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176 TEKSTL ve KONFEKSYON 2/2011

(REFEREED RESEARCH)

SUPPLY CHAIN MANAGEMENT IN APPAREL INDUSTRY:A TRANSSHIPMENT PROBLEM WITH TIME

CONSTRAINTS

HAZIR GYM ENDSTRSNDE TEDARK ZNCR YNETM:ZAMAN KISITLI BR AKTARIM PROBLEM

Deniz Trsel ELIIYIIzmir University of Economics

Department of Industrial Systems Engineeringe-mail: [email protected]

Emine Zehra YURTKULUIzmir University of Economics

Department of Logistics Management

Dicle YURDAKUL AHNIzmir University of Economics

Department of BusinessAdministration

ABSTRACT

Supply chain management is one of the main sources of competitive advantage for companies. As a useful tool for inventory andtransportation management in supply chains, transshipment points provide an effective mechanism for correcting discrepancies betweendemand and available inventory. This study aims to model the transshipment problem of a company in the apparel industry with multiplesubcontractors and customers, and a transshipment depot in between. Unlike a typical transshipment problem that considers only thetotal cost of transportation, our model also considers the supplier lead times and the customer due dates in the system and it can be usedfor both supplier selection and timely distribution planning. The proposed model can also be adapted easily by other companies in theindustry.

Keywords: Transshipment problem, Lead time constraints, Apparel industry.

ZET

Tedarik zinciri ynetimi irketler iin rekabet avantaj salamadaki temel kaynaklardan birini oluturmaktadr. Tedarikzincirlerinde envanter ve ulatrma ynetimi konusunda faydal kullanmlar olan aktarm noktalar zellikle talep ve envanter miktararasndaki fark kapatma konusunda etkin bir mekanizma sunmaktadr. Bu almann amac hazr giyim sektrnde birden ok fasonimalat ve mteri ile faaliyet gsteren ve aktarm deposuna sahip birirketin aktarm probleminin modellenmesidir. Yalnzca toplammaliyeti minimize etmeyi amalayan tipik aktarm modellerinden farkl olarak modelimiz tedarik srelerini ve mterilerin terminzamanlarn da dikkate almakta, bu sayede hem tedariki seiminde hem de zaman nda datm planlamasnda kullanlabilmektedir.nerilen model sektrdeki dier firmalar iin de kolaylkla adapte edilebilir.

Anahtar K elimeler: Aktarm problemi, Tedarik sresi kstlar, Hazr giyim sektr.

Received: 12.07.2010 Accepted: 31.03.2011

1. INTRODUCTION

Supply chain management is one ofthe main sources of competitiveadvantage for companies and itsimportance is increasing due to itseffects on solving problems faced bymany companies in terms ofmismatches between customerdemand and supply, which will lead tolow levels of customer satisfaction andeventually decreasing sales andmarket share (1). Logistics is a criticalpart of supply chain management, andis used to control the flow of materials,services and information taking into

account the cost of these activities onone side and the value created in

terms of both the customers and the

organization on the other (2, 3).Supply chain management entailseffective replenishment and inventorypolicies. The use of transshipmentpoints in supply chains rendersmonitored movement of stocks tointermediary storage locations betweentwo echelon levels. Transshipmentsare effective policies for correctingdiscrepancies between demand andinventory available at specificlocations, serving as a tool for effectivemanagement of stocks that are alreadyprocured and delivered into the system

(4). By using transshipments as a toolfor utilizing stocks, a company can

reduce its costs and improve the level

of service without increasing the stocklevel and bearing additional costs (5).

Transshipment problems are variationsof transportation problems in whichgoods and services are distributedbetween sources, storage points anddestinations. Like in many cases, theobjective function of transshipmentproblems is to minimize cost.Transshipments problems were firstdefined by Orden (6) as an extensionof transportation problems withtransshipment points between thesources and the destinations (7).

Transshipment models can be used toenhance cost efficient movement of

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TEKSTL ve KONFEKSYON 2/2011 177

goods and improve the level ofcustomer satisfaction. Dynamictransshipment problems involvinginventory decisions have severallocations, and in each of theselocations companies have to bear fixedreplenishment, per unit replenishment,and per unit holding costs.

Transshipping inventories betweenlocations also includes fixed and perunit costs. The objective in these kindof problems is to determine thereplenishment quantities and howmuch to transfer in each demandprocess to ensure cost minimization. Inthe studies by Herer and Tzur (8, 9),the authors develop optimal andheuristic algorithms for dynamictransshipment problems incorporatingfixed replenishment and transshipmentcosts. A dynamic and deterministicenvironment is considered, where the

transshipments are not used as a toolfor emergency source of supply, butinstead they can be used to offsetdifferent replenishment and holdingcosts at different stock locations.

In this study, we use integerprogramming to solve the transshipmentproblem of an apparel company. Oneof the core aims of this study is toensure that the offered model and thecorresponding solution can be usedpractically by the company, leading tomore efficient management of thesupply chain. In Section 2, we define

the problem in detail. Next, we developthe mathematical model in Section 3.Numerical results are presented inSection 4. Discussion and conclusionis presented in Section 5.

2. PROBLEM DEFINITION

We consider a real-life problem facedby an apparel company located inIzmir, Turkey. The company currentlyoperates in the segment of ready-to-wear garments. The company has twobasic branches of operations; namely,

the casual wear branch and personnelgarments branch. Personnel garmentsare manufactured partly in-house, but

most of the production is via contractmanufacturing.

Competition is dense in the textile andapparel industry. The main competitorsof the company are its ownsubcontractors, who are willing to selltheir products directly to thecustomers. The company works underthe pressure of strict due dates. Highpenalty fees apply in case thedeliveries are untimely. The relationshipswith both suppliers and customers playkey roles in the personnel garmentsindustry, and trust is a key factor inthese relationships. Therefore, conformityto quality standards and deadlines iscrucial. There are mainly five keyplayers in the transshipment process:

1. The customer: The source of therequest or order.

2. The company: The decision maker.This represents our company,which receives the order from thecustomer and outsources theproduction via different suppliersand ateliers.

3. Suppliers/Subcontractors:Companies that provide raw mate-rials, semi-finished and finishedproducts used in the productionprocess.

4. The workshop: The atelier in whichthe production activity is outsourced/performed.

5. The transportation company: Thefirm that is responsible for thetransportation of finished productsto customers.

The process flow of the orderfulfillment process is provided in Figure1. The process begins with the receiptof a customer order. Then, the companycommunicates with its suppliers todiscuss if required materials arealready available at stocks or if theyshould be manufactured. Hence the

lead time for each order is determinedand the order is scheduled forproduction. The workshop starts

production right after receipt of therequired materials. Upon completion ofproduction at the workshop, the orderis shipped via the transportationcompany.

The company has a depot used as atransshipment point. The productsmanufactured at varioussubcontracting facilities are supposedto be gathered at this depot for finalarrangements and packaging. Differentitems of personnel uniforms such ashats, shirts and trousers may beproduced by different subcontractors.The final packaging and labelingprocesses bring these items together.However, due to tight due dates of thecustomers, and as a result of workingwith many subcontractors, thecompany usually has to ship from thesupplier directly to the customer at thelast minute. This result stems from

ineffective planning of the wholetransshipment process. Thetransportation cost is considerably highfor these last-minute shipments as theusual modes of transportation cannotbe used. The decision makers in thecompany wish to use their depot andprovide timely deliveries at the sametime.

The problem is analyzed within thecontext of a transshipment scheme.Basic elements of the transshipmentproblem are the capacity of supply

points, requirements of the demandpoints, and the costs associated withshipping of one unit of product fromeach supply point to eachtransshipment point, from eachtransshipment point to each demandpoint, and from each supply point toeach demand point directly. Theobjective is to minimize the totaltransportation cost. We model theproblem as a transshipment problemwith due date restrictions. Unliketypical transshipment models, the duedate of an order is also considered in

our model since the company faceshigh penalty costs. We present ourmodel in the following section.

Figure 1. The order fulfillment process.

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3. THE MATHEMATICAL MODEL

We define the indices and parameters used in the model as below:

s: supplier index

t: transshipment point index

c: customer indexp: product type index

Dcp: Demand quantity depending on customer and product type.

DDcp: Deadline of order depending on customer and product type.

lsp: Lead time of production depending on supplier and product type.

cst: Cost of shipping one unit from supplier point to transshipment point.

csc: Cost of shipping one unit from supplier point to the customer.

ctc: Cost of shipping one unit from transshipment point to the customer.

tst: Shipping time from supplier point to transshipment point.

tsc: Shipping time from supplier point to the customer.ttc:Shipping time from transshipment point to the customer.

prp: The percentage of volume a specific productp occupies in a package.

1, if supplier is eligible for providing product

0, otherwisepss p

E

=

We define our decision variables are given below.

Binary variables:

1 if product p, which is produced by supplier s, is assigned to customer c on the route S C

0 otherwisescpX

=

1 if product p, which is produced by supplier s, is assigned to customer c on the route S

0 otherwisecpstT

Y

=

1 if product p, which is produced by supplier s, is assigned to customer c on the route T C

0 otherwisecptZ

=

Integer variables:

Xpcs: Number of packages shipped from suppliers to customerc.

Ypst: Number of packages shipped from suppliers to transshipment point t.

Zptc: Number of packages shipped from transshipment point tto customerc.

Our objective function in Equation 1 minimizes the sum of the batch-shipment-costs.

Min

1 1 1 1 1 1

* * *n n n n n n

sc sc st st tc tc

s c s t t c

Xp c Yp c Zp c= = = = = =

+ + (1)

Batch-shipment-cost is represented by three different cost components: The total cost of sending packages directly, the totalcost of sending packages from suppliers to transshipment points and the total cost of sending packages from transshipmentpoints to customers.

Every customer must be served with each product either directly from a supply point or through the transshipment point. Thisconstraint is reflected by the following equation:

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1 1

1n n

scp cpt

s t

X Z= =

+ = , ,c p (2)

Constraint set 3 below ensures time limits for direct shipments. The company works with strict deadlines for each order.These time constraints make our model different from the typical transshipment problems. Sum of the lead time and theshipping time from supplier to customer cannot exceed the deadline of an order. Note that, instead of including due datesand related penalty costs in the objective function, strict deadlines are included as constraints in the model. This is due to

the fact that there are very high penalty costs for late orders, and the company decision makers never prefer this situationregarding future relationships with customers. So it can be said that the company actually has deadlines rather than duedates.

( * (1 )),sp sc cp scpl t DD M X + + , ,c p s (3)

Constraint set 4 ensures time limits for shipments via transshipment points. Sum of the lead time, the shipping time fromsupplier to transshipment point and the shipping time from transshipment point to the customer cannot exceed the deadlineof an order.

( * (1 )),sp st tc cp cpstl t t DD M Y + + + , , ,c p t s (4)

The next constraint set assures that, at every transshipment point, if a product p for customerc is sent from one of thepossible suppliers to the transshipment point, then it must be sent out from the transshipment point to customerc. Hence,

these constraints ensure the conservation of flow for the transshipment points.

1

,n

cpst cpt

s

Y Z=

= , ,c p t (5)

Xpcsdenotes the number of packages shipped from the supplier to the customer directly. The next constraint set settles thetotal number of packages to be shipped, depending on the number of products to be shipped and their capacity usage in apackage.

1

* * ,n

sc scp cp p

p

Xp X D Pr=

,s c (6)

Ypstdenotes the number of packages shipped from the supplier to the transshipment point, and Zptcdenotes the number ofpackages shipped from the transshipment point to the customer. Constraint sets 7 and 8 compute the total number of

packages to be shipped in a similar way similar as constraint set 6.

1 1

* * ,n n

st cpst cp p

c p

Yp Y D Pr = =

,s t (7)

1

* * ,n

tc cpt cp p

p

Zp Z D Pr=

,t c (8)

Not all suppliers can provide all product types. Product p can only be sent from a supplier s if that supplier is eligible toprovide that product. There may be more than one eligible supplier for a product, and our model makes optimal supplierselections based on transportation cost, lead times and transshipment times. The following constraint sets ensure that onlyeligible suppliers are selected for each product in both direct shipments and shipments through the transshipment points.

,scp psX E , ,c p s (9)

,cpst psY E

, , ,c p s t (10)

Finally, types of variables in the model are defined.

Xpcs, Ypst, Zptc, 0 and integer, scpX , cpstY , cptZ binary, , , ,c p s t (11)

4. PROBLEM DATA

The data used is obtained from the

company by taking a recent snapshotof the system involving many orders.

In this problem instance with a 20-dayplanning horizon, there are 13potential suppliers, 11 customers and

5 product types. The unit directshipment cost from the suppliers to the

customers changes between 25 and31 monetary units and the shippingtakes 2 to 3 days. The unit shipment

costs from the suppliers to thetransshipment point is between 3 to 7

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monetary units depending on thelocation of the supplier. The unitshipment cost from the transshipmentpoints to each customer changesbetween 6 and 12 monetary units. Theshipment from the supplier to thetransshipment point, and from thetransshipment point to the customer

takes approximately 1 day each. Table1 shows the lead times of eachpotential supplier based on producttype. Theprp values, i.e. the percentageof volume that a specific product typepoccupies in a package are estimatedas 2% for product types 1, 2 and 3,and 8.3% for product types 4 and 5.The demand of each customer fromeach product is given in Table 2. Thedue date of each customer is 20 daysfor this instance. We provide the resultsof the computational study in the nextsection.

Table 1. Lead times of potential suppliersfor each product type (in days).

p1 p2 p3 p4 p5

s1 13 4 6 6 6

s2 5 7 6 6 6

s3 8 8 7 6 6

s4 5 5 5 6 6

s5 14 6 7 9 5

s6 12 7 8 5 6

s7 10 8 9 7 7

s8 4 9 5 6 6

s9 8 5 5 7 7

s10 9 6 6 7 6s11 8 7 7 8 6

s12 8 6 7 6 6

s13 7 7 8 8 8

Table 2. Customer demand data (in unit ofproduct).

p1 p2 p3 p4 p5

c1 0 0 46 0 138

c2 48 0 0 0 16

c3 1136 852 35 0 101

c4 54 36 18 0 0

c5 42 32 15 0 0c6 0 4 2 0 0

c7 21 14 8 0 0

c8 6 4 1 0 0

c9 21 8 14 0 0

c10 18 12 3 0 0

c11 0 0 0 5 0

5. COMPUTATIONAL RESULTS

The problem is modeled and solvedusing GAMS 22.5 optimization software.As it was stated in the previoussection, the gathered real life dataincludes a planning horizon where theorders from 11 customers should befulfilled using 13 supplier nodes

through 1 transshipment node. Thesupplier nodes are candidate suppliernodes, which provide different leadtimes for the incoming orders. Themodel therefore also performs supplierselection regarding the due dates ofthe orders at minimum total cost oftransportation.

According to the optimal solutionobtained from GAMS 22.5, only 4suppliers are selected to serve the 11customers. The optimal solution isdepicted in Figure 2 in a networkrepresentation. The numbers on thearcs of the network represent thenumber of shipped packages betweenany two nodes. The reasons forselecting only 4 suppliers out of 13supplier candidates are either the highcosts of transportation from the othersuppliers or the due date restrictions.The optimal solution suggests that all

packages should be shipped throughthe transshipment point, which is anexpected result of high direct shipmentcosts. The transshipment point alsofacilitates the distribution andtransportation of the packages. Forinstance, 72 packages come fromsuppliers in our data set. Since thesepackages are consolidated in thetransshipment point and then shippedto the customers, complete delivery tothe customer is possible in one shot.

Figure 2. The optimal solution.

Next, we explain how the companyactually proceeded in this specificproblem instance and compare theirintuitive solution with the optimalsolution. Because of the tight duedates and since one of their mostimportant accounts is among these 11

customers, the company actually didnot use transshipment point and

shipped the products from thesuppliers directly to the customers. Inaddition, the company had to make theconsolidation of the packages in thesuppliers workshops, and the packageswere transferred from one supplier toanother for rearranging andreconsolidation, which lead to conflicts

and higher labor and time costs.Labeling processes were delayed,interrupted or even cancelled, decreasingthe quality of shipments. This is partlydue to the fact that the company didnot prefer the suppliers giving the bestlead times, although the manufacturingprices were very similar among them.The total number of shipments in theoptimal solution of our model is 15 forthis instance while the company had tomake more than double this amount,i.e. 30 direct shipments plus the inter-supplier travels. The number of packages

shipped in the optimal solution is 76,while the company used 89 packagesfor shipments due to inefficientplanning. The companys intuitivesolution is depicted in Figure 3.

Figure 3. Solution of the company.

The solution time of the model inGAMS for this size of an instance with334 variables is ignorable due to thesimplistic network-type formulation ofthe problem. The optimization modelprovides a cost advantage to thecompany as well as improving customersatisfaction related with the timelyshipments. When the actual cost of thecompany is compared to the resultsobtained from the optimization model,it can be observed that there is areduction in the transportation costsalmost by 35%. This means that using

the transshipment point provides costadvantage and operational efficiency.

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6. CONCLUSION

In this study, we consider a real-lifeproblem of an apparel companyregarding the transportation of goods.We propose a transshipment model forthe problem that can be adaptedpracticably by other companies in theindustry. According to the findings ofthe study, use of the transshipmentpoint increases the overall efficiencyand decreases the total transportationcost.

Our transshipment model differs frompreviously used models in theliterature due to the addition of timeconstraints. The model also providesdecision support to the supplierselection problem by selecting the

optimal suppliers in terms of cost andtime constraints. The simplicity andeasy implementation are theadvantages of the developed model.GAMS is a commercial optimizationsoftware, and may not be readilyavailable in many companies. However,the proposed compact model can

easily be handled in widely availablespreadsheet software such asMSExcel and solved by built-insolvers. Introducing such optimizationmodels into the everyday operations ofsmall to medium size companies in thetextile and apparel industry will greatlyincrease their efficiency of operations.However, many of such companies areeither not aware that some optimizationmethods can be adapted to their

systems, or they are not capable ofusing the proposed methods easilydue to complex computational aspects.The simple optimization model in thisstudy is proves useful in improving theshipment operations in both time andcost terms. Hence, we believe that ourstudy contributes to the literature and

industry by closing the gap betweenthe theoreticians and practitioners.

ACKNOWLEDGEMENTS

We would like to acknowledge thesupport of the company managers forproviding the necessary data for ourcomputations.

REFERENCES

1. Reyes P.M., 2006, A game theory approach for solving the transshipment problem: a supply chain management strategy teaching tool, Supply Chain

Management: An International Journal, 11, 288293.

2. Wu Y., 2008, A mixed-integer programming model for global logistics transportation problems, International Journal of Systems Science, 39, 217228.

3. Harrison T.P., 2003, Principles for the strategic design of supply chains, in: The Practice of Supply Chain Management: Where Theory and Application

Converge, T.P. Harrison, H.L. Lee and J.J. Neale (Eds), USA: Kluwer Academic Publishers, 3-12.

4. Herer Y.T., Rashit A., 1999, Lateral Stock Transshipments in a Two-Location Inventory System with Fixed and Joint Replenishment Costs, Naval

Research Logistics, 46, 525-547.

5. Ozdemir D., Yucesan E., Herer Y.T., 2006, Multi-location transshipment problem with capacitated transportation, European Journal of Operational

Research, 175, 602-621.

6. Orden A., 1956, The transshipment problem, Management Science, 2, 276-286.

7. Hemaida R.S., Kwak N.K., 1994, A Linear Goal Programming Model for Trans-Shipment Problems with Flexible Supply and Demand Constraints,Journalof the Operational Research Society, 45, 215-224.

8. Herer Y.T., Tzur M., 2001, The Dynamic Transshipment Problem, Naval Research Logistics, 48, 386-408.

9. Herer Y.T., Tzur M., 2003, Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs, IIETransactions, 35, 419-432.

Bu aratrma, Bilim Kurulumuz tarafndan incelendikten sonra, oylama ile saptanan iki hakemin grne sunulmutur. Her iki hakemaptklar incelemeler sonucunda aratrmann bilimsellii ve sunumu olarakHakem Onayl Aratrmavasfyla yaymlanabileceine

karar vermilerdir.

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