An Integrated Computer Simulation-DEA and its Extension Models for Vendor Selection Problem

Transcription

1 ALI AZADEH et al.: AN INEGRAED COMPUER SIMULAION-DEA An Integrated Coputer Siulation-DEA and it Etenion Model for Vendor Selection Proble Ali Azadeh Departent of Indutrial Engineering, Departent of Engineering Optiization and Center of Ecellence for Intelligent Baed Eperiental Mechanic, College of Engineering, Univerity of ehran ehran, Iran Seyed Motafa Ale Departent of Indutrial Engineering, College of Engineering, Univerity of ehran ehran, Iran Salan Nazari-Shiroohi Departent of Indutrial Engineering, College of Engineering, Univerity of ehran ehran, Karan Rezaie Departent of Indutrial Engineering, College of Engineering, Univerity of ehran ehran, Iran Abtract hi tudy introduce a fraewor for deciion aing about the vendor election proble. hi fraewor i capable to cover the crip, tochatic, and uncertainty condition in the upply chain environent. he propoed fraewor include of Monte Carlo iulation analyi of three type of vendor election odel in the upply chain and preent a deciion aing plan for chooing the appropriate odel for the upplier election under pecial condition a tated above. hee three odel are Data Envelopent Analyi (DEA), Fuzzy DEA (FDEA), and Chance Contraint DEA (CCDEA). In FDEA odel, the α-cut ethod i ued to convert FDEA into interval prograing. Alo, the CCDEA odel in pecified level of probabilitie i olved and i aued that input are rando variable. For ore illutration, a cae tudy i applied. Obtained reult fro each odel i, average efficiency core of, variance of efficiency core, and 95% confidence interval for the average. Keyword- Supply chain; iulation; Data Envelopent Analyi; Fuzzy Logic; Chance Contrained prograing I. INRODUCION he Supplier election i one of the ot iportant function perfored by the purchaing departent. he upplier election i a ulti-criterion proble, which include both qualitative and quantitative factor. he relationhip between a copany and it upplier ha alway been critical and copanie generally etablih a et for evaluation criteria to be ued to copare potential ource. he baic criteria typically utilized for thi purpoe are pricing tructure, delivery product quality and ervice. Soetie thee evaluation criteria are in conflict with one another. Supplier election i a ey upply anageent deciion. For eaple, a tire anufacturer would be conidered a a upplier to an autoobile anufacturer. In thi cae, the tire upplier would view the autoobile anufacturer a the cutoer []. here are everal upplier election ethod in the literature. Soe of thee ethod are: Analytical Hierarchical Proce [2], Fuzzy Goal Prograing [3], Fuzzy Prograing Model [4], Interpretive Structural Modeling [5], Particle Swar Optiization [6], Siulation-Optiization Approach [7], intelligent odel[8], Multiple Attribute Utility Approach (MAU) [9]. Matheatical prograing odel often conider only the ore quantitative criteria. Alo, oe different ethod uch a, Fuzzy Logic approache [0-4, 32], Analytical Hierarchy Proce approache [5-9], Multi-Obective Prograing (MOP) [20-28], Mied Integer Prograing [33], Chance-Contrained and Genetic algorith [29], aguchi ethod [30, 3], Data Envelopent Analyi (DEA), Optiization echnique (OP) [2], OPSIS approach [22], Integrated Approach [23], otal Cot of Ownerhip approach (CO) [6], Hybrid AHP [34] and etc. are eitent. In thi tudy, a i defined a a upplier. Figure how a tructure in upply chain anageent []. Input (Vendor) Figure. Structure Output he deciion aing ethodology of thi paper i baed on DEA, FDEA, and CCDEA odel with Monte Carlo iulation approach for 200, 600, and 500 run. he ain goal of iulation approach ued in thi tudy i uing the achieved reult fro iulation run for deterine the ean and variance of efficiency core of and 95% IJSSS, Vol. 0, No. 3, April ISSN: online, print

2 ALI AZADEH et al.: AN INEGRAED COMPUER SIMULAION-DEA confidence interval of the ean. For illutrating the application of the propoed fraewor, we ue thi ethodology for olving the vendor election proble in the upply chain anageent. II. OBJECIVES he obective of thi tudy are the ue of the DEA, FDEA, and CCDEA ethod with iulation approach for contruct a deciion aing fraewor for taing a good deciion in certainty, uncertainty, and probabilitic condition. III. DECISION MAKING FRAMEWORK An appropriate odel ut be elected for etiating the efficiency of vendor in the upply chain according to the proviion of the proble. In thi tudy, a deciion aing fraewor i introduced which help the analyt to ae a good deciion about the vendor election proble in variou proviion. hi fraewor i baed on Data Envelopent Analyi (DEA) ethod and two etenion odel of DEA uch a Fuzzy DEA (FDEA) and Chance Contrained DEA (CCDEA). hi deciion fraewor cover the crip, tochatic, and uncertainty condition. he crip condition are odeling by the DEA; tochatic condition are odeling by the CCDEA and uncertainty condition odeling by the FDEA ethod. Before of repreentation of our ethodology for deciion aing about the upplier election proble in the upply chain anageent, we hould decribe the ued odel in our ethodology. hee odel are the DEA, FDEA, and CCDEA with rando input and output. A. Data Envelopent Analyi Data Envelopent Analyi (DEA) introduced by Charne, Cooper and Rhode [35] i a ethod for evaluating the relative efficiency of coparable entitie referred to a Deciion Maing Unit (). he are characterized by everal input and output. Aue there are n, each with input and output. he relative efficiency core of a tet p i obtained by olving the following odel propoed by Charne et al. [35]: Ma = = i =.. () v i = t v IJSSS, Vol. 0, No. 3, April 2009 p p he nonlinear progra hown a () can be converted to a linear progra a hown in equation Ma t.. p = = p = (2) i i = = v v 0 Where = to, = to, i = to n, y i i the aount of output produced by i, i i the aount of input utilized by, v i the weight given to input, and u i the weight given to output. We hould run the progra (2), n-tie to calculate the efficiency of n. In general, a i conidered a efficient if it obtain a core of. While, a core of le than iplie that the correponding i inefficient. B. Fuzzy Data Envelopent Analyi (FDEA) Evaluating the perforance of one deciion aing unit () by traditional data envelopent analyi (DEA) odel require the crip input/output data. However, in realworld proble input and output are often iprecie. he FDEA odel i a odel which deal with the iprecie data. here are different type of fuzzy nuber, but triangular fuzzy nuber are coon to ue, o that we conider the input and output of a triangular fuzzy nuber. he CCR odel with fuzzy data can be written a (3). Ma t.. = = p v% = (3) p % v% 0 i i = = u y% Where, ~ indicate the fuzzine. If triangular fuzzy nuber indicate by % (, l, u i = i i i ) and l u y% i = ( yi, yi, yi ) equation (3) can be written a follow: l u Ma u ( y, y, y ) = p p p t.. l u v (,, ) (4) p p p = = l u l u u ( y, y, y ) v (,, ) 0 i i i i i i = = v, u 0 ISSN: online, print

3 ALI AZADEH et al.: AN INEGRAED COMPUER SIMULAION-DEA he baic idea i to tranfor the fuzzy CCR odel into a crip linear prograing proble by applying an alternative α-cut approach. With conidering our ethod, the odel convert into two odel. he firt odel give an upper bound of efficiency and the econd odel give lower bound of efficiency. he aiu efficiency occur when input ite value equal to it iniu value and the output ite value equal to it aiu value. Alo, the iniu efficiency occur when input ite value equal to it aiu value and the output ite value equal to it iniu value. hee two odel are (5) and (6): u Ma u ( αy + ( α) y ) t.. l u vi αi + α i u αy + α y i= = u vi( αip + ( α) ip) = i= p p = ( ( ) ) ( ( ) ) (5) l Ma u ( αy + ( α) y ) t.. = u l vi αi + α i u αy + α y i= = l vi( αip + ( α) ip) = i= p p ( ( ) ) ( ( ) ) (6) C. Chance Contraint Data Envelopent Analyi (CCDEA) In thi ection, we illutrate a odel that deigned to etend DEA to the cae of tochatic input and output. In thi odel, we aue that only input are rando variable, therefore the CCDEA odel i a follow: Mau y p v X + v X u Y + v X P( v X u Y) = P( ) β uy+ vx φ ( β) uy + vx φ ( β) When i the tandard deviation of v X we have following equation. 2 2 = v var( X ) 2 v v Cov ( X, X ) i i + i= i= = i+ i i herefore, Chance Contraint DEA ultiplier for i a (8). Ma u y p.t. u Y + v X φ ( β ) v X = (8) u,v = v var( X ) 2 v v cov i i i + = i (X i,x ) i= = i+ Where: X = [ X,..., X ] i the input vector fro n, Y = [ Y,..., Y ] i the output vector fro n. Y i the vector of ean value of output fro the -th, X i the vector of ean value of input fro the -th, β i the probability level, i the tandard deviation of v X and φ ( β) i the fractile fro the tandard noral ditribution at the probability level α. In the CCDEA a ight be β-tochatically efficient. t.. Pr( u Y v X ) β (7) v X = u, v 0 Proof. v X u Y ϕ ( β ) i certainty equivalent to Pu ( Y v X ) β. With attention to (7), we have: Figure 2. Frontier he CCDEA i baed on tochatic data for input and output. By uing chance contrained prograing, we can achieve the efficient frontier. We can aue two ide for efficient frontier uch a the wrong ide and the true ide. By IJSSS, Vol. 0, No. 3, April ISSN: online, print

4 ALI AZADEH et al.: AN INEGRAED COMPUER SIMULAION-DEA uing chance contrained prograing oe oberved data located on the wrong ide and eliinated fro efficient vendor et. Figure 2 graphically epre the concept of frontier. he true ide i copoed of all point located on the under frontier and the wrong ide i copoed of all point located on the upper frontier. D. Deciion Maing Flowchart Figure 3 how the flowchart of the propoed deciion fraewor. he ethodology of thi flowchart i a follow: After collection of data, it i checed for it tatu: crip or non-crip. After deterining the data tatu, checed the value of β that how the percent of the will produce output eceeding the bet-practice level. he value of β divide to two clae: equal to, or not equal to. Start Data Collection ABLE I. Noral ditribution VENDORS INFORMAION Input of Eponential ditribution Lognoral ditribution output of Unit cot Accept rate On-tie rate Maiu.00 (0.0) (0.03) (0.02) (0.03) (0.03) (0.03) (0.0) (0.03) (0.05) (0.03) (0.03) (0.03) (0.05) (0.03) (0.06) (0.03) (0.07) (0.03) (0.08) (0.03) 4000 In accordance with the reult of DEA odel, V7 i the bet upplier. he CCDEA (β=0.5) and CCDEA (β=0.75) alo recognize V7 a the bet upplier. V6 in DEA, CCDEA (β=0.5) and CCDEA (β=0.75) i recognized a the wort upplier. I Data Crip FDEA End β= CCDEA DEA ABLE II. RANKING OF S Supplier Applied odel Ran DEA CCDEA(β=0.5) CCDEA(β=0.25) CCDEA(β=0.75) Figure 3. Deciion Maing Flowchart Baed on thi approach, we deal with three below condition: If data are crip, and β= (certainty condition), then ue DEA ethod. If data are crip, and β (tochatic condition), then ue CCDEA ethod. If data are non-crip, then ue FDEA ethod. IV. CASE SUDY hi cae tudy involve a et of 0 upplier each with epected cot, quality acceptance level, and on-tie delivery ditribution. We ut chooe the bet upplier. able provide data for the upply chain odel vendor. Data given i ean (tandard deviation) [27]. According to the proble auption and condition, we can ue the DEA and CCDEA (β=0.25, β=0.5, β=0.75) odel. A tated above, in β=0.5 the CCDEA odel i equal to DEA odel. hi i in accordance with thi fact that the raning of upplier by DEA ut be iilar to raning of by CCDEA (β=0.5). able 2 how the raning of upplier with propoed deciion aing fraewor. Evidence confir the both raning of by DEA and CCDEA (β=0.5) odel are copletely iilar and raning of upplier by CCDEA in β=0.25, β=0.5, and β=0.57 are conitent. V. CONCLUSION In thi tudy, a deciion aing fraewor baed on the DEA, FDEA, and CCDEA i repreented for electing the bet upplier according to the proble condition. hi fraewor wa capable to help the analyt to elect the bet upplier. hi propoed fraewor cover certainty, uncertainty, and probabilitic condition. he ethodology of thi fraewor wa a follow: when data are crip, and β=, we ued DEA odel. On the other hand, when data are non-crip, we ued the FDEA odel. Finally, when data are crip and β, we ued the CCDEA odel for the upplier election. In the ection 3.3 tated that CCDEA odel in β =0.5 i equal to DEA. For illutrating the application of the propoed fraewor, a cae tudy i repreented. According to the propoed fraewor for electing the bet upplier, we ued the DEA and CCDEA (β=0.5) odel. Derived evidence howed that the DEA and CCDEA (β=0.5) are equal. he raning of upplier baed on the DEA and CCDEA (β=0.5) odel were a follow: V7, V8, V2, V, V0, V3, V9, V5, V4 and V6. he bet upplier wa V7 and the wort upplier wa V0. Baed on the CCDEA (β=0.75), V7 and V0 alo were recognized a the bet and wort upplier, repectively. For future tudy, we can etend the deciion aing flowchart for a pecial condition for dealing with both the uncertainty and tochatic condition. IJSSS, Vol. 0, No. 3, April ISSN: online, print

5 ALI AZADEH et al.: AN INEGRAED COMPUER SIMULAION-DEA REFERENCES [] M. Sira Uuddin and P. K. Varghee, Supply chain anageent and bet upplier election practice, Mater of cience, Departent of Innovation, Deign and Product Developent, Mälardalen Univerity, Eiltuna, Sweden, [2] O. Bayazit and B. Karpa, An AHP application in vendor election, Departent of Buine Adinitration, College of Buine, Central Wahington Univerity, [3] M. Kuar, P. Vrat, and R. Shanar, A fuzzy goal prograing approach for vendor election proble in a upply chain, Coputer & Indutrial Engineering vol. 46, pp , [4] W. Junyan, Z. Ruiqing, and. Wanheng, Fuzzy prograing odel for vendor election proble in a upply chain, inghua Science and technology, Vol. 3, pp. 06-, [5] A. Mandal and S.G. Dehuh, Vendor election uing interpretive tructural odeling (ISM), International Journal of Operation & Production Manageent, Vol. 4, No. 6, pp , 994. [6] C. Mouli, V. Subbaiah, and M. Rao, Particle war optiization approach for vendor election, Journal of the Intitution of Engineer (India) Part PR, Vol. 87, [7] H. Ding, L. Benyoucef, and X. Xie, A iulation-optiization approach uing genetic earch for upplier election, Proceeding of the 2003 Winter Siulation Conference. [8] S. K. Da and H. Shahin, Model for upply chain vendor election in e-aret, Journal of the Chinee Intitute of Indutrial Engineer, Vol. 20, No. 3, pp , [9] H. Min, International upplier election: a ulti-attribute utility approach, International Journal of Phyical Ditribution and Logitic Manageent, Vol. 24, No. 5, pp , 994. [0] M. Bevilacqua and A. Petroni, Fro traditional purchaing to upplier anageent: a fuzzy logic baed approach to upplier election, International Journal of Logitic, Vol. 5, No. 3, pp , [] Y. ying, Reearch on vendor election under fuzzy ituation, Modeling & Siulation, AICMS 08. Second Aia International Conference, pp , [2] J. L. Yang, H. N. Chiu, and G. H. zeng, Vendor election by integrated fuzzy MCDM technique with independence andinterdependence, Inforation Science: An International Journal, NO.78, pp , [3] J. Wanga, R. Zhaoa, and W. ang, Fuzzy prograing odel for vendor election proble in a upply chain, inghua Science and technology, Volue 3, pp [4] H. Ay and I. Lee, A fuzzy upplier election odel with the conideration of benefit, opportunitie, cot and ri, Epert Syte with Application [5]. N. Al-fara, A. S. Alidi, and J. A. Al-zayer, Vendor election via a preadheet analytical hierarchy proce, Coputer and Indutrial Engineering, Vol. 25, No. -4, pp , 993. [6] K. S. Bhutta and F. Huq, Supplier election proble: a coparion of total cot of ownerhip and analytical hierarchy proce approach, Supply Chain Manageent: An International Journal, Vol. 7,No. 3, pp.26-35, [7] F.. S. Chan, Interactive election odel for upplier election proce: an analytical hierarchy proce approach, International Journal of Production Reearch, Vol. 4,No. 5, pp , [8] F. Yao and L. Hongli, Inforation yte outourcing vendor election baed on analytic hierarchy proce, Wirele Counication, Networing and Mobile Coputing, WiCo International Conference, pp , [9] R. V. Rao, Vendor election in a upply chain uing analytic hierarchy proce and genetic algorith ethod, International Journal of Service and Operation Manageent, Vol. 3, NO. 3, pp , 2007). [20] B. Karpa, R. Kauganti, and E. Kucn, Multi-obective deciion aing in upplier election: an application of viual interactive goal prograing, he Journal of Applied Buine Reearch, Vol. 5, No. 2, pp. 57-7, 999. [2] N. Arunuar, L. Karunaoorthy, A. Arih, L. Shenoy, N. haizhvaanan, and V. B. Naidu, Multiobective upplier election uing optiiation technique for balancing upply chain, International Journal of Indutrial and Syte Engineering, Vol. 3, NO. 5, pp , [22] W. Li, Y. Chen, and Y. Fu, Cobination of OPSIS and 0- prograing for upplier election in upply chain anageent, Networing, Sening and Control, ICNSC IEEE International Conference, pp , [23] S.C. ing and D. I. Cho, An integrated approach for upplier election and purchaing deciion, Supply Chain Manageent: An International Journal, Vol. 3, NO. 2, pp. 6-27, [24] S. alluri and Silberan, Data envelopent analyi: odel and etenion, Deciion Line, May [25] A. Azadeh, S.F.Ghaderi, Z. Javaheri, and M. Saberi, A fuzzy atheatical prograing approach to DEA odel, Aerican Journal of Applied Science Vol. 5, NO. 0, pp , [26] O. B. Oleen, Coparing and cobining two approache for chance contrained DEA, Journal of Productivity Analyi, Vol. 26, NO. 2, [27] D. Wu and D. L. Olon, Supply chain ri, iulation, and vendor election, International Journal of Production Econoic, [28] N. Arunuar, L. Karunaoorthy, S. Anand, and. R. Babu, Linear approach for olving a piecewie linear vendor election proble af quantity dicount uing leicographic ethod, International Journal of Adv Manufacturing echnology, Vol. 28, pp , [29] S. He, S. S. Chaudhry, and Z. Lei, Stochatic vendor election proble: chance-contrained odel and genetic algorith, Annal of Operation Reearch, [30] W. N. Pi and C. Low, Supplier evaluation and election uing taguchi lo function, International Journal of Adv Manufacturing echnology, vol.26, pp , [3] W. N. Pi and C. Low, Supplier evaluation and election via taguchi lo function and an AHP, International Journal of Adv Manufacturing echnology, vol. 27, pp , [32] A. N. Haq and G. Kannan, Fuzzy analytical hierarchy proce for evaluating and electing a vendor in a upply chain odel, International Journal of Adv Manufacturing echnology, vol. 29, pp , [33] H. Stadtler, A general quantity dicount and upplier election ied integer prograing odel, Operation Reearch Spectru, vol. 29, pp , [34] M. Sevli and et al. Hybrid analytical hierarchy proce odel for upplier election, Indutrial Manageent & Data Syte, Vol. 08 No., pp , [35] A. Charne, W.W. Cooper, and E. Rhode, Meaureent the efficiency of deciion aing unit, European Journal of Operational Reearch, vol. 2, 978, pp IJSSS, Vol. 0, No. 3, April ISSN: online, print