural products in su-permarkets D which is dependent on the freshness sellingprice and market demand can be calculated as follows

D(t) λt middot (c minus d middot p)

λt λ1 middot eminus αt

(1)

where λ1 is the freshness of fresh agricultural products whenit arrives at the supermarket λt is the freshness of freshagricultural products at time t 0lt tltT T is the sales cycle offresh agricultural products α is a sensitive factor of freshnessto time αgt 0 c is the maximum market demand rate whichis unaffected by the sales price and freshness of products d isthe sensitive factor of demand rate to sales price and p is theselling price of fresh agricultural products

31 Inventory Model of Farmersrsquo Professional CooperativeTaking the process of farmersrsquo professional cooperative jsupplying to distribution center k as an example during thesupply interval lfloor(xjk minus 1) middot Tjk xjk Tjkrfloor the inventory level

at time t when the farmersrsquo professional cooperative j

supplies to the distribution center k is influenced by theproductivity and the quantitative change of fresh agricul-tural products of farmersrsquo professional cooperative Whencombining it with the inventory change formula in classicmetamorphic products proposed by Ghare and Schrader[29] we can get the following formula

dIjk(t)

dt εj minus θ1 middot Ijk(t) (2)

At the beginning of the supply interval xjk that is whent (xjk minus 1) middot Tjk the inventory of the farmersrsquo professionalcooperative j is zero so we get

Ijk xjk minus 11113872 1113873 middot Tjk1113960 1113961 0 (3)

Combining equations (2) and (3) we can get the solution

Ijk(t) εj

θ1middot 1 minus e

minus θ1 middot tminus xjk minus 1( 1113857middotTjk1113858 11138591113876 1113877 (4)

It can be calculated that the total inventory of thefarmersrsquo professional cooperative j supplying to the distri-bution center k during the supply intervallfloor(xjk minus 1) middot Tjk xjk Tjkrfloor is

Ijk 1113946xjk middotTjk

xjk minus 1( 1113857middotTjk

Ijk(t)dt εj

θ1middot Tjk minus

eminus θ1 middotTjk minus 1θ1

1113888 1113889 (5)

+e production cost FS inventory cost FK and distri-bution expense FP of the farmersrsquo professional cooperative j

during the supply interval lfloor(xjk minus 1) middot Tjk xjk Tjkrfloor when thefarmersrsquo professional cooperative j supplies to the distri-bution center k are as follows

FSjk εj middot Pj middot Tjk

FKjk fj middot Ijk

FPjk C2jk middot 1113944n

i1g1jki middot yjk middot yki

(6)

All costs above are generated during the process of singlesupply interval xjk and the supply of the farmersrsquo profes-sional cooperative j to the distribution center k +ereforein the process of producing and supplying to all distributioncenters the total cost FC of all farmersrsquo professional co-operatives is

FCjk 1113944K

k11113944

m

j1yjkajk(FS + FK + FP) (7)

In the process of producing and supplying to all dis-tribution centers the total revenue FY of all farmersrsquo pro-fessional cooperatives is

FY 1113944

n

i11113944

K

k11113944

m

j1yjk middot yki middot ajk middot P1j middot g

1jki (8)

+us the total profit of all farmersrsquo professional coop-eratives FL during the process of producing and supplyingto all distribution centers is

FL FY minus FC (9)


32 Inventory Model of the Distribution Center In the casethat a distribution center k supplies the product j to su-permarket i the inventory level of distribution center k isonly influenced by the quantitative change loss duringsupply interval +us the inventory level of product j

(supplied to supermarket i) of the distribution center k attime t during the supply interval lfloor(zjki minus 1) middot tjki zjki tjkirfloor isas follows

dIIzjki

jki (t)

dt minus θ2 middot IIzjki

jki (t) (10)

At the end of the supply interval lfloor(zjki minus 1) middot tjki zjki tjkirfloorthat is when t zjki middot tjki the closing inventory of the freshagricultural product j (supplied to supermarket i) at distri-bution center k is equal to the sum of the initial inventoryg

zjki+1jki of the next supply interval lfloorzjki middot tjki (zjki + 1) middot tjkirfloor

and the quantity gjki of product j supplied by the distributioncenter k to the supermarket i +us we get

IIzjki

jki zjki middot tjki1113872 1113873 gzjki+1jki + gjki (11)

Combining equations (10) and (11) and using differentialequation we can get the solution

IIzjki

jki (t) gzjki+1jki + gjki1113874 1113875 middot e

minus θ2 middot tminus zjki middottjki( 1113857 (12)

When t (zjki minus 1) middot tjki we can get the initial inventoryof the supply interval by substituting equation (12)

IIzjki

jki zjki minus 11113872 1113873 middot tjki1113872 1113873 gzjki+1jki + gjki1113874 1113875 middot e

θ2 middottjki (13)

According to the analysis of inventory level changes ofdistribution center in the previous example we can see thatthe closing inventory when t bjki middot tjki of the product in adistribution center at the supply interval (the last supplyinterval) is the single replenishment quantity of the su-permarket replenished from the distribution center+erefore

gjki IIbjki

jki bjki middot tjki1113872 1113873 gbjki+1jki + gjki1113874 1113875 middot e

minus θ2middot bjki middottjki minus bjki middottjki( 1113857

gjki + gbjki+1jki

(14)

From the above formula we get gbjki+1jki 0

When t (zjki minus 1) middot tjki the initial inventory of thesupply interval lfloor(zjki minus 1) middot tjki zjki middot tjkirfloor is g

zjki

jki IIzjki

jki

((zjki minus 1) middot tjki) (gjki + gzjki+1jki ) middot eθ2 middottjki so the initial in-

ventory gbjki

jki of the supply interval bjki can be obtained +atis

gbjki

jki gjki + gbjki+1jki1113874 1113875 middot e

θ2 middottjki gjki middot eθ2 middottjki (15)

+us

gbjkiminus 1jki gjki + g

bjki

jki1113874 1113875 middot eθ2 middottjki (16)

By substituting equation (15) in equation (16) we can get


bjki

jki1113874 1113875 middot eθ2 middottjki gjki + gjki middot e

θ2 middottjki1113872 1113873

gjki eθ2 middottjki + e

2θ2 middottjki1113872 1113873

(17)

With the same method we get


bjkiminus 1jki1113874 1113875 middot e

θ2 middottjki gjki

middot eθ2 middottjki + e

2θ2 middottjki + e3θ2 middottjki1113872 1113873



θ2 middottjki gjki


2θ2 middottjki + e3θ2 middottjki + e

4θ2 middottjki1113872 1113873

(18)

After many times of iterations we can get the initialinventory g

zjki

jki of the product j (supplied to the supermarketi) at the distribution center of the supply interval zjki whent (zjki minus 1) middot tjki which can be expressed as

gzjki

jki gjki middot eθ2 middottjki + e

2θ2 middottjki + middot middot middot + ebjkiminus zjki+1( 1113857middotθ2 middottjki1113876 1113877

(19)

Consequently we get

gzjli+1jki gjki middot e

θ2 middottjki + e2θ2 middottjki + middot middot middot + e

bjkiminus zjki( 1113857middotθ2 middottjki1113876 1113877

(20)

By substituting equation (20) in equation (12) we get

IIzjki

jki (t) gjki middot 1 + eθ2 middottjki + e

2θ2 middottjki + middot middot middot + ebjki minus zjki( 1113857middotθ2 middottjki1113874 11138751113876 1113877

+ eminus θ2 middot tminus zjki middottjki( 1113857

(21)

+erefore the total inventory of the product j (suppliedto supermarket i) at the distribution center k during thesupply interval zjki is

IIzjki

jki 1113946zjki middottjki

zjkiminus 1( 1113857middottjki

IIzjki

jki (t)dt minus1θ2

middot gjki

middot 1 minus ebjkiminus zjki+1( 1113857middotθ2 middottjki1113876 1113877

(22)

According to the analysis of inventory level changes ofdistribution center in the previous example we can see thatthe initial inventory g1

jki of the first supply interval (0 tjki)

(that is when zjki 1) for distribution center k to supplyproduct j to supermarket i is the amount of replenishmentfrom farmersrsquo agricultural cooperatives

g1jki II1jki(0) gjki middot e

θ2tjki + e2θ2tjki + middot middot middot + e

bjkiθ2tjki1113872 1113873

(23)

Moreover within a single replenishment interval xjk theordering cost DG processing cost DJ and inventory cost DKof the product (supplied to the supermarket) of the distri-bution center are as follows


DGjki P1j middot g1jki

DJjki P3jk middot g1jki

DKjki djk middot 1113944

bjki

zjki1II

zjki

jki

(24)

Distribution center is responsible for the transportationservice of fresh agricultural products In order to meet theneeds of supermarket i during a single replenishment in-terval xjk the distribution center k replenishes the product j

with the quantity of g1jki from farmersrsquo agricultural coop-

eratives and supplies the product with the quantity of bjki middot

gjki to the supermarket i So the distribution cost distri-bution revenue and sales revenue can be calculated asfollows

DPjki C1jk middot g1jki + C1jk middot bjki middot gjki

DSjki C2jk middot g1jki + C2jk middot bjki middot gjki

DXjki P2jk middot bjki middot gjki

(25)

All above costs and revenues are generated in the processthat a distribution center k supplies product j to super-market i within a single replenishment interval xjk +e totalcost DC generated by all distribution centers in the processof replenishment and supply is

DC 1113944n

i11113944

K

k11113944

m

j1yjk middot yki middot ajk middot (DG + DJ + DK + DP)

(26)

+e total revenues generated by all distribution centersin the process of replenishment and supply is

DY 1113944n

i11113944

K

k11113944

m

j1yjk middot yki middot ajk middot (DS + DX) (27)

We can now obtain the total profits generated by alldistribution centers in the process of replenishment andsupply as follows

DL DY minus DC (28)

33 Inventory Model of the Supermarket Assume a super-market i replenishes product j from distribution center kDuring the replenishment interval lfloor(zjki minus 1) middot tjki zjki middot tjkirfloorthe changes of the inventory level of product j (replenishedfrom the distribution center k) in supermarket i are influ-enced by the quantitative change loss and the demand rate+us the amount of the inventory change of fresh agri-cultural products at time t is as follows

dIIIjki(t)

dt minus Dji(t) minus θ3 middot IIIjki(t) minus λ1 middot e

minus αmiddott

middot c minus d middot Pji1113872 1113873 minus θ3 middot IIIjki(t)

(29)

When t zj1i middot tj1i the closing inventory of the super-market i in the replenishment interval lfloor(zjki minus 1) middot tjki zjki middot

tjkirfloor is 0

IIIjki zjki middot tjki1113872 1113873 0 (30)

Combining equations (29) and (30) and using differ-ential equation we can get

IIIjki(t) λ1 middot c minus d middot Pji1113872 1113873

θ3 minus αe

minus θ3 middott+zjki middottjki middot θ3minus α( ) minus eminus αmiddott

1113876 1113877

(31)

+us in the replenishment intervallfloor(zjki minus 1) middot tjki zjki middot tjkirfloor the total inventory of the productj (replenished from distribution center k) in supermarket Ican be expressed as IIIjki 1113938

zjki middottjki

(zjki minus 1)middottjkiIIIjki(t)dt By taking

(31) here the following equation can be obtained

IIIjki λ1 middot c minus d middot Pji1113872 1113873

θ3middot

1α

minus1θ3

1113888 11138891113890 1113891 middot eminus αmiddotzjki middottjki

+1θ3

middot etjki middot θ3minus αmiddotzjki( 1113857

minus1α

middot eminus αmiddottjki middot zjkiminus 1( 1113857

(32)

During the replenishment intervallfloor(zjki minus 1) middot tjki zjki middot tjkirfloor the total market demand xjk ofproduct j (replenished from the distribution center k) insupermarket i is as follows

Xjki 1113946zjki middottjki


Dji(t)dt minusλ1 middot c minus d middot Pji1113872 1113873

α

middot eminus αmiddotzjki middottjki minus e

minus αmiddottjki middot zjkiminus 1( 11138571113876 1113877

(33)

According to the analysis of inventory level changes ofsupermarket in the previous example the single replen-ishment amount gjki of product j of supermarket i fromdistribution center k is the initial inventory of the replen-ishment interval zjki In other words whent (zjki minus 1) middot tjki the following equation can be obtained

gjki IIIjki zjki minus 11113872 1113873 middot tjki1113872 1113873 λ1 middot c minus d middot Pji1113872 1113873

θ3 minus α


minus eminus αmiddottjki middot zjki minus 1( 1113857

1113876 1113877

(34)

+us during the single replenishment interval zjki theordering cost SG the inventory cost SK and the distributionexpenditure cost SP of product j (replenished from thedistribution center k) at supermarket i are as follows

SGjki P2jk middot gjki

SKjki sji middot IIIjki

SPjki C2jk middot gjki

(35)

All above costs are generated in the process that su-permarket i replenishes product j from distribution center k

within the single replenishment interval zjki +e total cost


SC generated by all supermarkets in replenishment andsupply process is

SC 1113944n

i11113944

K

k11113944

m

j1yjk middot yki middot ajk middot bjki(SG + SK + SP) (36)

+e total revenue SY generated by all supermarkets inthe replenishment and supply process is

SY 1113944n

i11113944

K

k11113944

m

j1yjk middot yki middot ajk middot bjki middot Pji middot Xjki (37)

From equations (36) and (37) we get the total profit SLthat is generated by all supermarkets in the process ofreplenishing from all distribution centers and selling

SL SY minus SC (38)

34Optimizationof Integrated Inventory In order to achievethe goal of optimal management of integrated inventory themaximum value of the overall profit in the supply chain isconsidered as the objective function that is

maxU ajk bjki gjki1113872 1113873 FL + DL + SL (39)

+ree decision variables are involved in the maximiza-tion process including ajk bjki and gjki ajk is the number oftimes that a farmersrsquo professional cooperative j supplies todistribution center k within the limited period A bjki is thenumber of times that a distribution center k supplies productj to supermarket i within the period of Tjk and gjki is thesingle replenishment quantity that the supermarket i re-plenishes the product j from the distribution center k

Given the objective of maximizing total profile eachstakeholder in the three-stage supply chain has to meet theminimum requirement regarding profits and inventorymanagement which can be expressed as follows

FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)

+e aforementioned equation indicates that the profits offarmersrsquo professional cooperatives distribution centers andsupermarkets are not negative while it indicates that theinventory of farmersrsquo professional cooperatives distributioncenters and supermarkets are not negative Considering thecomplexity of the model and simplicity in algorithmicsettings this paper utilizes a genetic algorithm to find theoptimal solutions alowastjk blowastjki and glowastjki

4 Case Study

41 Data and Parameters +e case study considers thesupply chain of fresh agricultural products which is com-posed of three farmersrsquo professional cooperatives two dis-tribution centers and three supermarkets +e finite timeperiod is eight days +e specific distribution process of thesupply chain is described in Figure 1

Based on an empirical investigation of the purchase andsale price of three types of fresh agricultural products

pomegranate bayberry and cherry and combined with thedata of inventory costs and production costs of fresh agri-cultural products in the literature (Fan and Shi) [21 30] thispaper obtains the data of unit inventory cost and unitproduction cost of the three types of fresh agriculturalproducts Moreover the actual proportion of the distribu-tion cost rate and the distribution price rate of the distri-bution center of company M to the selling price of freshagricultural products are obtained (the distribution cost rateis from 45 to 47 and the distribution price rate is from5 to 55) Detailed data arelated to fresh agriculturalproducts of farmersrsquo professional cooperatives distributioncenters and supermarkets as well as the parameters used inthe calculation are presented in Tables 1ndash4

42 Implementation of the Genetic Algorithm

421 Encoding Structure +is paper uses the real numbercoding of the genetic algorithm According to the inde-pendent decision variables of the objective function thispaper uses segmented gene coding to express a group oforders (genotype individual) +e genotype individual iscomposed of three loci +e three decision variables ajk bjkiand gjki correspond to the gene values of the three locirespectively +e changes in each group of genes affect thestate of the genotype individuals

422 Fitness Function +e fitness of chromosomes is(FVAL) minus U In other words the smaller the chromosomefitness the larger value of the objective function

423 Crossover Operation +is paper uses single-pointcrossover For parent chromosomes arbitrary selection of acrossover bit and exchange of all the gene bits from theselected crossover bit were carried out For example thegene A is 110011 the gene B is 100101 and if the crossoverbit is three then the new genes with exchange are 110101 and100011

In this paper the adaptive crossover operator was addedto the design of the genetic algorithm +e crossoverprobability is adjusted according to the adaptive valuefunction of each generation of individuals so that the wholeevolution is carried out along the direction that is conduciveto algorithm convergence +e formula is shown as follows

pi fmax minus fi( 1113857

fmax minus fmin( 1113857 (41)

where i represents an individual pi is the crossover prob-ability of the individual fi is the individual fitness and fminand fmax are the minimum and maximum of populationfitness respectively

424 Mutation Operation +rough the mutation operationof individuals (selected according to the mutation proba-bility) in the population the mutation probability of thegene value of the three loci in the chromosome is 13 Bygenerating random numbers it is determined which loci has


mutated When the random number is less than 0333 thegene value of the first gene loci of the chromosome ismutated When the random number is greater than 0667the gene value of the second loci of the chromosome ismutated When the random number is between 0333 and0667 the gene value of the third loci of the chromosome ismutated

425 Catastrophic and Sort Selection Operation Some in-dividuals in the population are selected by catastropheprobability to suffer catastrophe +is paper puts theprogeny and parent population generated after the aboveoperation of crossover mutation and catastrophic togetherand then ranks the fitness of population in order from smallto large and selects the number of individuals of the original

Farmersrsquo professional cooperative 1



Supermarket 1

Supermarket 2

Supermarket 3

Distribution center 1


Supply process of farmersrsquo professional cooperative 1Supply process of farmersrsquo professional cooperative 2Supply process of farmersrsquo professional cooperative 3

Figure 1 Supply process of agricultural superdocking

Table 1 Data table of farmersrsquo professional cooperatives

A 8 Unit inventory cost Unit production cost Unit sales price Productivityfj Pj P1j εj

j 1 004 2 55 098j 2 012 82 135 095j 3 014 95 15 091Note +e unit of cost and price in this table is yuan per half a kilogram

Table 2 Data table of distribution centers

A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice

Distributioncost rate

Distributionprice rate

Unitinventory

cost

Unitprocessing

cost

Unitsalesprice



djk P3jk P2jk C1jk C2jk djk P3jk P2jk C1jk C2jkj 1 006 01 828 037 041 007 014 864 039 044j 2 014 026 17 078 087 013 02 164 075 083j 3 017 027 192 089 099 016 036 20 094 104Note +e unit of cost price and distribution price unit in this table is yuan per half a kilogram

Table 3 Data table of supermarkets

A 8i 1 i 2 i 3

Unit inventory cost Unit sales price Unit inventory cost Unit sales price Unit inventory cost Unit sales pricesji Pji sji Pji sji Pji

j 1 01 258 01 203 012 24j 2 017 35 016 32 021 345j 3 037 50 038 60 03 53Note +e unit of cost and price in this table is yuan per half a kilogram


population size according to the fitness value of populationfrom small to large so as to generate new population

426 Stop Condition +e stopping condition is set whenthe maximum number of iterations of population evolutionis reached

5 Result Analysis

51 Performance of the Genetic Algorithm A program wasmade using Matlab to implement the genetic algorithm +ealgorithm was run on a computer with an i5 processor and4GB memory It takes about 25 seconds to converge Fig-ure 2 shows the results of the value of the objective functionOne can see that the optimal solution is finally obtainedwhereas the overall profit of the supply chain reaches themaximum

52 Best Replenishment Strategy By running the geneticalgorithm the best solution of replenishment was found+eresults shown in Table 5 present the detailed distribution ofdifferent products between three stakeholders More spe-cifically in the limited period of time the farmersrsquo pro-fessional cooperative 1 supplies products 5 times and 3 timesto the distribution centers 1 and 2 respectively +e dis-tribution center 1 supplies the first type of fresh agriculturalproducts 8 3 and 10 times to the supermarkets 1 2 and 3respectively Distribution center 2 supplies the first type offresh agricultural products 5 times to supermarket 3Farmersrsquo professional cooperative 2 supplies products 10times and 1 time to the distribution centers 1 and 2 re-spectively Distribution center 1 supplies the second type offresh agricultural products 9 times to supermarket 1 Dis-tribution center 2 supplies the second type of fresh agri-cultural products 3 times and 1 time to the supermarkets 2and 3 respectively Farmersrsquo professional cooperative 3supplies products 5 times and 9 times to the distributioncenters 1 and 2 respectively Distribution center 1 suppliesthe third type of fresh agricultural products 4 times and 3times to the supermarkets 1 and 2 Distribution center 2supplies the third type of fresh agricultural products 9 timesto supermarket 1

At the optimal level of replenishment the maximumvalue of overall profit in the supply chain is 72687 thousandyuan among which the profit of all farmersrsquo professionalcooperatives is 69586 thousand yuan the profit of all

distribution centers is 1919 thousand yuan and the profit ofall supermarkets is 1182 thousand yuan as shown in Table 6

One can see from the results that when considering allkinds of costs the fresh agricultural product with large valueis in general replenished more frequently in supermarketsIt also means that in the context of ldquofarmerrsquo professionalcooperative + distribution center + supermarketrdquo the re-plenishment frequency of fresh agricultural products cannotbe considered solely from commodity value sales price ordistribution cost but all kinds of factors in a comprehensiveway

53 Parametric Sensitivity Analysis In order to analyze theinfluence of productivity and inventory cost of fresh agri-cultural products of farmersrsquo professional cooperative on theprofit of farmersrsquo professional cooperative and the overallprofit of the supply chain a sensitivity analysis was con-ducted More specifically we examine the change of profit bychanging the productivity inventory cost distribution profitrate sales price and freshness

531 Influences of Productivity and Inventory CostResults presented in Table 7 show that the overall profit offarmersrsquo professional cooperatives and supply chain increasewhen the productivity of fresh agricultural products in-creases +e change of productivity has a greater impact onthe profits of farmersrsquo professional cooperatives than on theoverall profits of the supply chain However when theproductivity continues to rise by 10 the amount of profitincreases of farmersrsquo professional cooperatives and thewhole supply chain declines +at is because the rise inproductivity leads to the accumulation of fresh agriculturalproducts and the increase in the inventory cost at all levels ofthe supply chain which reduces the profits of farmersrsquoprofessional cooperatives and the whole profits of the supplychain

Moreover the increase in inventory cost reduces theoverall profits of farmersrsquo professional cooperatives and thesupply chain Comparing with productivity it can be foundthat when both inventory cost and productivity increase by5 the impact of productivity on the farmersrsquo professionalcooperatives and the overall profit of the supply chain isgreater than the impact of the inventory cost on both profits

532 Influence of Distribution Profit Rate Results of thechanging distribution profit rate are shown in Table 8 It canbe found that when the distribution profit rate of the dis-tribution center increases by 5 the profit of the distri-bution center and the supply chain increases Further thechange of the distribution profit rate has a greater impact onthe profits of distribution centers than on the overall profitsof the supply chain But when the distribution profit ratecontinues to rise by 10 the amount of increase in the profitof the whole supply chain shows a downward trend +is ismainly because the continuous increase of the distributionprofit rate of the distribution center increases the distri-bution cost of other members of the supply chain which

Table 4 Other parameters used in the equations

λ1 α c d θ1 θ2 θ3098 02 300 5 015 018 02Note λ1 is the freshness of agricultural products when it arrives at thesupermarket α is a sensitive factor of freshness to time αgt 0 c is themaximum market demand rate which is unaffected by the sales price andfreshness of products d is the sensitivity factor of demand rate to sales priceand θ1 θ2 and θ3 represent the quantitative change coefficient of freshagricultural products of farmersrsquo agricultural cooperative distributioncenter and supermarket respectively


reduces the profits of the whole supply chain In practice itmight be beneficial to adjust the distribution profit rateappropriately for improving the efficiency of the supplychain members and overall benefits

533 Influence of Sales Price and Freshness +e sensitivityanalysis results based on the changing sales price andfreshness are shown in Table 9 It can be seen that in theinitial rising period of the sales price of fresh agriculturalproducts in supermarkets (a rise of 5) the profits of

10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50

The fitness curve of total objective function

60 70 80 90 100

times107

The optimum fitnessThe average fitness

Figure 2 Fitness value of the genetic algorithm

Table 5 +e best replenishment strategy

Farmerrsquo professional cooperative 1 Farmerrsquo professionalcooperative 2

Farmerrsquo professionalcooperative 3

a11 a12 a21 a22 a31 a325 3 10 1 5 9b111 b112 b113 b123 b211 b222 b223 b311 b312 b3218 3 10 5 9 3 1 4 3 9

Table 6 Results of the total profit

Farmerrsquo professional cooperative Distribution center Supermarket Supply chain system69586 1919 1182 72687Note +e profit unit in this table is thousand yuan

Table 7 Sensitivity analysis results-changes in productivity and inventory cost

Amplitude of change Productivity Inventory cost+5 +10 +5 +10

Farmersrsquo professional cooperatives Profit after change 76292 71919 64663 61392Amplitude of change +964 +335 minus 707 minus 1178

Supply chain whole Profit after change 79586 74967 67303 64216Amplitude of change +949 +314 minus 741 minus 1165

Note +e unit of profit in this table is ten million yuan

Table 8 Sensitivity analysis results-changes in distribution profitrate

Amplitude of changeDistributionprofit rate

+5 +10

Distribution center Profit after change 02023 02102Amplitude of change +542 +954

Supply chain whole Profit after change 73377 73220Amplitude of change +095 +073



supermarkets and the whole profits of the supply chain havebeen increased Furthermore the range of the rising su-permarket profits is greater than that of the overall profits ofthe supply chain But when the sales price continues toincrease by 10 the market demand rate of fresh agricul-tural products is negatively associated with the sales price inthe sense that decreasing demand rate reduces the profits ofsupermarkets and the overall profit of the supply chain

In addition the decrease of freshness of agriculturalproducts leads to the decline of supermarket profits and theoverall profit of the supply chain When freshness equals tothe amplitude of drop the profit of supermarket and theoverall profit of the supply chain decrease in an upwardtrend +rough the horizontal comparison with the changesof sales price it can be seen that the change in freshness ofagricultural products has a larger impact than the change insales prices on the overall profits of supermarkets and thesupply chain

6 Summary and Conclusions

Based on the agricultural superdocking mode this paperinvestigated the inventory management issue of fresh ag-ricultural products in order to improve the whole opera-tional process of the supply chain +e model incorporatesthe main influencing factors of market demand to describethe inventory change supply chain members in detail whichalso helps improve consumersrsquo perception of purchasingdecisions +e coordination mechanism identified throughthe case study enriches the theoretical understanding ofsupply chain coordination and optimization

More specifically the agricultural superdocking modepenetrates in the simulation of the logistics operationprocess for fresh agricultural products supply chain whereasan integrated inventory pattern of fresh agricultural prod-ucts involving farmersrsquo professional cooperatives distribu-tion centers and supermarkets was determined consideringthe diversity of supply chain members at all levels Study theimpact of changes of inventory level of supply chainmembers on the whole supply chain profit Considering thatthe market demand of fresh agricultural products is affectedby the freshness and sales price an optimal supply chainoptimization not only improves the overall profit but alsoconsumer values achieving a win-win situation

+e main research work and achievements of this paperinclude as follows

+e integrated inventory model of the three-level supplychain of fresh agricultural products considers that themarket demand rate of fresh agricultural products is

influenced by freshness and sales price at the same time anddistribution centers are responsible for the processingtransporting and distribution of fresh agricultural productsand participate in the sales of products +e best supply andreplenishment strategy of each member of the supply chainwere obtained by maximizing the overall profit of the supplychain Moreover the sensitivity analysis puts forward somepractical suggestions on the whole operation planning ofsupply chains

In spite that a three-level supply chain network structurewas established in the current study the subnetworks amongthe levels and the nodes at each level of the supply chain werenot addressed yet+e supply chain optimization of complexstructures may be a natural extension of future researchMoreover the current study assumes a fixed demandHowever the actual demand can be highly uncertain +usfuture research may further study the inventory optimiza-tion under stochastic demand

Data Availability

+e data used to support the findings of this study are in-cluded within the article (Tables 1ndash4)

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by EU H2020 Project (AMD no777742-56) the National Natural Science Foundation ofChina (no 71301108) the Ministry of Education of Hu-manities and Social Science Project (no 18YJC630061) theChina Postdoctoral Science Foundation Funded Project (no2019M661085) the General Program of National NaturalScience Foundation of China (no 71571025) and the SocialScience Planning Fund Project of Liaoning Province (noL19BJL005)

References

[1] M Shin H Lee K Ryu Y Cho and Y-J Son ldquoA two-phasedperishable inventory model for production planning in a foodindustryrdquo Computers amp Industrial Engineering vol 133pp 175ndash185 2019

[2] F Li Optimization Research on Integrated Inventory of FreshAgricultural Products Supply Chain Based on ldquoAgriculturalSuper-dockingrdquo Mode Dalian Maritime University DalianLiaoning 2018

Table 9 Sensitivity analysis results-changes in sales price and freshness

Amplitude of change Sales price Freshness+5 +10 minus 5 minus 10

Supermarket Profit after change 01216 00980 01094 00871Amplitude of change +288 minus 1709 minus 745 minus 2631

Supply chain whole Profit after change 74175 72140 72204 71085Amplitude of change +198 minus 075 minus 066 minus 220



[3] J-F Li and Z-X Wang ldquoResearch on coordination of multi-product ldquoagricultural super-dockingrdquo supply chainrdquo ProcediaManufacturing vol 30 pp 560ndash566 2019

[4] J Guo and L Xu ldquoStability of farmer cooperatives ldquoagri-culture-supermarket dockingrdquo and its impact factor analysisrdquoJournal of Business Economics vol 10 pp 13ndash23 2017

[5] H Yang Y Sun and J Ma ldquoA research on the order defaultfor ldquofarmer-supermarket direct-purchaserdquordquo Science ResearchManagement vol 40 no 6 pp 225ndash233 2019

[6] Qi Zheng T Fan and L Zhang ldquoRevenue-sharing contract offresh product in ldquofarming-supermarket dockingrdquo moderdquoJournal of Systems ampManagement vol 28 no 4 pp 742ndash7512019

[7] J Yang ldquoProfit distribution of farmer-supermarket directpurchase model with unequal powerrdquo Issues in AgriculturalEconomy vol 7 pp 93ndash102 2019

[8] H Yao and X Ran ldquoProfit allocation in agricultural supplychain considering risk factorsrdquo International Journal ofManufacturing Technology and Management vol 33 no 3-4pp 176ndash188 2019

[9] J Chen H Dai and Q Sun ldquoAn empirical study on therelationship between farmersrsquo psychological contract andchannel opportunistic behavior under ldquoagricultural superdockingrdquo moderdquo Journal of Agrotechnical Economics vol 7pp 41ndash51 2017

[10] J Fan and Z Zhang ldquoAn empirical study on the developmenttrend of intensive circulation of fresh agricultural productsunder the condition of ldquoagricultural super dockingrdquordquo Journalof Commercial Economics vol 2 pp 122ndash124 2018

[11] J Wang Research on the Fruit Inventory Control of FreshSupermarket Chains in the Background of ldquoFarmer-super-market Dockingrdquo Jilin University Changchun China 2017

[12] X Wang P Liu and S Wang ldquoInventory ordering andpricing policy for cold chain items with Weibull survival anddeath characteristicsrdquo Operations Research and ManagementScience vol 26 no 1 pp 45ndash52 2017

[13] Y Tang T Fan and S Liu ldquoPricing and inventory decision-making for fresh agricultural products with strategic con-sumersrdquo Chinese Journal of Management Science vol 26no 11 pp 105ndash113 2018

[14] L Shen K Govindan A B Borade A Diabat andD Kannan ldquoAn evaluation of vendor managed inventorypractices from small and medium Indian enterprisesrdquo Journalof Business Economics and Management vol 14 no 1pp S76ndashS95 2013

[15] H Liu J Zhang C Zhou and Y Ru ldquoOptimal purchase andinventory retrieval policies for perishable seasonal agriculturalproductsrdquo Omega vol 79 pp 133ndash145 2018

[16] S Banerjee and S Agrawal ldquoInventory model for deterio-rating items with freshness and price dependent demandoptimal discounting and ordering policiesrdquo Applied Mathe-matical Modelling vol 52 pp 53ndash64 2017

[17] L Janssen A Diabat J Sauer and F Herrmann ldquoA stochasticmicro-periodic age-based inventory replenishment policy forperishable goodsrdquo Transportation Research Part E Logisticsand Transportation Review vol 118 pp 445ndash465 2018

[18] SWang Y Jiang and J Mou ldquoInventory and pricing decisionof an integrated cold chain based on freshnessrdquo ChineseJournal of Management Science vol 26 no 7 pp 132ndash1412018

[19] J Mou M Zhang and S Wang ldquoInventory strategy of freshagricultural productsrsquo freshness and price influencing demandtogetherrdquo Statistics amp Decision vol 35 no 6 pp 54ndash57 2019

[20] K Chen and T Xiao ldquoPricing and replenishment policies in asupply chain with competing retailers under different retailbehaviorsrdquo Computers amp Industrial Engineering vol 103pp 145ndash157 2017

[21] X Fan e Analysis of Integrated ree-Echelon Cold ChainInventory-Distribution Optimization Model Based on Distri-bution Center Yantai University Yantai China 2016

[22] Y Jiang An Integrated ree-Echelon Inventory Model andEmpirical Analysis Based on Distribution Center YantaiUniversity Yantai China 2014

[23] Z Dai F Aqlan and K Gao ldquoOptimizing multi-echeloninventory with three types of demand in supply chainrdquoTransportation Research Part E Logistics and TransportationReview vol 107 pp 141ndash177 2017

[24] G Xu and J Feng ldquoSimulation-based optimization of controlpolicy on multi-echelon inventory system for fresh agricul-tural productsrdquo International Journal of Agricultural andBiological Engineering vol 12 no 2 pp 184ndash194 2019

[25] S C Tsai and S T Chen ldquoA simulation-based multi-objectiveoptimization framework a case study on inventory man-agementrdquo Omega vol 70 pp 148ndash159 2017

[26] X Ma S Wang S M N Islam and X Liu ldquoCoordinating athree-echelon fresh agricultural products supply chain con-sidering freshness-keeping effort with asymmetric informa-tionrdquo Applied Mathematical Modelling vol 67 pp 337ndash3562019

[27] W Zhao and D Wang ldquoSimulation-based optimization oncontrol strategies of three-echelon inventory in hybrid supplychain with order uncertaintyrdquo IEEE Access vol 6pp 54215ndash54223 2018

[28] S M Mousavi A Bahreininejad and S N Musa ldquoAmodifiedparticle swarm optimization for solving the integrated loca-tion and inventory control problems in a two-echelon supplychain networkrdquo Journal of Intelligent Manufacturing vol 28no 1 pp 191ndash206 2017

[29] P M Ghare and G F Schrader ldquoA model for exponentiallydecaying inventoryrdquo Journal for Industrial Engineeringvol 14 no 5 pp 238ndash143 1963

[30] Y Shi Distribution Ordering Strategy and Supply ChainCoordination Based on Fresh Agricultural Product Meta-morphic Loss Nanjing University of Science amp TechnologyNanjing China 2017


In general the demand and supply of fresh agriculturalproducts fluctuate considerably with climatic variationsseasonal changes and various social factors [1] thus eachmember in the supply chain should not hold high inventoryToo high or too low inventory will increase procurement costsor lead to lost opportunity costs +erefore it is necessary tooptimize the integrated inventory of the ldquoagriculturalsuperdockingrdquo mode+e goal of inventory optimization is todetermine a reasonable inventory level or replenishmentquantity reduce inventory costs and improve overall benefit+is paper establishes an integrated inventory model of freshagricultural products based on ldquofarmersrsquo professional coop-eratives + distribution centers + supermarketsrdquo mode Withan objective tomaximize the overall profit of the supply chainthe integrated inventory optimization model of fresh agri-cultural products supply chain based on the ldquoagriculturalsuperdockingrdquomode is established and examined by adjustingthe replenishment and supply strategies between variouslevels of the supply chain

2 Literature Review

ldquoAgricultural superdockingrdquo has become an important modeof fresh agricultural products supply chain In recent yearsrelated research on the ldquoagricultural superdockingrdquo modemainly includes the following aspects (1) analysis of de-velopment status and problems In practice the ldquoagriculturalsuperdockingrdquo supply chain has gradually formed multiplemodes Li [2] summarized five types of the ldquoagriculturalsuperdockingrdquo mode ldquofarmersrsquo professional coopera-tives + supermarketsrdquo mode ldquofarmersrsquo professional coop-eratives + distribution centers + supermarketsrdquo modeldquoagricultural product bases + leading enterprises of agri-cultural products + supermarketsrdquo mode direct sales modeand joint direct mining mode +e ldquoagricultural super-dockingrdquo mode in China is mainly the ldquofarmersrsquo professionalcooperatives + distribution centers + supermarketsrdquo mode[3] Guo and Xu [4] studied the stability of farmer coop-eratives in the ldquoagricultural superdockingrdquomode and itsdeterminants +e research found that the requirements ofsupermarkets for agricultural products the effects of gov-ernment policies the capacity of cooperatives and the levelof the regional economy are the most important factors thataffect the stability of the ldquoagricultural superdockingrdquo rela-tionship In the process of ldquoagricultural superdockingrdquo Yanget al [5] established a multiagent simulation model of theldquoagricultural superdockingrdquo order default problem based onthe development of ldquoagricultural superdockingrdquo in NingxiaHui Autonomous Region +e study found that the defaultrate is mainly related to agricultural products prices agri-cultural products qualification rates information trans-mission mechanisms and policy support

Zheng et al [6] constructed the profit function of therevenue sharing contract for two-stage fresh products supplychain and improved revenue sharing contract +e resultsshowed that the improved revenue sharing contract canpromote the information sharing of the fresh products supplychain so that the profit function of the farmersrsquo professionalcooperatives and supermarkets will reach the level of Pareto

optimal Yang [7] studied the unequal rights in the ldquoagri-cultural superdockingrdquo mode from the perspective of con-tribution degree and alliance position Based on the modifiedShapley value method that considers the weight power indexand the average tree solution (A-T solution) that limits thealliance structure the profit distribution strategy concerningunequal rights is given Based on the traditional Shapley profitallocation method Yao and Ran [8] proposed a modifiedprofit allocation method considering risk factors of agricul-tural supply chain participants Li and Wang [3] used therevenue sharing contract to coordinate the ldquoagriculturalsuperdockingrdquo supply chain and the optimal decision-making behavior of eachmember in the coordinationmode isobtained By adjusting the value of the revenue sharing factorthe revenue of the farmersrsquo cooperative and supermarket canachieve Pareto improvement

Chen et al [9] studied the relationship between channelopportunistic behavior and farmersrsquo psychological contractunder the ldquoagricultural superdockingrdquo mode +e studyfound that in the channel relationship the farmersrsquotransactional psychological contract will promote the gen-eration of opportunistic behavior and the relational psy-chological contract will inhibit the generation of channelopportunistic behavior Fan and Zhang [10] made an em-pirical analysis on the production and circulation data ofagricultural products in Langfang Hebei province It isconfirmed that under the guidance of the market and policythe circulation of fresh agricultural products is graduallymoving towards intensification and making full use of thepolicy advantages to develop intensive circulation will be themost advantageous way to distribute fresh agriculturalproducts

Inventory management research includes research onsingle entity two-echelon supply chain and three-echelonsupply chain Wang [11] studied the inventory of single-variety fruit in fresh supermarkets According to the per-ishability and discontinuous demand of fresh fruit a fruitinventory control model of fresh food supermarket chainswas constructed under the conditions of optimal order cycleand optimal price Wang et al [12] established a replen-ishment pricing model in which the deterioration rate obeysthe three-parameter Weibull distribution under a randomenvironment+e direct method is used to solve the retailerrsquosoptimal inventory strategy and commodity price when theprofit is largest Tang et al [13] integrated the decision-making behavior of strategic consumers constructed single-stage and two-stage pricing and inventory decision modelsof retailers and analyzed the influencing mechanism of freshagricultural productrsquos value residual rate on consumerrsquosbehavior retailerrsquos optimal pricing optimal inventory leveland profit Shen et al [14] took small and medium enter-prises in India as an example to study supplier inventorymanagement +e amount to purchase in the harvest seasonas well as how much to retrieve for each selling periodstrongly impact the profit for a wholesaler +erefore Liuet al [15] analyzed the optimal purchase and inventoryretrieval quantities for perishable seasonal agriculturalproducts considering the costs of storage underage andoverage prospects of future prices and demands and


























zjki

jki (t) IIzjki





gzjki






(1)





dIjk(t)





Ijk(t) εj

θ1middot 1 minus e





Ijk(t)dt εj

θ1middot Tjk minus


1113888 1113889 (5)




FKjk fj middot Ijk



(6)


FCjk 1113944K

k11113944

m



FY 1113944

n

i11113944

K

k11113944

m


1jki (8)


FL FY minus FC (9)




dIIzjki

jki (t)


jki (t) (10)




IIzjki



IIzjki




IIzjki


θ2 middottjki (13)


gjki IIbjki



gjki + gbjki+1jki

(14)



zjki

jki IIzjki

jki


ventory gbjki


gbjki



+us


bjki




bjki


θ2 middottjki1113872 1113873


2θ2 middottjki1113872 1113873

(17)




θ2 middottjki gjki





θ2 middottjki gjki



4θ2 middottjki1113872 1113873

(18)


zjki


gzjki



(19)

Consequently we get




(20)


IIzjki




(21)


IIzjki



IIzjki

jki (t)dt minus1θ2

middot gjki


(22)






bjkiθ2tjki1113872 1113873

(23)






bjki

zjki1II

zjki

jki

(24)








(25)


DC 1113944n

i11113944

K

k11113944

m


(26)


DY 1113944n

i11113944

K

k11113944

m



DL DY minus DC (28)


dIIIjki(t)


minus αmiddott


(29)


tjkirfloor is 0




θ3 minus αe


1113876 1113877

(31)


zjki middottjki




θ3middot

1α

minus1θ3


+1θ3


minus1α


(32)





α



(33)



θ3 minus α



1113876 1113877

(34)





(35)





SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References






























































zjki

jki (t) IIzjki





gzjki






(1)





dIjk(t)





Ijk(t) εj

θ1middot 1 minus e





Ijk(t)dt εj

θ1middot Tjk minus


1113888 1113889 (5)




FKjk fj middot Ijk



(6)


FCjk 1113944K

k11113944

m



FY 1113944

n

i11113944

K

k11113944

m


1jki (8)


FL FY minus FC (9)




dIIzjki

jki (t)


jki (t) (10)




IIzjki



IIzjki




IIzjki


θ2 middottjki (13)


gjki IIbjki



gjki + gbjki+1jki

(14)



zjki

jki IIzjki

jki


ventory gbjki


gbjki



+us


bjki




bjki


θ2 middottjki1113872 1113873


2θ2 middottjki1113872 1113873

(17)




θ2 middottjki gjki





θ2 middottjki gjki



4θ2 middottjki1113872 1113873

(18)


zjki


gzjki



(19)

Consequently we get




(20)


IIzjki




(21)


IIzjki



IIzjki

jki (t)dt minus1θ2

middot gjki


(22)






bjkiθ2tjki1113872 1113873

(23)






bjki

zjki1II

zjki

jki

(24)








(25)


DC 1113944n

i11113944

K

k11113944

m


(26)


DY 1113944n

i11113944

K

k11113944

m



DL DY minus DC (28)


dIIIjki(t)


minus αmiddott


(29)


tjkirfloor is 0




θ3 minus αe


1113876 1113877

(31)


zjki middottjki




θ3middot

1α

minus1θ3


+1θ3


minus1α


(32)





α



(33)



θ3 minus α



1113876 1113877

(34)





(35)





SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References






































gzjki






(1)





dIjk(t)





Ijk(t) εj

θ1middot 1 minus e





Ijk(t)dt εj

θ1middot Tjk minus


1113888 1113889 (5)




FKjk fj middot Ijk



(6)


FCjk 1113944K

k11113944

m



FY 1113944

n

i11113944

K

k11113944

m


1jki (8)


FL FY minus FC (9)




dIIzjki

jki (t)


jki (t) (10)




IIzjki



IIzjki




IIzjki


θ2 middottjki (13)


gjki IIbjki



gjki + gbjki+1jki

(14)



zjki

jki IIzjki

jki


ventory gbjki


gbjki



+us


bjki




bjki


θ2 middottjki1113872 1113873


2θ2 middottjki1113872 1113873

(17)




θ2 middottjki gjki





θ2 middottjki gjki



4θ2 middottjki1113872 1113873

(18)


zjki


gzjki



(19)

Consequently we get




(20)


IIzjki




(21)


IIzjki



IIzjki

jki (t)dt minus1θ2

middot gjki


(22)






bjkiθ2tjki1113872 1113873

(23)






bjki

zjki1II

zjki

jki

(24)








(25)


DC 1113944n

i11113944

K

k11113944

m


(26)


DY 1113944n

i11113944

K

k11113944

m



DL DY minus DC (28)


dIIIjki(t)


minus αmiddott


(29)


tjkirfloor is 0




θ3 minus αe


1113876 1113877

(31)


zjki middottjki




θ3middot

1α

minus1θ3


+1θ3


minus1α


(32)





α



(33)



θ3 minus α



1113876 1113877

(34)





(35)





SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References








































dIIzjki

jki (t)


jki (t) (10)




IIzjki



IIzjki




IIzjki


θ2 middottjki (13)


gjki IIbjki



gjki + gbjki+1jki

(14)



zjki

jki IIzjki

jki


ventory gbjki


gbjki



+us


bjki




bjki


θ2 middottjki1113872 1113873


2θ2 middottjki1113872 1113873

(17)




θ2 middottjki gjki





θ2 middottjki gjki



4θ2 middottjki1113872 1113873

(18)


zjki


gzjki



(19)

Consequently we get




(20)


IIzjki




(21)


IIzjki



IIzjki

jki (t)dt minus1θ2

middot gjki


(22)






bjkiθ2tjki1113872 1113873

(23)






bjki

zjki1II

zjki

jki

(24)








(25)


DC 1113944n

i11113944

K

k11113944

m


(26)


DY 1113944n

i11113944

K

k11113944

m



DL DY minus DC (28)


dIIIjki(t)


minus αmiddott


(29)


tjkirfloor is 0




θ3 minus αe


1113876 1113877

(31)


zjki middottjki




θ3middot

1α

minus1θ3


+1θ3


minus1α


(32)





α



(33)



θ3 minus α



1113876 1113877

(34)





(35)





SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References









































bjki

zjki1II

zjki

jki

(24)








(25)


DC 1113944n

i11113944

K

k11113944

m


(26)


DY 1113944n

i11113944

K

k11113944

m



DL DY minus DC (28)


dIIIjki(t)


minus αmiddott


(29)


tjkirfloor is 0




θ3 minus αe


1113876 1113877

(31)


zjki middottjki




θ3middot

1α

minus1θ3


+1θ3


minus1α


(32)





α



(33)



θ3 minus α



1113876 1113877

(34)





(35)





SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References







































SC 1113944n

i11113944

K

k11113944

m



SY 1113944n

i11113944

K

k11113944

m



SL SY minus SC (38)





FLDL SLge 0

Ijk IIzjki

jki IIIjki ge 0

⎧⎨

⎩ (40)


4 Case Study



















Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References











































Supermarket 1

Supermarket 2

Supermarket 3









A 8

k 1 k 2Unit

inventorycost

Unitprocessing

cost

Unitsalesprice



Unitinventory

cost

Unitprocessing

cost

Unitsalesprice





A 8i 1 i 2 i 3






5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References








































5 Result Analysis















10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References








































10

95

9

85

8

75

7

65

6

55

50 10 20 30 40 50


60 70 80 90 100

times107
















+5 +10














Data Availability




Acknowledgments


References















































Data Availability




Acknowledgments


References






































Inventory Optimization of Fresh Agricultural Products Supply...

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Transcript of Inventory Optimization of Fresh Agricultural Products Supply...