Implementation of Supplier Evaluation and. Ranking by Improved TOPSIS

Transcription

1 Appled Mathematcal Scences, Vol. 7, 2013, no. 46, HIKARI Ltd, Implementaton of Suppler Ealuaton and Rankng by Improed TOPSIS C. Katha Department of Mathematcs Sathyabama Unersty, Chenna, Inda C.Vayalakshm Department of Mathematcs VIT chenna campus, Chenna, Inda. Copyrght 2013 C. Katha and C. Vayalakshm. Ths s an open access artcle dstrbuted under the Create Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, proded the orgnal work s properly cted. Abstract Ths paper proposes a new hybrd algorthm for suppler selecton and ealuaton for quanttate, qualtate factors n supply chan management. Suppler selecton and ealuaton s formulated by ntegratng Mult-crtera decson makng approach such as Analytc herarchy process(ahp) mproed by Rough set theory and Technque for order performance by smlarty to deal soluton (TOPSIS) to rank the supplers based on ther oerall performances. Rough set theory s used to screen the supplers by the decson makers. AHP was appled to determne the relate weghts of ealuaton crtera. TOPSIS was appled to rank supplers n terms of ther oerall performances. Ths method helps the decson maker to select the best suppler who meets all the requrements of supply chan management. To ealuate the algorthm a case study s done n hgh technology Company named Mult-Flex Lam-Prnt Ltd whch manufactures Flexble Packagng materals n Inda. Keywords: Rough set theory, Analytc Herarchy Process, TOPSIS, Mult crtera decson makng, Supply chan Management

2 2266 C. Katha and C. Vayalakshm 1. INTRODUCTION Supply chan management (SCM) plays an mportant role n all the ndustres because t must satsfy the market demand based on all crtera s. Management of an organzaton manly depends on ther supplers therefore selecton of supplers and ealuaton s a complex decson makng process. AHP s the best tool to decde the complex crtera n dfferent leels. It s one of the most wdely used multple crtera decson-makng tools [T.L. Saaty]. To calculate the relate weght of multple crtera [quanttate, qualtate] or multple optons aganst gen crtera AHP s used. It s an Egen alue approach to par wse comparson. It also prodes a numerc scale for the measurement of qualtate and quanttate performances [Taha]. The tradtonal AHP utlzes exact alues to express the decson maker s opnon n a comparson of alternates (Wang & Chen).But n many practcal cases human preference model s uncertan and t s ery dffcult for the decson maker to express the preferences usng exact numercal alues. To mproe the AHP method Rough set theory s appled. AHP mproed by rough set theory and mult_objecte mxed nteger programmng to determne the number of supplers to employ the order quantty (Weun Xa, Zhmng Wu., 2007). Rough set theory s a mathematcal tool for mperfect data analyss [Z. Pawlak]. Rough set theory s used to analyze the decson table composed of attrbutes. It s sutable for analyzng both quanttate and qualtate features, and results of Rough Set Model are easy to understand [Tay, F.E. and Shen, L]. TOPSIS was founded by Hwang and Yoon. TOPSIS (Technque for Order Preference by Smlarty to Ideal Soluton) s a Mult attrbute Decson Makng [MADM] technque whch was appled to manage real world problems whch smultaneously consders the deal and the ant-deal soluton for the correspondng attrbutes [K. Yoon, C.L. Hwang]. TOPSIS method s based on the concept that the best alternate among seeral alternates that should hae the shortest Eucldean dstance from the poste deal soluton (PIS), and the farthest from the negate deal soluton (NIS). Due to ts straghtforward nature, TOPSIS has been wdely appled n supply chan management (Boran, Genc, Kurt & Akay). Ths paper proposed a structured methodology for suppler selecton and ealuaton n supply chan management. Supplers are screened by Rough set theory and the selected suppler s qualtate data are analyzed and the weghts of the supplers are obtaned by Analytc herarchy process (AHP). To analyze the quanttate data s and rank the supplers, Technque for order preference by smlarty to deal soluton (TOPSIS), a mult-attrbute decson-makng (MADA) method s adapted. To llustrate the applcaton and feasblty of the proposed methodology a case study s done n hgh technology Company named Mult-Flex Lam-Prnt Ltd whch manufactures Flexble Packagng materals n Inda. Ths approach s able to help the decson maker to ealuate and rank the sutable supplers among many supplers.

3 Implementaton of suppler ealuaton METHODOLOGY Step 1: Supply chan herarchy s formulated by defnng the crtera, sub crtera and alternates. Step 2: To reduce the ealuaton bas n decson table the concept of rough set theory s used for nformaton regardng the objects suppled n the form of data table. Here the data set s represented as a table where each row represents an object and each column represents an attrbute that can be measured for each object whch s suppled by a human expertse. Step 3: To obtan the oerall weghts of each alternate for qualtate and quanttate factors n multple crtera decson makng problem for each suppler AHP s used. In AHP crtera s and subcrtera s are wrtten n square matrx form based on the preference wth respect to each tem.for square matrx A and ector x, λ = Egen alue of A. When Ax = λx, x non zero egen ector assocated wth λ. Compute by solng the characterstc equaton det(λi A) = λi A = 0. Then check for consstency by ( λ max n / n 1). Step 4: Supplers rankng s done by TOPSIS method for quanttate factors by usng the suppler weghts obtaned by Rough set theory and AHP. In TOPSIS normalzed decson matrx s calculated as x =. Then the weghted normalzed matrx s calculated as V = w *r. Determne the deal and negate deal soluton as + ' = {(max j J),(mn j ) = 1,2,... m} A A = {(mn j J ),(max j J J ' ) = 1,2,... m} Calculate the separaton measure of poste deal as s j= 1 2 n ( ) and negate deal as = ( ) n + + = j the relate closeness deal soluton as 3. APPLICATION c * s = ( s + s + s j= 1 ) x j 2. Calculate Supply chan management has appled to a professonally managed company namely Mult-Flex Lam-Prnt Ltd., who manufactures Qualty Flexble Packagng Materals aganst specfc orders from ther customers lke Hndustan Unleer Ltd., ITC Ltd., Tata Tea Ltd., Cankare Pt Ltd etc wll produce r m = 1 2

4 2268 C. Katha and C. Vayalakshm mportant raw materals lke Polyester flm, B-axally orented Poly Propylene flm, Polyethylene flm etc from the best sutable suppler s for arous producton processes such as Prntng-Lamnaton-Slttng-Fnshng. Supplers of Polyester flm are Garware Polyesters Ltd (Suppler 1), Polyplex Ltd (Suppler 2), Jndal Flms Ltd (Suppler 3), and U Flex Flms Ltd (Suppler 4). 3.1 Selecton Crtera for Supplers The leel of herarchy whch we hae taken here s four leels whch nclude objectes, dfferent decson crtera, attrbutes and the decson alternates. The man objecte here s the selecton of best suppler for a manufacturng frm. The oerall objecte s placed at leel 1, crtera at leel 2, attrbutes at leel 3 and decson alternates at leel Cost of the product (C 1 ) Product cost (A 1 ), Perod cost (A 2 ). 3.3 Qualty of the Product (C 2 ) Standardzaton (A 3 ), Research and Deelopment (A 4 ), Defects (A 5 ). 3.4 Serce performance of suppler (C 3 ) Preente acton (A 6 ), On tme delery (A 7 ), Response speed (A 8 ), Flexblty (A 9 ), After sales serce (A 10 ). Table 1 determned the global weghts for all crtera and sub-crtera by mproed AHP. Suppler s ratngs are calculated by formng par wse comparson matrx for dfferent crtera and sub crtera. Then the suppler s weghts are obtaned as , , and The weghts obtaned by mproed AHP are used to calculate the relate closeness to the deal soluton by TOPSIS method and the alues are , , , and Supplers rankng s done as 2, 4, 3, and 1.

5 Implementaton of suppler ealuaton 2269 Table 1: Composte prorty weghts for crtera and sub crtera Crtera Local weghts Sub crtera Local weghts Global weghts Prorty order Prce Product cost Perod cost Standardzaton Qualty Research & Deelopment Defects Preente acton On tme delery Serce Response speed Flexblty After sales serce CONCLUSION Suppler selecton and ealuaton s the complex mult crtera decson makng n supply chan management whch ncludes quanttate and qualtate factors wth human judgment. In ths approach quanttate and qualtate factors are ealuated wth respect to the supplers and they are ranked. To aod ealuaton bas here human judgment s done by rough set, preferences wth respect to the crtera s, sub crtera s done by analytc herarchy process and the oerall weghts wth respect to the quanttate, qualtate factors among the supplers s calculated. Suppler s weghts are ntegrated wth Technque for order performance by smlarty to deal soluton to rank the oerall performance of the suppler wth respect to the qualtate, quanttate factors. Therefore the proposed approach s smple and easy to aod bas n human judgment and rankng the supplers whle comparng to conentonal approaches. As a result ths can be appled to other areas such as warehouse locaton selecton, dstrbuton centre, project selecton n supply chan management.

6 2270 C. Katha and C. Vayalakshm References [1].Boran, F.E., Genc, S., Kurt, M. & Akay, D.. A mult-crtera ntutonstc fuzzy group decson makng for suppler selecton wth TOPSIS method, Expert Systems wth Applcatons, 36, , (2009). [2].H.A.Taha., Operaton Research, Pearson Educaton Inc, Fayettelle. [3]. K. Yoon, C.L. Hwang., Manufacturng plant locaton analyss by multple attrbute decson makng: part II. Mult-plant strategy and plant relocaton, Internatonal Journal of Producton Research, 23 (2) (1985), pp [4]. Predk, B. et al.. ROSE- Software mplementaton of the Rough Set Theory. In Polkowsk, L. and Skowron, A. (Eds) Rough Sets and Current Trends n Computng, Proceedngs of the RSCTC98 Conference. Lectures Notes n Artfcal Intellgence ol. 1424, Berln pp [5].T.L. Saaty, The Analytc Herarchy Process, McGraw-Hll, [6].Tay, F.E. and Shen, L.. Economc and fnancal predcton usng rough set model. European Journal of Operatonal Research 141, pp [7].Wang, T. C., & Chen, Y. H., Applyng consstent fuzzy preference relatons to partnershp selecton. Omega, 35(4), , (2007). [8].Weun Xa, Zhmng Wu., Suppler selecton wth multple crtera n olume dscount enronments. Omega 35, PP , [9].Z.Pawlak, Rough sets, Internatonal Journal of Computer and Informaton Scences, 1982, 11, Receed: February 21, 2013