A THREE-PHASE MULTICRITERIA METHOD TO THE SUPPLIER SELECTION PROBLEM

Transcription

1 Iteratioal Joural of Idustrial Egieerig, 5(2), 95-20, A THREE-PHASE MULTICRITERIA METHOD TO THE SUPPLIER SELECTION PROBLEM A. Medoza, E. Satiago, ad A. Ravi Ravidra Departmet of Idustrial ad Maufacturig Egieerig, Pesylvaia State Uiversity, Uiversity Park, PA 6802, USA Correspodig author s {Abraham Medoza, amedoza@up.edu.mx} This paper describes a ew multi-criteria method to solve the geeral supplier selectio problem. The supplier selectio problem is complicated ad risky, owig to a variety of qualitative ad quatitative factors affectig the decisio-makig process. For this matter, we preset a uique three-phase methodology to reduce the base of potetial suppliers to a maageable umber ad optimize the allocatio of orders by meas of multi-criteria techiques, amely ideal solutio approach, Aalytical Hierarchy Process (AHP) ad Goal Programmig (GP). Fially, a real-life example is provided to illustrate how the method ca be used i practice. Sigificace: Keywords: For those compaies where the umber of potetial suppliers is large, the procuremet decisio process becomes icreasigly complicated. I respose to this, i this paper we preset a appropriate method to simplify the fial selectio of suppliers. Supplier Selectio, Aalytical Hierarchy Process, Goal Programmig. ISSN (Received 2 February 2006; Accepted i revised form 20 December 2007). INTRODUCTION AND OVERVIEW Oe of the most importat strategic decisios i a compay is the purchasig strategy. I most idustries the cost of raw materials ad compoet parts represets the mai cost of a product. For istace, i high techology firms, purchased materials ad services accout for up to 80% of the total product cost, as ackowledged by Weber et al. (99). The idetificatio, evaluatio, ad motivatio of the right sources esure that the firm will receive the proper quality, quatity, time, ad price from its suppliers. Therefore, selectig the right suppliers becomes a critical activity withi a compay ad cosequetly affects its efficiecy ad profitability. The paper is divided as follows. Sectio 2 presets a brief literature review. Sectio 3 presets our proposed methodology for supplier selectio alog with a umerical example that illustrates each oe of the phases ivolved i this methodology. Sectio 4 presets a real applicatio of the goal programmig model (Phase 3) alog with a aalysis of the results. Sectios 5 presets some importat maagerial implicatios ad coclusios derived from curret research. The above statistics idicate the disparity that exists i employmet rates betwee the disabled ad o-disabled ad also withi the various groups amog the disabled. Further, from figures 2 ad 3, it ca be also iferred that there exists a strog relatioship betwee the employmet of a idividual ad his reliace o disability beefits via SSDI ad/or SSI, his/her ecoomic well-beig (i terms of each group s aual media earigs). This has bee observed particularly i the case of idividuals with sesory disabilities who had higher employmet rates, better ecoomic well-beig ad higher media earigs (show i figures,2, ad 3), compared to the other groups ad hece lesser reliace o the disability beefits through SSDI ad/or SSI. This implies that idividuals with disabilities ca fuctio better i the society whe they ca make avail of the employmet opportuities. 2. LITERATURE REVIEW As metioed above, several factors ad criteria affect the supplier selectio problem, amely price, quality, techical capabilities, ad service, amog others. For example, Stamm ad Golhar (993), ad Ellram (990) idetified 3 ad 8 criteria, respectively, for supplier selectio. A importat review of these criteria is preseted by Weber et al. (99). Table presets the top fiftee supplier selectio criteria aalyzed i their article (i order of relevace). There has bee a comprehesive effort to develop decisio methods ad techiques for the supplier selectio which cosider some of these differet factors ad criteria. Several decisio makig steps prior to the ultimate choice of suppliers have bee idetified i the literature. De Boer et al. (200) divided these steps as follows: () problem defiitio, (2) formulatio of criteria, (3) qualificatio, ad (4) fial choice. INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING

2 Medoza et al. Table : Supplier Selectio Criteria Rak Criteria Net Price 2 Delivery 3 Quality 4 Productio facilities ad capabilities 5 Geographical locatio 6 Techical capability 7 Maagemet ad orgaizatio 8 Reputatio ad positio i idustry 9 Fiacial positio 0 Performace history Repair service 2 Attitude 3 Packagig ability 4 Operatioal cotrols 5 Traiig aids I terms of models for problem defiitio ad formulatio of criteria there has bee very limited research. A example is the work by Vokurka et al. (996), i which they developed a expert system that covers multiple phases i the supplier selectio process, icludig the formulatio of supplier selectio criteria. Differet methods exist for pre-qualificatio of suitable suppliers. Importat oes are: Categorical Methods, Data Evelopmet Aalysis (DEA), ad Cluster Aalysis (CA). Timmerma (986) discussed the categorical method thoroughly, Weber ad Ellram (992) preseted DEA, ad Holt (998) discussed the cocept of CA alog with its fudametal beefits. The majority of the decisio models or methodologies developed for supplier selectio fall ito the fial choice phase. A commo classificatio of these methodologies icludes weightig models, statistical approaches, ad mathematical programmig models. By far, the most utilized approach i practice has bee the weightig models. These models place a umerical weight o each criterio (typically subjectively determied) ad provide a total score for each vedor by summig up the vedor s performace o the criteria multiplied by these weights. Although these approaches are very simple, they heavily deped o huma judgmet ad proper scalig of criteria values. They also assume a liear value fuctio which is ot true i practice. A example is the Cost Ratio method preseted by Timmerma (986). Very few statistical approaches have bee published to date. A example i this category is the work by Dig et al. (2005). Their approach uses discrete-evet simulatio for performace evaluatio of a supplier portfolio ad a geetic algorithm (GA) for optimum portfolio idetificatio based o performace measures estimated by the simulatio. Several mathematical programmig models have bee proposed to solve the fial choice problem. Most of these models iclude approaches with a sigle objective such as cost miimizatio or profit maximizatio. Some of the techiques applied to these methods are liear ad o-liear programmig, mixed iteger programmig, goal programmig, ad multi-objective programmig. Moore ad Fearo (973) stated that price, quality ad delivery are importat criteria for supplier selectio. They discussed the use of liear programmig i the decisio makig. Athoy ad Buffa (977) developed a sigle objective liear programmig model to support strategic purchasig schedulig (SPS). The liear model miimized the total cost by cosiderig limitatios o purchasig budget, supplier capacity ad buyer s demad. Narasimha ad Stoyoff (986) applied a sigle objective, mixed iteger programmig model to a large maufacturig firm i the Midwest, to optimize the allocatio procuremet for a group of suppliers. Pa (989) proposed multiple sourcig for improvig the reliability of supply for critical materials, i which more tha oe supplier is used ad the demad is split betwee them. The author used a sigle objective liear programmig model to choose the best suppliers based o three criteria: price, quality, ad service. Ghoudsypour ad O Brie (200) applied a mixed iteger oliear programmig model to select ad properly allocate orders to suppliers. I this model, they took ito accout orderig, holdig, ad purchasig costs. Despite the multiple criteria ature of the problem, very little work has bee devoted to the study of the supplier selectio problem by usig multi-criteria techiques such as goal programmig, multi-objective programmig, or other similar approaches. For example, Weber ad Curret (993) used multi-objective liear programmig for supplier selectio with aggregate price, quality ad late delivery as objectives. As oted i the literature review most attetio has bee paid to the fial choice phase i the supplier selectio process. However, the quality of the fial choice largely depeds o the quality of the steps prior to that phase. To our kowledge, 96

3 Multicrıteria Method to the Supplier Selectio Problem there has ot bee a itegrated approach ivolvig all the phases i supplier selectio. The importace of this paper is that it cosiders the various phases of the supplier selectio process ad presets a efficiet methodology that itegrates them. The advatages of the itegrated approach are that the decisio makers (DM) ca () reduce a large umber of suppliers ito a maageable oe ad (2) make the fial choice ad order allocatio by meas of multicriteria techiques. To reduce the large umber of potetial suppliers we use the ideal solutio approach ad AHP techiques, whereas the order allocatio is made by meas of goal programmig. Ulike most mathematical programmig models, goal programmig provides the DM with eough flexibility to set target levels o the differet criteria ad obtai the best compromise solutio that comes as close as possible to each oe of the targets. 3. THE THREE-PHASE MULTICRITERIA METHODOLOGY FOR SUPPLIER SELECTION The itegrated methodology preseted i this paper first screes a iitial list of potetial suppliers ad reduces it to a maageable umber. This makes it easier for compaies to aalyze a short list of suppliers i detail. The our methodology allocates the proper order quatities to the differet suppliers i order to comply with some pre-specified goals set by the Purchasig Departmet. These goals, i tur, deped upo some specific criteria, related to the supplier selectio process ad defied by the purchasig fuctio; e.g. quality, miimum cost, service levels, etc. The beefits of this methodology become evidet whe a compay wats to choose just a few suppliers from a list of a large umber of potetial suppliers. The Three-Phase approach uses the L 2 metric to scree a iitial list of suppliers; the, the Aalytical Hierarchy Process (AHP) is utilized to determie the weights of both, qualitative ad quatitative criteria i a very powerful ad easy way. For a complete tutorial o AHP, readers may refer to Saaty (994). Aother importat tool implemeted i our approach is Goal Programmig (GP). Sectio 3.3 shows how a GP model ca be built to solve the supplier selectio problem. I geeral, our model ca be applied to compaies i ay type of idustry. For illustrative purposes, the methodology was applied to a maufacturig facility located i Tijuaa, Mexico. Because of cofidetiality issues, the data used i this paper have bee disguised. The criteria ad goals show do reflect the actual procedure developed joitly with the Purchasig Maager of this compay. 3. Phase : Screeig Process with a Lp Metric The first phase i our methodology requires that the compay defie the criteria that will be used to select their suppliers. The set of criteria chose is uique to every compay ad compoet/product, though they all reflect several similarities. As we have already metioed, the purpose of usig a L p metric i this phase is to reduce the iitial list of suppliers with miimal effort. A short maageable list is ot oly easy to hadle but will allow us to efficietly collect detailed data o the suppliers ad apply AHP i Phase 2. The techical details o how to implemet the L p metric (Phase ) are described ext ad summarized i Figure. The L p metric represets the distace betwee two vectors x, y with the same umber of elemets. Oe of the most commoly used L p metrics is the L 2 metric, which measures the Euclidea distace betwee vectors. The rakig of alteratives is doe by calculatig the L 2 metric betwee the ideal solutio ad each vector represetig the supplier s ratigs for the criteria. Mathematically, this is computed as follows: i= 2 x y = 2 x i y i () The algorithm for this phase is described ext: STEP. Defie the ideal value for each criterio ad sub-criterio. The ideal value represets the best value attaiable for each criterio/subcriterio from the list of potetial suppliers. STEP 2. Use these values to form the ideal vector (deoted by y) as i Table 2. STEP 3. Use the L 2 metric to measure how close the ratig vector x i for each supplier matches the ideal supplier vector y (Table 3). I case the differet criteria ad sub-criteria chose are ot measured usig the same scale, i.e. 0-, 0-0, 0-00, the iitial list of criteria values of the suppliers must be ormalized before computig the L 2 metric. To ormalize the data it must be recogized whether each criterio is improved whe miimized or maximized. Oce this is established, oe of the followig two equatios is used to ormalize the data: H j fij fij L j If Miimized, use ; otherwise use R j R j th where H j is the maximum value for the j criterio, L j is the miimum value, f ij is the score of the i th supplier for the j th criterio ad R j represets the correspodig rage, H j L j. Scores that represet or match the 97

4 Medoza et al. ideal value get a ormalized value of oe, while the lowest scores get a ormalized value of zero. Table 4 shows the ormalized data for Table 3. Note that this ormalizatio method coverts all criteria to maximizatio. Hece the ideal values are all oes. Price ($) Figure : Phase Screeig the Iitial List of Suppliers C pk (idex) Table 2: Ideal values for each criterio Defective Parts (ppm) 98 Ideal Values Flexibility (%) Service (%) Distace (km) Leadtime (hrs/part) Ideal Vector y Table 3: Iitial Supplier Data List of Potetial Suppliers Price C Supplier pk Defective Flexibility Service Distace Leadtime ($) (idex) Parts(ppm) (%) (%) (km) (hrs/part) , , , , , , , , , , , , , , , ,

5 Multicrıteria Method to the Supplier Selectio Problem , , , , , , , , , , , , , , , , , , , , , , Table 4: Normalized Supplier Data List of Potetial Suppliers Price C Supplier pk Defective Flexibility Service Distace Leadtime ($) (idex) Parts(ppm) (%) (%) (km) (hrs/part) Sometimes it is easy to idetify domiated alteratives, i.e. alteratives (suppliers) whose idividual scores are less tha or equal to the criterio scores for aother alterative (supplier). The domiated alteratives are obviously ot good choices; hece they ca be elimiated from the aalysis. To compute the L 2 metric use Equatio. STEP 4. Rak the suppliers by orderig them i ascedig order; i.e., the supplier with the smallest L 2 value should be raked as # ad so o (See Table 5). Pre-select the list of suppliers to a short list for further cosideratio based o their rakig (e.g. the top 5, top 0, etc). 99

6 Medoza et al. For illustratio, we choose the first seve suppliers for further cosideratio. The umber of selected suppliers is up to the decisio maker (DM), but geerally this umber should be less tha 0. The data for the top raked suppliers will be used i later sectios i Phases 2 ad 3. Table 5: Rakig Orderig of Suppliers Based o L 2 Value Supplier L 2 value Rak Supplier L 2 value Rak.92 # # # # # # # #7 5.5 # # # # # # # # # # # #2 3.2 Phase 2: Criteria Weights ad Rakig of Suppliers with AHP The relevace of usig AHP i this phase relies o the fact that may compaies cosider exclusively quatitative factors i their respective supplier selectio aalysis. It is precisely this techique that allows a compay to ivolve the decisio maker (DM) i the assessmet of ot oly umerical but also itagible factors as well (e.g. supplier s prestige, fiacial stability, or the matureess of their quality maagemet system). Figure 2 shows a typical example of the criteria used for supplier selectio. The structure give by Figure 2 will be show to be very useful whe we perform AHP to compute the criteria weights. Figure 2: Supplier Selectio Criteria Figure 3: Growth i the Number of Questios 200

7 Multicrıteria Method to the Supplier Selectio Problem The value of Phase becomes obvious whe AHP is implemeted i Phase 2 because AHP ca be a tedious ad iefficiet process for rakig more tha 0 suppliers. AHP requires a umber of pair-wise compariso questios betwee criteria/sub-criteria ad betwee alteratives. Figure 3 shows how the umber of questios to be aswered by the DM icreases whe usig AHP; this umber exceeds 500 questios for more tha 0 alteratives (suppliers) ad ie criteria. Figure 4 summarizes the steps for Phase 2. The two outputs from this phase cosist of the weights for the criteria ad a list of suppliers with their respective total scores. This output will be used i Phase 3, durig the formulatio of the GP model. Figure 4: Phase 2 Defiig the Weights with AHP ad Supplier Screeig 3.2. AHP Algorithm This sectio summarizes the basic blocks i the AHP algorithm. The figures ad tables show were used to develop the example i this paper. AHP uses a ratig scale, show i Table 6, for the pairwise compariso questios. Table 6: Ratig Scale for Pairwise Compariso Degree of Importace Defiitio Equal Importace Weak importace of oe over 3 aother 5 Essetial or Strog Importace 7 Demostrated importace 9 Absolute importace Itermediate values betwee the 2, 4, 6, 8 two adjacet judgmets 20

8 Medoza et al. STEP. Do a pairwise compariso of the mai criteria usig the scale i Table 6. Form the matrix A x = [ a ij ], where the a ij etry represets the relative importace of criterio i with regard to criterio j. Let a ji = / a ij. This is show i Table 7. Table 7: Pairwise Compariso Matrix Criteria Quality Delivery Flexibility Service Price Quality Delivery Flexibility Service Price 3 5 a ii = i ad STEP 2. Compute the ormalized weights for the mai criteria from matrix A. The most commo way to do this is by ormalizig each colum with the L orm. Usig the followig formulas, we ca get the results displayed i Table 8: Compute r a ij ij = i= a ij, the average the r ij values to get the weights, Table 8: Normalized Matrix rij j wi =. Criteria Quality Delivery Flexibility Service Price Weights Quality Delivery Flexibility Service Price Steps ad 2 are cotiuously performed throughout every sub-level of criteria ad sub-criteria. As show i Figure 5, we would first determie the weights for the five mai criteria, ad the we would proceed to compare the two sub-levels of Quality ad Delivery separately. The fial weight of a sub-criterio is the product of the weights alog the correspodig brach. Figure 5: Supplier Selectio Criteria Weights 202

9 Multicrıteria Method to the Supplier Selectio Problem STEP 3. Check for cosistecy of the pairwise compariso matrix, usig the Cosistecy Idex (CI) ad Cosistecy Ratio (CR). AHP has a procedure to check the cosistecy of the DM s resposes. If the DM is perfectly cosistet the, A (before ormalizatio) has the followig property: r w / w A w 2 = M w / w w / w w / w M 2 2 L L O L w / w w w / w w 2 2 r = w. M M w If A is perfectly cosistet the λ max = ; also λ max, where λ max = Average[ A w / w, A2 w / w2, L, A w / w ]. To measure the degree of icosistecy, we ca use the followig idicators: Cosistecy Idex (CI) ad the Cosistecy Ratio (CR). λ CI = max ; CR = where RI is a radom idex, obtaied from Table 9. If CR < 0., accept the pairwise compariso matrix. 203 CI RI Table 9: Radom Idex (RI) Values (Saaty (994)) RI Fially, for our example, the respective computatios lead to the results show i Figure 6. A x w (A x w)/w i λmax Cosistecy Idex: Cosistecy Ratio: Figure 6: Cosistecy Ratio ad Cosistecy Idex At this poit, we should have a small list of suppliers available ad proceed to rak all the suppliers by comparig the suppliers with regard to each criterio usig AHP. The weights computed for each criterio form a colum of the Score matrix (S). The Total Scores (TS) of the suppliers is determied by Equatio 2, where w correspods to the criteria weights previously computed., [ S w] The suppliers are raked based o their TS values (higher the better). TS = (2) 3.3 Phase 3: Allocatio of Orders with a Preemptive GP Model The model described i this phase is used to allocate the right quatities to be purchased from each supplier. Therefore, model variables are the plaed purchases from each vedor. As metioed before, we make use of goal programmig (GP) as a appropriate techique. I goal programmig, all the objectives are assiged target levels for achievemet ad a relative priority o achievig these levels. GP treats these

10 Medoza et al. targets as goals to aspire for ad ot as absolute costraits. There are two types of goal programmig: preemptive ad opreemptive. I the preemptive case, goals at higher priority must be satisfied as far as possible before lower priority goals are eve cosidered. Therefore, the problem reduces to a sequece of sigle-objective optimizatio problems. I the opreemptive case, differet weights are assiged to each goal turig the problem ito a sigle-objective optimizatio problem, cosequetly assumig a liear utility fuctio. Sice the ature of the Supplier Selectio problem suggests that the utility fuctio is oliear, implemetig a o-preemptive GP model might ot be very realistic; therefore we propose a preemptive GP model to emulate the behavior of such utility fuctios. The advatages of usig goal programmig are that () it allows the firm to set plaig goals related to the supplier selectio criteria ad policies, (2) GP also lets the compay assig priorities o these goals, reflectig their relative importace, ad (3) settig goals allows a compay to cotrol the deviatio from targets ad achieve tradeoffs for goals i coflict. It is importat to ote that sice purchasig decisios usually spa the log-term, these are made oce for a give demad over some period of time. I this case, the demad is cosidered to be sufficiet to satisfy the market over a period of oe year; decisios are made as to allocate the right amout withi the set of selected suppliers to fulfill this demad Goal Costraits Goal costraits must be developed together with maagemet ad must be defied accordig to the compay s mai goals. I our case, the costraits were derived from the Scorecard used i the Supplier s Evaluatio process. Some costraits had to be redefied or chaged to meet the model s specific eeds. Table 0 presets the otatio ad termiology used. X i D C i TS L i l i i Number of suppliers Table 0: Problem Notatio Ordered quatity from i th supplier Aual demad Capacity of i th supplier Total score of th i supplier Compay s required leadtime for the i th supplier Time required by th i supplier to procure oe uit of product C Compay s required level of pk C pk C pi C pk of i th supplier q i SL S i F Δ i P Z Y i i i + d d Defects of i th supplier (i parts per millio) Service level required Service level of i th supplier Level of flexibility required Flexibility level of th i supplier Price of th i supplier Distace from th i supplier to buyer, if a order is allocated to i th supplier; 0, otherwise Amout of deviatio above the goal Amout of deviatio below the goal The goal costraits icluded i the model alog with their formulatio are itroduced ext. Weighted Value of Purchase WVP. I this goal costrait, the total scores obtaied i Phase 2 form the coefficiets TS i for each supplier. The aim is to maximize the total WVP. I other words, the total scores idicate particular prefereces of the DM whe comparig the suppliers with respect to the criteria. We the try to maximize the umber of uits allocated to suppliers with higher total scores. I geeral, WVP is maximized by settig a ideal value (M) to the goal costrait ad tryig to miimize the uderachievemet as much as possible. d 204

11 Multicrıteria Method to the Supplier Selectio Problem i= TS + i X i + d d = M. (3) Distace goal. Globalizatio seems to be chagig paradigms i idustry with iteratioal suppliers. Ufortuately there is still a strog egative correlatio betwee quick delivery ad distace. JIT requires that ideally suppliers should be close to the buyer; as a matter of fact several compaies keep as may suppliers as possible to a distace where they ca supply ay order withi miutes. The followig costrait miimizes the total distace to the suppliers selected. The distace is miimized by settig a ideal goal of zero, ad by miimizig the overachievemet d. i= + i i + d d2 =. Z Y 2 0 (4) Process Capability (C pk ). Curret Six Sigma treds motivate compaies to esure certai quality level throughout the value stream. Cosequetly, it is logical to avoid as much as possible, suppliers that do ot meet a specific quality level. This costrait is strictly o the average, hece the restrictio does ot discrimiate ay supplier for ot achievig this goal, but it does select a group of suppliers satisfyig such costrait. For our example, this idex represets the supplier s sigma level with respect to a critical quality feature, give the respective LSL (Lower Specificatio Limit) ad USL (Upper Specificatio Limit) provided by the compay. The objective is established as to miimize d 3, the uderachievemet of C pk. + C pi Yi + d d3 = C pk Yi. i= i= 3 (5) Flexibility goal. Oe of the most importat competitive advatages of world class compaies is their ability to satisfy a dyamic demad. Flexibility allows a compay to expad its capacity ad respod to chages i demad. Hece, we must try to select suppliers that maximize the compay s flexibility. The objective of this goal is to miimize d 4, the uderachievemet of a flexibility level required by the purchaser. + i Yi + d4 d4 = F Yi. i= i= Δ (6) Quality Defective parts per millio (ppm). This goal costrait was chose to miimize the defective percetage rate of our suppliers. It is kow that there is a direct relatioship betwee C pk ad ppm, but we are distiguishig it by cosiderig ppm i a more geeral sese; i.e., cosiderig ot oly as defective products, those who do ot meet the compay s specificatios for a certai critical quality feature, but for ay o-coformace issue that may appear. The objective of this goal is set to miimize d 5 +, the overachievemet of defective parts. i= + i i + d d5 =. q Y 5 0 (7) Service level goal. With the icreasig importace i keepig a performace idicator to moitor service satisfactio, most of the compaies keep track of their supplier service level. It is a prudet choice to keep suppliers that provide a average satisfactio level (SL). The service level required is kept at a optimal value by miimizig d 6. + Si Yi + d d6 = SL Yi. i= i= 6 (8) Purchasig expeses. We wat to avoid purchasig from suppliers with the highest prices. Whe we talk about prices we are assumig that this cost reflects the total cost i the buyer s locatio warehouse, icludig cost of distace for freight, ad broker costs as well. This costrait miimizes the purchasig expeses made by the compay, accordig to the orders placed ad the idividual price (total cost) offered by every supplier. The objective i this case, is to miimize + 7 the overachievemet ( d ) of a urealistic target of zero cost. i= + i i + d d7 =. P X 7 0 (9) Leadtime goal. Take l i to be the productio rate at which a order ca be satisfied by the i th supplier. Therefore, the time it takes the supplier to fulfill a order is directly proportioal to this variable. The compay, usually has a

12 Medoza et al. maximum allowed leadtime for every sigle supplier ( L i ), usually beig more strict with local suppliers. There will be at most costraits of this type. The objective is established as to miimize d 8 +, the overachievemet of L i. l ix i + d8 d8 = Li, i =, 2,...,. (0) Real Costraits The followig two costraits must be always satisfied. Equatio implies that the orders placed over a give period must satisfy the demad. Equatio 2 refers to the fact that a particular order ca ot exceed the correspodig capacity of that supplier. i= X X i = D, + () C, i =,,...,. (2) i i 2 Figure 7 summarizes the steps for Phase 3. The two outputs from this phase cosist of the goal priorities ad the GP model. 4. APPLICATION AND ANALYSIS Figure 7: Phase 3 Goal Programmig I this sectio, we preset the applicatio of the GP model alog with a aalysis of the results. It is importat to ote that this aalysis is performed o the top seve suppliers obtaied i Phase (Sectio 3.). For this applicatio a preemptive GP model is cosidered, as explaied before. The specific goal priorities used i this model are preseted i Table. This priority structure is defied by the compay ad reflects the importace give (by the DM) to the differet criteria cosidered i the supplier selectio process. Based o this priority structure, we obtai the objective fuctio as preseted i Equatio 3. Mi Z ( d ) + P2 ( d2 ) + P3 ( d3 ) + P4 ( d4 ) + P5 ( d5 + d6 + d d + d + d ) + P ( d ) + P ( d ) + P ( ) = P d4 d (3) I order to test the model, differet profiles (characterizatios) for each supplier are proposed. These profiles represet characteristics of each supplier with respect to each criterio. The data for the illustrative example correspodig to each supplier is provided i Table 2. Supplier : supplier offers a low price for the product ad a relatively bad performace i all the remaiig criteria. Supplier 2: supplier 2 provides a excellet service. It also offers products with superior quality but at a high price. Supplier 3: supplier 3 presets a excellet flexibility but at the expese of low quality. Supplier 4: supplier 4 offers a average performace i all criteria. 206

13 Multicrıteria Method to the Supplier Selectio Problem Table : GP Model Priorities Priority Goal Costrait Deviatioal Variables : P Weighted value of purchase 2: P 2 Purchasig expeses 3: P 3 Quality (ppm) 4: P 4 Flexibility 5: P 5 Leadtime 6: P 6 Service Level d + d 2 + d 3 d 4 d ,d6,d7,d8,d9,d0, d d 2 7: P 7 Process Capability ( C pk ) d 3 8: P 8 Distace + d 4 Supplier 5: supplier 5 stads out for its very low price, although it is far away i terms of travel distace. Supplier 6: supplier 6 also offers a average performace but, ulike supplier 4, its service level is early perfect. Also, i terms of quality level (ppm), supplier 6 offers a higher level tha supplier 4. Supplier 7: supplier 7 maitais the shortest leadtime of all suppliers (give its proximity to the purchasig compay); it also provides a excellet service; however, it offers poor techical capability. Supplier s Profile Price ($) C pk (idex) Table 2: Iput Model Data Defective Parts(ppm) C r i t e Flexibility (%) r i a Service (%) Distace (km) Leadtime (hrs/part) Supplier , Supplier , Supplier , Supplier , , Supplier , , Supplier , , Supplier , I additio, a costat yearly demad (D) of 3,000 uits is cosidered. Oe supplier or a combiatio of them must satisfy this demad i its etirety. 4. Computatioal Results O this fial stage, the results obtaied with the preemptive GP model are preseted. All results were geerated usig the optimizatio software LINDO. I particular, the preemptive goal optio available i this software is applied i solvig the model. This optio solves preemptive (lexicographic) goal programs sequetially by priority. Table 3 shows the fial allocatio quatities for each supplier. As it ca be see, suppliers 2 ad 4 were ot chose. I particular, they both possess the lowest Total Score values ( TS i ) for the first priority (WVP). Moreover, Supplier 2 offers the highest price amog all suppliers. This makes it less likely to be chose give the priority structure, o which Purchasig Expeses is defied as the secod most importat criterio to cosider. I the case of Supplier 4, although it offers a average performace o all criteria, its performace is surpassed by other suppliers. Aother importat result is the achieved levels for each criterio. These results are summarized i Table 4. Based o the results, oly the leadtime goal was fully achieved. That is, suppliers, 3, 5, 6, ad 7 loosely fulfilled the levels set by the compay as goals i terms of total leadtime (hrs). The rest of the goals are partially achieved with respect to the correspodig deviatioal variables ad target levels iitially set by the DM. 207

14 Medoza et al. Table 3: Orders Allocated (i uits) to Each Supplier Supplier Quatity 2, , ,200 6, ,00 Total Cost $665, Table 4: Goal Achievemets Criteria Achievemets Weighted value of purchase 7,79.00 Purchasig expeses ($) 665, Quality level (ppm) 73,650 Flexibility achieved (%).60 Leadtime uderachievemet (hrs) Service Level achieved (%) Process Capability achieved (C pk ).5 Average distace (km) 3, Sesitivity Aalysis As part of the aalysis performed, several scearios were aalyzed. Each sceario defies a differet priority structure with respect to the criteria. Scearios are evaluated to check the robustess of the respose for the GP model. The scearios are described i Table 5. The first sceario correspods to the priority structure origially defied by the DM, while the rest of them reflect situatios where price may ot be as importat ad leadtime or distace are crucial, etc. Table 5: Aalysis of Scearios P r I o r i t i e s Sceario P P 2 P 3 P 4 P 5 P 6 P 7 P 8 WVP P.Exp. Quality Flexib. Leadtime Service P.Cap. Distace 2 P.Exp. Quality Flexib. Leadtime Service P.Cap. WVP Distace 3 P.Exp. Quality WVP Leadtime P.Cap. Distace Flexib. Service 4 Flexib. Leadtime Service Quality Distace P.Exp. P.Cap. WVP 5 Service WVP Quality Distace Leadtime Flexib. P.Cap. P.Exp. 6 Distace P.Cap. Service Leadtime Flexib. Quality P.Exp. WVP 7 Quality Flexib. Leadtime P.Cap. P.Exp. WVP Service Distace 8 Leadtime Distace Flexib. P.Exp. Quality Service WVP P.Cap. It is worthwhile to metio that there are a total of 8!, or equivaletly 40,320 differet scearios, may of them providig the exact same aswer. Oly a few of them were chose, for beig cosidered as represetative of actual scearios i idustry. The results displayed i Table 6 show the allocatio of orders uder each sceario. We ca see that there are several solutios, but they are all i the same form as the origial solutio for Sceario. I geeral, there seems to be a tedecy to choose Suppliers, 3, 5, 6 ad 7. Order quatities do t seem to vary that much ad actually a more careful aalysis o the deviatioal variables shows that the priorities are optimized to similar values for all solutios. 208

15 Multicrıteria Method to the Supplier Selectio Problem Table 6: Allocatio for the Differet Scearios 209 Supplier Sceario X X 2 X 3 X 4 X 5 X 6 X 7 2,200-3,000-3,200,500 3,00 2 2,200-3, ,200 4, ,200-3, ,200 4, ,200-2,400,240 3,60 4, ,000-3,200 3,700 3,00 6 2,200 3,200 3,000, , , ,200 4,200 2, ,200,700 2, ,000 2,700 The solutios preseted i Table 3 could be show to the DM alog with iformatio regardig the achieved values for each priority (as i Table 4). This should provide the DM with a good visio of possible alteratives for the fial decisio. 5. MANAGERIAL IMPLICATIONS AND CONCLUSIONS The Three-Phase itegrated methodology preseted herei allows maagers to make soud decisios with respect to supplier selectio. I particular, Phase offers a easy way to scree a large umber of potetial suppliers to a maageable umber. The, the advatage of AHP (i Phase 2) is that it ca help maagers i formulatig decisios cocerig the impact of alterative suppliers based o the multiple criteria of the orgaizatio. It also provides a strategic approach to evaluate alteratives. AHP is very useful for maagerial decisio makig because it is flexible eough to accommodate a larger set of evaluatio criteria. This eables maagers to make soud selectios based o both qualitative ad quatitative criteria. I Phase 3, maagers ca evaluate the impact of chagig busiess coditios (e.g., icrease service level, chage the required flexibility, leadtime, etc.) ad obtai the proper allocatio of orders to each supplier by meas of goal programmig, which ulike other mathematical programmig approaches, allows maagers to cosider differet criteria levels of achievemet ad give their respective priority with certai flexibility. Differet criteria ad goal costraits ca be itroduced to accout for specific eeds of a compay. I summary, use of this methodology ca facilitate the supplier selectio ad the purchasig problems. I coclusio, supplier selectio is a essetial part of the purchasig process. The objective is to fid the optimal set of suppliers offerig the best goods with respect to a compay s specific criteria. Compaies must cosider multiple criteria i their attempts to differetiate betwee products offered by potetial suppliers. I this research, we have cosidered both quatitative ad qualitative criteria ad itroduced a approach to first, reduce the base of suppliers, rak the supplier selectio criteria i order of importace, ad the, to allocate orders to each supplier from the reduced base of potetial suppliers. Specific criteria ad goal costraits were defied i cojuctio with the Purchasig Departmet of a particular maufacturig compay. Results provide importat isights ito the Three-Phase methodology preseted i this research. 6. REFERENCES. Athoy, T.F., Buffa, F.P., 977. Strategic Purchasig Schedulig. Joural of Purchasig ad Materials Maagemet, 3(3), De Boer, L., Labro, E., Morlacchi, P., 200. A Review of Methods Supportig Supplier Selectio. Europea Joural of Purchasig ad Supply Maagemet, 7(2), Dig, H. W., Beyoucef, L., Xie, X. L., A Simulatio Optimizatio Methodology for Supplier Selectio Problem. Iteratioal Joural of Computer Itegrated Maufacturig, 8(23), Ellram, L.M., 990. The Supplier Selectio Decisio i Strategic Parterships. Joural of Purchasig ad Materials Maagemet, 26(), Ghoudsypour, S. H., O Brie, C. O., 200. The Total Cost of Logistics i Supplier Selectio, Uder Coditios of Multiple Sourcig, Multiple Criteria ad Capacity Costrait. Iteratioal Joural of Productio Ecoomics, 73(), Holt, G. D., 998. Which Cotractor Selectio Methodology? Iteratioal Joural of Project Maagemet, 6(3):53 64.

16 Medoza et al. 7. Moore, D.L., Fearo, H.E., November 973. Computer-Assisted Decisio-Makig i Purchasig. Joural of Purchasig, 9(4), Narasimha, R., Stoyoff, K., Sprig 986. Optimizig Aggregate Procuremet Allocatio Decisios. Joural of Purchasig ad Materials Maagemet, 22(), Pa, A.C., Fall 989. Allocatio of Order Quatity Amog Suppliers. Joural of Purchasig ad Materials Maagemet, 25(3), Saaty, T.L., 994. How to make a decisio: The Aalytic Hierarchy Process. Iterfaces, 24(6), Stamm, C.L., Golhar, D.Y., 993. JIT Purchasig: Attribute Classificatio ad Literature Review. Productio Plaig ad Cotrol, 4(3), Timmerma, E., Witer 986. A Approach to Vedor Performace Evaluatio. Joural of Purchasig ad Materials Maagemet, 22(4), Vokurka, R. J., Choobieh, J., Vadi, L., 996. A Prototype Expert System for the Evaluatio ad Selectio of Potetial Suppliers. Iteratioal Joural of Operatios ad Productio Maagemet, 6(2), Weber, C.A., Curret, J.R., 993. A Multiobjective Approach to Vedor Selectio. Europea Joural of Operatioal Research, 68(2), Weber, C.A., Curret, J.R., Beto, W.C., 99. Vedor Selectio Criteria ad Methods. Europea Joural of Operatioal Research, 50(), Weber, C. A., Ellram, L. M., 992. Supplier Selectio Usig Multi-Objective Programmig: a Decisio Support System Approach. Iteratioal Joural of Physical Distributio ad Logistics Maagemet, 23(2), 3 4. BIOGRAPHICAL SKETCH Abraham Medoza received his M.S. ad Ph.D. degrees i Idustrial Egieerig ad Operatios Research from the Pesylvaia State Uiversity i 2004 ad 2007, respectively. Sice 2008 he has bee at Uiversidad Paamericaa i Mexico where he is curretly a Assistat Professor of Idustrial Egieerig. His research iterests iclude supply chai logistics, operatios maagemet, trasportatio ad facility layout/material hadlig. He is a member of IIE ad INFORMS. Eduardo Satiago received his M.Eg. i Idustrial Egieerig from the Pesylvaia State Uiversity i He is curretly pursuig a Ph.D. i Idustrial Egieerig ad Operatios Research from Pe State. His research iterest focuses o the use of optimal experimetal desig, ad the applicatio of Statistics to Quality Egieerig. He is a member of IIE. Dr. Ravidra is a Professor ad the past Departmet Head of Idustrial ad Maufacturig Egieerig at the Pesylvaia State Uiversity. Formerly, he was a faculty member i the School of Idustrial Egieerig at Purdue Uiversity for 3 years ad at the Uiversity of Oklahoma for 5 years. He holds a B.S. i Electrical Egieerig with hoors from Idia. His graduate degrees are from the Uiversity of Califoria, Berkeley, where he received a M.S. ad a Ph.D. i Idustrial Egieerig ad Operatios Research. Dr. Ravidra s area of specializatio is Operatios Research with research iterests i multiple criteria decisio-makig, fiacial egieerig, ad health plaig ad supply chai optimizatio. He has published two major text books (Operatios Research: Priciples ad Practice ad Egieerig Optimizatio: Methods ad Applicatios) ad over 00 joural articles i operatios research. 20