Production and Transportation Integration for aMake-to-Order Manufacturing Company with aCommit-to-Delivery Business Mode

Kathryn E. SteckeKathryn E. Stecke

Xuying ZhaoXuying Zhao

University of Texas at Dallas University of Texas at Dallas

Texas A&M Monday, Feb 27, 2006Texas A&M Monday, Feb 27, 2006

Outline

Problem and motivationProblem and motivation Literature reviewLiterature review Problem settingsProblem settings Analysis when partial delivery is allowedAnalysis when partial delivery is allowed Analysis when partial delivery is not allowedAnalysis when partial delivery is not allowed ExtensionsExtensions ConclusionsConclusions

Ship and Delivery Dates

Ship date: the date when a manufacturing company gives products to a logistics company to deliver to a customer.

Delivery date: the date when the logistics company delivers products to a customer.

Two Business Modes

Commit-to-shipCommit-to-shipthe manufacturing company commits a ship date

for an order. Customers pre-specify a shipping mode, e.g.,

overnight shipping.

Commit-to-deliveryCommit-to-deliverythe manufacturing company commits a delivery

date for an order.The ship mode can be decided dynamically by

the company.

Commit-to-ship at Dell

Profit increase opportunity in Dell

Dell ships Dell ships 95% 95% of customer orders within of customer orders within eight eight hours. hours. Based on this fact, Dell could increase profit by Based on this fact, Dell could increase profit by

adopting adopting commit-to-deliverycommit-to-delivery..For example:For example:

Customers pay $450 for a computer and $160 for overnight shipping.

Dell gets $450 in commit-to-shipcommit-to-ship.Dell promises a 5-days-later ship date. The logistics

company gets $160. Dell gets $510 in commit-to-deliverycommit-to-delivery.

Dell could ship the order within eight hours by adjusting the production schedule. Then a slow ship mode can be adopted. The logistics company gets $100. Dell gets $450+$60.

Profit increases over 10%.

Problem Description

Production schedule is important when adopting a Production schedule is important when adopting a commit-to-delivery mode.commit-to-delivery mode.A good production schedule saves shipping costs. A bad production schedule incurs expediting costs.

How to schedule production for accepted orders so How to schedule production for accepted orders so thatthatAll orders meet their delivery due dates.The total shipping cost is reduced as much as

possible.

Literature Review

Our research is related to two literature streams:Our research is related to two literature streams:

1. 1. Production schedulingProduction scheduling Pinedo (2000), …

2. 2. Integration between transportation and productionIntegration between transportation and production Bhatnagar, Chandra, and Goyal (1993), Thomas an

d Griffin (1996), and Sarmiento and Nagi (1999), Chen and Vairaktarakis (2005)

Production Environment

Finished products are assembled from Finished products are assembled from partly-partly-finished productsfinished products and customized and customized components.components.

DifferencesDifferences among orders exist in different among orders exist in different models/typesmodels/types of components. of components.

SSwitchingwitching production from one order to another production from one order to another order order rarelyrarely incurs any extra production costs. incurs any extra production costs.

Production Schedule Setting

We specify the production schedule for We specify the production schedule for n new, just n new, just arrivedarrived orders with delivery due dates. orders with delivery due dates.

A manufacturer can wait for customer orders to A manufacturer can wait for customer orders to accumulateaccumulate as long as its master production as long as its master production schedule is schedule is notnot emptyempty..

The schedule for the n new orders will be The schedule for the n new orders will be addedadded to to the endthe end of the current master production schedule. of the current master production schedule.

Transportation Setting

Outsourced to a Outsourced to a third partythird party logistics company, e.g., FedE logistics company, e.g., FedExx

The The logisticslogistics company comes to collect products company comes to collect products atat the e the endnd of each day. of each day.

Shipping Cost Setting

Shipping Cost Setting

The shipping cost is a general function of shipping time and the quantity of computers shipped.

From the table in the previous slide, shipping cost is convex decreasing in shipping time.

From the table in the previous slide, shipping cost is linearly increasing with shipping weight.

Since all computers’ weights are similar, shipping cost is linearly increasing with the quantity of computers shipped.

Problem Settings Summary

OrdersOrders There are n orders to be scheduled for production;Each order Oi has a production due date di and requires qu

antity Qi. ProductionProduction

The production planning horizon is m daysDaily production capacity is c productsSingle machine or a paced assembly line

TransportationTransportationOutsourced to a third party logistics company, e.g., FedExThe logistics company comes to collect products at the en

d of each day.

Table of Notation

cc Daily production Daily production capacitycapacity (in number of products) (in number of products)

mm Number of production daysNumber of production days in the planning in the planning horizonhorizon

QQii Number of productsNumber of products requiredrequired in order i in order i

ddii Production due dateProduction due date for order i; d for order i; dii ≤ m ≤ m

ttii Ship dateShip date for order i; t for order i; tii ≤ m ≤ m

rrii Ship modeShip mode for order i; r for order i; ri i = d= dii- t- tii

Process Timeline

ProductionProductionPlanningPlanningHorizonHorizon00 2211

……O1

rr11=1=1

O1

rr11=0=0dd11

mm33

tt11=2=2tt11=1=1

Ship cost for one order i: G(rShip cost for one order i: G(rii, Q, Qii), convex decreasing with r), convex decreasing with rii an an

d linearly increasing with Qd linearly increasing with Qii

Feasibility Condition

mjcjQjAi

i,...,1 ,

where

denotes a set of orders having a production due date on or before production day j in the planning horizon.

}|{ jdiA ij

m][1,jn];[1,i integer, is Q m][1,jn];[1,i 0,Q

m1,...,j c,Q

n1,...,i ,QQ

subject to

)Q j,dG( Minimize

ij

ij

n

1iij

i

d

1jij

iji

n

1i

d

1j

i

i

When Partial Delivery is Allowed

Quantity produced in day j for order iQuantity produced in day j for order i

Ship dateShip date is the same as is the same asthe the production dateproduction date

Order i is produced Order i is produced before its due datebefore its due date

Daily production Daily production capacity constraintcapacity constraint

MIP-PD:MIP-PD:

When Partial Delivery is Allowed

MIP-PDMIP-PDTotally unimodular ILOG CPLEX

AlgorithmAlgorithmNonpreemptive Earliest Due Date Schedule (NED

D) : orders are sorted according to earliest due date first and processed nonpreemptively and continuously without idle time.

ProductionProductionPlanningPlanningHorizonHorizon00 2211 ……

O1 O2

mm

O3 O4 O5

dd11=1=1 dd22==dd33=2=233

dd44= = dd55== 33

……

0f

n1,...,i 1,Y

n1,...,k 1,X

n1,...,i 1,X

subject to

)Q j,G(dY Minimize

0

m

1jij

n

1iik

n

1kik

ii

n

1i

m

1jij

YYijij=1 means that the =1 means that the last productlast product

in order i is produced in day j.in order i is produced in day j.

The The ship dateship date is the last is the last product’s product’s production dateproduction date..

When Partial Delivery is Not Allowed

MIP-NPD:MIP-NPD:

number positive large a is M

n] [1,i&k m], [1,j 1} {0,Z,Y,Xn1,...,i ,df

n1,...,i ,jYf

n1,...,ik, ,Z1Xn1,...,ik, ,MZff

n1,...,k ,c

XQff

ikijik

i'i

m

1jij

'i

ikik

ik'ik

ik

n

1ii

1kk

When Partial Delivery is Not Allowed

When Partial Delivery is Not Allowed

CCjj: number of products which are produced in day j but s: number of products which are produced in day j but s

hipped in day j+1 or later.hipped in day j+1 or later.

ProductionProductionPlanningPlanningHorizonHorizon00 2211

……O1 O2

mm

O3

CC11=150=150 CC22=160=160

1m

1jjii

n

1i

m

1jij

C Minimizej))a(d(bQY Minimize

(100(100))

(150(150))

(90)(90) (160(160))

(100(100))

……

(100(100))

(150+90)(150+90)

Algorithm NPD: try to reduce each Algorithm NPD: try to reduce each CCj j as much as pas much as p

ossible. ossible. Get an initial Get an initial feasiblefeasible schedule by schedule by NEDDNEDD..Start reducing Start reducing CCm-1m-1 by producing smaller orders first. by producing smaller orders first.

Reduce each CReduce each Cjj the same way. the same way.

The algorithm stops when The algorithm stops when CC11 is reduced. is reduced.

O1 O3

O1 O3

Day m-1Day m-1

O5

O5

CCm-1m-1

O2 CCm-1m-1

O2

When Partial Delivery is Not Allowed

O4

O4

Day mDay m

Algorithm Performance When n=5 and m=5

OptimalSolution

CPU Time

(Seconds)

HeuristicAlgorithm NPD

CPUTime

(Seconds)Gap

1 3876.61 0.04 3876.61 0.03 0.00%

2 3464.25 0.03 3464.25 0.03 0.00%

3 2263.46 0.16 2263.46 0.05 0.00%

4 1939.83 0.05 1939.83 0.03 0.00%

5 3872.58 0.64 3872.58 0.04 0.00%

6 3623.87 0.03 3623.87 0.03 0.00%

7 1927.18 0.03 1927.18 0.02 0.00%

8 1875.28 0.02 1875.28 0.02 0.00%

9 2446.02 0.25 2446.02 0.03 0.00%

10 1792.73 0.02 1792.73 0.02 0.00%

Algorithm Performance When n=8 and m=8

OptimalSolution

CPUTime

(Seconds)

HeuristicAlgorithm NPD

CPUTime

(Seconds)Gap

1 8037.38 50 8075.96 0.03 0.48%

2 3907.34 46 3907.34 0.04 0.00%

3 2890.97 74 2971.63 0.03 2.79%

4 9078.63 20 9078.63 0.09 0.00%

5 4739.02 40 4739.02 0.03 0.00%

6 8439.89 16 8439.89 0.06 0.00%

7 2890.73 11 2890.73 0.08 0.00%

8 3878.27 9 3878.27 0.05 0.00%

9 2382.08 14 2387.80 0.07 0.24%

10 6793.45 54 6793.45 0.09 0.00%

Performance of Lower Bounds When n=5 and m=5

Optimal

CPU LP_relaxation CPU Gap PD_relaxation CPU GAP

1 3876.61 0.04 2790.00 0.03 28.03% 3557.56 0.03 8.23%

2 3464.25 0.03 2969.21 0.03 14.29% 3285.49 0.02 5.16%

3 2263.46 0.16 1802.39 0.07 20.37% 2062.01 0.05 8.90%

4 1939.83 0.05 1847.05 0.04 4.78% 1939.83 0.03 0.00%

5 3872.58 0.64 3357.91 0.08 13.29% 3852.44 0.06 0.52%

6 3623.87 0.03 2666.44 0.02 26.42% 3617.71 0.02 0.17%

7 1927.18 0.03 1766.65 0.02 8.33% 1902.70 0.03 1.27%

8 1875.28 0.02 1179.74 0.02 37.09% 1800.08 0.02 4.01%

9 2446.02 0.25 1584.78 0.05 35.21% 2358.21 0.04 3.59%

10 1792.73 0.02 1662.58 0.02 7.26% 1792.73 0.02 0.00%

Performance of Lower Bounds When n=8 and m=8

Optimal CPU LP_relaxation CPU Gap PD_relaxation CPU Gap

1 8037.38 50 5373.79 0.45 33.14% 8012.46 0.37 0.31%

2 3907.34 46 2874.24 0.18 26.44% 3706.50 0.14 5.14%

3 2890.97 74 2157.24 0.52 25.38% 2866.11 0.47 0.86%

4 9078.63 20 5905.65 0.91 34.95% 8689.16 0.72 4.29%

5 4739.02 40 4173.18 0.15 11.94% 4718.64 0.11 0.43%

6 8439.89 16 7764.70 0.60 8.00% 8437.36 0.36 0.03%

7 2890.73 11 2620.16 0.43 9.36% 2882.93 0.29 0.27%

8 3878.27 9 3530.78 0.76 8.96% 3867.41 0.47 0.28%

9 2382.08 14 2010.00 0.29 15.62% 2364.93 0.21 0.72%

10 6793.45 54 4762.89 0.82 29.89% 6652.15 0.30 2.08%

Algorithm Performance When n=500 and m=15

PD_relaxation

CPU Time(Seconds)

HeuristicAlgorithm NPD

CPU Time(Seconds)

Gap

1 736792.20 27 734434.46 0.05 0.32%

2 1097625.86 64 1097406.33 0.07 0.02%

3 862985.47 71 862381.38 0.15 0.07%

4 973284.03 64 972992.04 0.07 0.03%

5 1198024.59 98 1190477.04 0.14 0.63%

6 794362.87 44 792059.22 0.14 0.29%

7 1083242.39 90 1082700.77 0.06 0.05%

8 1175462.73 52 1174169.72 0.18 0.11%

9 927816.42 77 925404.10 0.21 0.26%

10 892542.15 58 885848.08 0.09 0.75%

Extensions

Considering Considering customer locationscustomer locations in the shipping cost in the shipping cost function function

Considering Considering quantity discountsquantity discounts in the shipping cost in the shipping cost functionfunction

Shipping Cost Varies with Customer Locations

Considering Customer Locations in Models

When partial delivery is When partial delivery is allowedallowed..

When partial delivery is When partial delivery is not allowednot allowed

Considering Quantity Discounts

Some 3PL companies offer Some 3PL companies offer quantity discountsquantity discounts when when multiplemultiple items are sent in items are sent in a batcha batch. .

When partial delivery is allowed, there exists a When partial delivery is allowed, there exists a tradeofftradeoff..

We propose another MIP to consider this tradeoffWe propose another MIP to consider this tradeoff

00 2211……

O1

mm(150(150))

(150(150))

……

(150)(150) (150)(150)(300)(300)(0)(0)

Conclusions

We analyzed a production and transportation integration prWe analyzed a production and transportation integration problem for make-to-order industries.oblem for make-to-order industries.

When partial delivery is allowed, NEDD provides the optiWhen partial delivery is allowed, NEDD provides the optimal production schedule.mal production schedule.Mixed integer programming model: MIP-PDTotally unimodular ILOG CPLEX

When partial delivery is not allowed, an effective and efficiWhen partial delivery is not allowed, an effective and efficient heuristic algorithm is provided. ent heuristic algorithm is provided. Mixed integer programming model: MIP-NPDHeuristic algorithm NPD

Thank You!