A Multi-Product Reverse Logistics Model for Third Party Logistics

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1 2011 Internatonal Conference on Modelng, Smulaton and Control IPCSIT vol.10 (2011) (2011) IACSIT Press, Sngapore A Mult-Product Reverse Logstcs Model for Thrd Party Logstcs Tsa-Yun Lao, Agatha Rachmat Graduate Insttute of Maretng and Logstcs/Transportaton, Natonal Chay Unversty, Tawan, ROC Abstract. Recently, accordng to an exhauston of resources and envronment problems, reverse logstcs has been an mportant ssue among ndustres n the past few years. The obectve of ths research s to propose a mathematcal model for reverse logstcs of thrd party logstcs (3PLs). The model s developed consderng uncertanty condtons wth mult-product n a mult-echelon networ to mnmze the total cost of the reverse logstcs. The developed model s solved usng LINGO and the results are verfed usng smulaton model PROMODEL. Results from the numercal analyss and smulaton show that the process of reverse logstcs managed by a 3PL yelds better results, wth total cost decreases of 13.8%. Keywords: mathematcal model, smulaton, reverse logstcs, thrd party logstcs. 1. Introducton Reverse logstcs has been an mportant ssue among ndustres n the past few years, thus t s vewed n the past as a secondary operaton to the new product sde of busness, has now moved to the forefront as a strategc and ntegral part of the drve to ncrease customer satsfacton. Such progresson has stretched the responsblty of producers beyond the producton and dstrbuton to the responsblty of the end of product lfe cycle. Reverse logstcs actvtes nvolve product returns, source reducton, conservaton, recyclng, substtuton, reuse, dsposal, refurbshment, repar, and remanufacturng [1]. Reverse logstcs focuses not only on end-of-lfe (EOL) product but also on servcng returned products whch nclude non-used product as one of the servce provded by manufactures. Therefore, wth the complexty of reverse logstcs, many companes wth lmted resources outsource ther reverse logstcs operatons to thrd-party logstcs provders (3PLs). 3PLs can provde multple logstcs servces ncludng transportaton, warehousng, crossdocng, nventory management, pacagng, and freght forwardng servces. Preferably, these servces are managed or ntegrated by the provders. The management of a reverse logstcs networ s not smlar to a logstc networ. Product recovery not only reverses the product stream wth the conseuence of recycled or non-used products, but that the process s severely complcated by hgh uncertanty n many factors [2]. Because of the complexty of reverse logstcs, developng a mathematcal model has been commonly used n order to solve the problem [1-8]. Most of the prevous researches focus on developng dscrete mathematcal models wthout consderng the uncertanty factors. Ths research develops a mathematcal model of reverse logstcs networ whch ncludes customers, collectng centers, processng centers, manufactures, and landfll. The obectve of the model s to mnmze the total operaton cost, consderng mult-product, mult-echelon, and demand uncertanty to be handled by 3PLs. Numercal experments are conducted to llustrate the developed model. The expermental data are collected from Envronmental Protecton Bureau (EPB), Chay Cty, Tawan and Envronmental Protecton Correspondng author. Tel.: ; fax: E-mal address: tylao@mal.ncyu.edu.tw. 48

2 Admnstraton (EPA), Tawan to calbrate the results of the developed model. The model s solved and analyzed usng LINGO software and the results are verfed usng smulaton model PROMODEL. 2. Model Development Ths research develops a mathematcal model of reverse logstcs networ whch ncludes customers, collectng centers (CC), processng centers (PC), manufactures, and landfll. The model s developed nto a generc model that represents the actual concept of product returns, source reducton, conservaton, recyclng, substtuton, reuse, dsposal, refurbshment, repar, and remanufacturng n the reverse logstcs. Ths obectve of the model s to mnmze total operatonal cost wthn the networ wthout degradng servce ualty for each customer and to consder dfferent scenaros n actual processes. Operatonal cost consdered n ths study ncludes monthly fxed and varable costs, such as labor cost, management cost, ncludng transportaton cost and penalty cost. Monthly fxed cost n each collectng center and processng center ncludes labor cost and servce cost, whch servce cost refers to cost such as electrc and water blls, product process cost. These costs consder the capacty of each collectng center and processng center. Transportaton cost covers cost of delverng returned products from customers to each collectng center, processng center and all the way to the landfll or to manufactures. Penalty cost presents the cost to be charged f the returned products are faled to be collected. The mathematcal model, parameters, and varables are defned as follows: Obectve functon: Mn FD Y π s [ RD s s FD Y RP J K s S I J Q I K Q DP DL QH s s PL QM s J K Q J Q K Q Subect to: J m M Q s DM QN m ms K m M Q PM mqoms PE QPs ] (1) Q QZ s Q, s S (2) QPs β s QZs Q, s S (3) QPs s = s QZ s Q, s S (4) S Y s J,s S (5) s U Y s s S Y J,s S (6) s s s K, s S (7) U Y K, s S (8) QH s QM s α QZ s Q, s S (9) m m s s γ s Q, s S (10) QN ms s QH s s J,s S (11) QO ms QM s s s K, s S (12) Y J, Y K (13) Parameters: s,,, QH, QM, QN, QO, QP 0 s { 0,1} s s s ms ms Y, Y (15) FD = Fxed cost of CC, s (14) 49

3 FP = Fxed cost of PC, RD = Transportaton cost of product from customer to CC, RP = Transportaton cost of product from customer to PC, DP = Transportaton cost of product from CC to PC, DL PL πs Varables: = Transportaton cost of product from CC to the landfll, = Transportaton cost of product from PC ste to the landfll, DM m = Transportaton cost of product from CC to the manufacture m, PM m = Transportaton cost of product from PC ste to the manufacture m, PE = Penalty cost for product not collected, S = Maxmum capacty of CC ste, S = Mnmum capacty of CC ste, U = Maxmum capacty of PC ste, U = Mnmum capacty of PC ste, QZ s = Returned product n customer n scenaro s, β s = Maxmum percentage of product faled to be collected n scenaro s, α s = Maxmum percentage of waste from PC and CC to landfll n scenaro s, γ s = Mnmum percentage of product from CC to PC n scenaro s, = Probablty n scenaro s Y = 1 f ste s open, otherwse =0, Y = 1 f ste s open, otherwse =0, s = Quantty of product from customer transferred to CC n scenaro s, s = Quantty of product from customer transferred to PC n scenaro s, s = Quantty of product from CC transferred to PC n scenaro s, QH s = Quantty of product from CC transferred to landfll n scenaro s, QM s = Quantty of product from PC transferred to landfll n scenaro s, QN ms = Quantty of product from CC transferred to manufacture m n scenaro s, QO ms = Quantty of product from PC transferred to manufacture m n scenaro s, QP s = Quantty of product faled to be transferred n scenaro s. Euaton (1) s the obectve functon of ths model, and the obectve s to mnmze total cost n the reverse logstcs networ, such as management cost n each CC and PC, transportaton cost and penalty cost. Euaton (2) states the balance flow from each customer to CC. Euaton (3) presents the lmtaton of product whch are faled to be collected. Euaton (4) presents the constrant for total balance flow of product collected. Euaton (5) and (6) are the maxmum and mnmum capacty constrants of CC. Euaton (7) and (8) are the maxmum and mnmum capacty constrants of PC. Constrants of unwanted products are presented by Euaton (9) and (10). Euaton (11) states balance flow of products n CC. Euaton (12) states balance flow of products n PC. Constrant for maxmum number of CC and PC s n Euaton (13). The Euaton (14) and (15) are non-negatve and the bnary constrants. 3. Numercal Experments 3.1. Numercal results The data for the numercal experments are collected from EPB, Chay Cty, Tawan and EPA, Tawan. Table 1 shows the average uantty of returned products for each month n Chay, Tawan. Other data ncludng operatonal cost, transportaton cost, and penalty cost are collected or calbrated from the nown nformaton. 50

4 Table 1 Average monthly uantty of returned products n Chay, Tawan Type of Product Quantty (Kg) Paper Glass Plastc Metal Electronc Three scenaros are desgned to descrbe dfferent characterstcs of uncertan uantty of returned products collected from customers. The three scenaros are: (1) Scenaro 1: Total products from customer are assumed n the normal condton wth the probablty of 50%. (2)Scenaro 2: Total products from customer are assumed decreased wth the probablty of 30%. (3)Scenaro 3: Total products from customer are assumed ncreased wth the probablty of 20%. To analyze the current stuaton of reverse logstcs n Chay Cty and to compare that wth the reverse logstcs handled by 3PLs, related condtons are assumed to represent the characterstcs n each stuaton. 1. Condton I: Consders the current stuaton of general reverse logstcs networ n Chay Cty, whch the collectng center s controlled by the government and the processng centers and manufactures are handled by prvate companes. 2. Condton II: Consders the entre networ s managed by a 3PL. Table 2 shows the numercal results. The processng centers reured are 4, 3, and 3 for Condton I wthout optmum, Condton I wth optmum, and Condton II, respectvely. In Condton I, the results wthout optmum represent the current stuaton of reverse logstcs controlled by the cty government, and results wth optmum ndcate that the cty government can reduce total cost of 7.3% f the proposed model s appled to the process of reverse logstcs. In Condton II, total cost has declned 13.8 % by comparng wth the current condton. Snce the entre networ s managed by a 3PL, fxed cost, transportaton cost, and total cost are the lowest compared to those of other condtons. The results show that the optmum of the reverse logstcs can be obtaned wth centralzaton of the networ by a 3PL. Table 2 The numercal results Condton Optmum Processng Center Fxed Cost (NT$) Transportng Cost (NT$) Total Cost (NT$) Cost % I Wthout optmum 1,2,3, % - Optmum 1,3, % -7.3% II Optmum 1,3, % -13.8% 3.2. Smulaton results The numercal data collected from EPB, Chay ndcate that after all the product collected n the collectng centers; generally the product wll be ept n the collectng centers for one to three days before transportng to the processng centers. The average tme for the recovery process n the processng centers s one to three days, too. The data and results of numercal experments are used to smulate the process of the reverse logstcs n smulaton model PROMODEL. In verfcaton stage, the smulaton model s tested and compared wth the desgned networ. Fg. 1 shows the verfcaton stage for model of condton II wth 3 processng centers. As t s shown n the fgure, the smulaton model s able to run wthout any computaton error. It means the model has passed verfcaton and valdaton stage. When the products are processed for one day n processng centers, utlty of each processng center s hgher than 80%; and the utlty of each processng center s over 90% when the products are ept n processng centers for 2 days. It shows that 3 processng centers for 3PLs nstead of 4 processer centers for current stuaton n Chay can provde more effectveness n reverse logstcs, thus the reverse logstcs managed by 3PLs can obtan better results. 51

5 4. Conclusons Fg. 1: Smulaton process n smulaton model PROMODEL Ths research has developed a mathematcal model consderng uncertanty condtons wth multproduct n a mult-echelon reverse logstcs networ. In order to valdate the capablty of the proposed model, numercal data collected from EPB, Chay Cty and EPA, Tawan are appled to solve the model usng LINGO software and the results are verfed usng smulaton model PROMODEL. The results from the numercal analyss and smulaton results ndcate that the proposed model s able to represent a general process of reverse logstcs and a practcal operaton of reverse logstcs networ managed by 3PLs. It shows that the total cost of reverse logstcs can be mnmzed by applyng the proposed model and the stuaton of reverse logstcs managed by a 3PL yelds better results, wth total cost decreases of 13.8%. 5. Acnowledgements The authors than Envronmental Protecton Bureau, Chay Cty, Tawan for provdng the data for the numercal experments. 6. References [1] A. Mutha and S. Poharel. Strategc networ desgn for reverse logstcs and remanufacturng usng new and old product modules. Computers & Industral Engneerng , pp [2] O. Lstes, and R. A. Deer, stochastc approach to a case study for product recovery networ desgn. European Journal of Operatonal Research , pp [3] D.W Krumwede, and C. Sheu. A model for reverse logstcs entry by thrd-party provders. Omega , pp [4] M. El-Sayed, N. Afa, and A. El-Kharbotly. A stochastc model for forward reverse logstcs networ desgn under rs. Computers & Industral Engneerng , pp [5] O. Lste. A generc stochastc model for supply-and-return networ desgn. Computers & Operatons Research , pp [6] Y.M. Zhang, G.H. Huang, and L. He. An nexact reverse logstcs model for muncpal sold waste management systems. Journal of Envronmental Management , pp [7] Y.H. Cheng and F. Lee. Outsourcng reverse logstcs of hgh-tech manufacturng frms by usng a systematc decson-mang approach: TFT-LCD sector n Tawan. Industral Maretng Management , pp [8] J.E. Lee, M. Gen, and K.G. Rhee. Networ model and optmzaton of reverse logstcs by hybrd genetc algorthm. Computers & Industral Engneerng , pp