Coordination of Collection and Disassembly Planning for End-of-Life Product

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(14) . Habibi, M. K. Khakim and Battaïa, Olga and Cung, Van-Dat and Dolgui, Alexandre Coordination of Collection and Disassembly Planning for End-of-Life Product. (2015) In: IFAC Symposium on Information Control in Manufacturing (INCOM 2015), 11 May 2015 - 13 May 2015 (Ottawa, Canada).. .

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(24) Proceedigs of the 15th IFAC Symposium on Proceedigs the IFAC on Information Control Problems in Manufacturing Proceedigs of of the 15th 15th IFAC Symposium Symposium on Proceedigs of the 15th IFAC Symposium on Information Control Problems in Manufacturing May 11-13, 2015. Ottawa, Canada Information Control Problems in Manufacturing Information Control Problems in Manufacturing May 11-13, 2015. Ottawa, Canada May May 11-13, 11-13, 2015. 2015. Ottawa, Ottawa, Canada Canada. Coordination Coordination Coordination Planning Planning Planning. of Collection and Disassembly of Collection and Disassembly of Collection and Disassembly for End-of-Life Product for End-of-Life Product for End-of-Life Product . M. K. Habibi ∗∗ O. Batta¨ıa ∗∗ V.–D. Cung ∗∗ A. Dolgui ∗∗ ∗∗ ∗ ∗∗ M. K. Habibi ∗∗ O. Batta¨ ıa Cung Dolgui ∗∗ ∗ V.–D. ∗∗ A. M. K. Habibi O. Batta¨ ıa V.–D. Cung M. K. Habibi O. Batta¨ıa V.–D. Cung A. A. Dolgui Dolgui ∗ ´ ´ Ecole Nationale Sup´ e rieure des Mines de Saint– Etienne ∗ ´ ∗ ´ Nationale Sup´ des Mines Etienne ´ ´ ∗ Ecole ´de Ecole Nationale Sup´eeerieure rieure des Saint– Mines Etienne de Saint– Saint– Etienne ´ ´ 2, France Lab. LIMOS, CNRS UMR6158, 42023 cedex Ecole Nationale Sup´ rieure des Mines de Saint– Etienne ´ Lab. LIMOS, CNRS UMR6158, 42023 Saint– Etienne cedex ´ Lab. LIMOS, LIMOS, CNRS UMR6158, 42023 42023 Saint– Saint–Etienne Etienne cedex 2, 2, France France ´ (e-mail: {muhammad.habibi,battaia,dolgui}@emse.fr). Lab. CNRS UMR6158, cedex 2, France {muhammad.habibi,battaia,dolgui}@emse.fr). ∗∗ (e-mail: (e-mail: {muhammad.habibi,battaia,dolgui}@emse.fr). Univ. Grenoble Alpes, G-SCOP, F-38000 Grenoble, France (e-mail: {muhammad.habibi,battaia,dolgui}@emse.fr). ∗∗ ∗∗ Univ. Grenoble Alpes, G-SCOP, F-38000 Grenoble, France ∗∗ Univ. CNRS, Grenoble Alpes, F-38000 F-38000 Grenoble,Grenoble, France France Univ. CNRS, GrenobleG-SCOP, Alpes, G-SCOP, G-SCOP, F-38000 Grenoble, France G-SCOP, F-38000 Grenoble, France CNRS, G-SCOP, F-38000 Grenoble, France (e-mail: van-dat.cung@grenoble-inp.fr) CNRS, G-SCOP, F-38000 Grenoble, France (e-mail: (e-mail: van-dat.cung@grenoble-inp.fr) van-dat.cung@grenoble-inp.fr) (e-mail: van-dat.cung@grenoble-inp.fr). Abstract: This work proposes a formulation for coordinating between collection and disasAbstract: This work a formulation for coordinating between collection and disasAbstract: This work proposes a for between collection and disassembly planning anproposes End-of-Life (EOL) product. The coordination deals with the Abstract: This for work proposes a formulation formulation for coordinating coordinating between collection andbalance disassembly planning planning for an End-of-Life (EOL) product. The coordination deals with the balance sembly for an End-of-Life (EOL) product. The coordination deals with the balance between the number of products collected, the inventory level and the number of products sembly planning for an End-of-Life (EOL) product. The coordination deals with the balance between the number of products collected, inventory level and the number of products between the of collected, the inventory level and the of disassembled. The objective function aims to the minimize the total the disassembly between the number number of products products collected, the inventory level cost and including the number number of products products disassembled. The objective function aims to minimize the total cost including the disassembly disassembled. The objective function aims to minimize the total including disassembly cost, the penalty cost, the holding cost and the running cost ofcost vehicle. Two the strategies with disassembled. The objective function aims to minimize the total cost including the disassembly cost,without the penalty penalty cost, the thewere holding cost and and the running running cost of of vehicle. vehicle. Two strategies strategies with cost, the cost, holding cost the cost Two with and coordination compared via numerical experiments. The results obtained show cost, the penalty cost, the holding cost and the running cost of vehicle. Two strategies with and without coordination were compared numerical The results obtained show and without coordination were compared via numerical experiments. that the coordinated strategy totalvia cost reducing.experiments. and without coordination wereallows compared via numerical experiments. The The results results obtained obtained show show that the coordinated strategy allows total cost reducing. that the coordinated strategy allows total cost reducing. that the coordinated strategy allows total cost reducing. Keywords: Disassembly Process, Vehicle Routing, Inventory Control, End-of-Life Product, Keywords: Disassembly Disassembly Process, Vehicle Routing, Routing, Inventory Control, Control, End-of-Life Product, Product, Keywords: Process, Vehicle Coordination, Reverse Supply Chain. Keywords: Disassembly Process, Vehicle Routing, Inventory Inventory Control, End-of-Life End-of-Life Product, Coordination, Reverse Supply Chain. Coordination, Chain. Coordination, Reverse Reverse Supply Supply Chain. 1. INTRODUCTION 6 gives conclusion based on the results obtained as well as 1. INTRODUCTION INTRODUCTION 6the conclusion on the results obtained as well as 1. 66 gives gives conclusion based on future researchbased directions. 1. INTRODUCTION gives conclusion based on the the results results obtained obtained as as well well as as the future research directions. future research directions. The public awareness and economical interest in reverse the the future research directions. The public public awareness and currently economical interestdue in reverse reverse The awareness and economical interest in supply chain (RSC) are growing to the 2. LITERATURE REVIEW The public awareness and currently economical interestdue in reverse supply chain (RSC) are growing to the the 2. LITERATURE REVIEW supply chain (RSC) are currently growing due to environmental legislation, customers’ attention to the en2. supply chain (RSC) are currently growing due to the 2. LITERATURE LITERATURE REVIEW REVIEW environmental legislation, customers’ attention to the the enenvironmental legislation, customers’ attention to environmental impact of products and the potential benefit environmental legislation, customers’ attention to the enSince processing EOL products is time consuming and vironmental impact of products and the potential benefit vironmental impact of products benefit processing EOL products is time of End-of-Life (EOL) To the dealpotential efficiently with Since vironmental impact of products. products and and the potential benefit Since processing EOL products is consuming and (Ilgin and 2011), the consuming integrationand of Since processing EOL Gupta, products is time time consuming and of End-of-Life End-of-Life (EOL) products. To deal efficiently with expensive of (EOL) products. To deal efficiently with expensive (Ilgin and Gupta, 2011), the integration of growing amount of EOL products, the disassembly process of End-of-Life (EOL) products. To deal efficiently with expensive (Ilgin and Gupta, 2011), the integration of several processes in RSC is important for implementing (Ilgin and Gupta, 2011), the integration of growing amount of EOL products, products, the the disassembly disassembly process process expensive growing amount of EOL several processes in RSC is important for implementing is required to be implemented. growing amount of EOL products, the disassembly process several processes in RSC is important for implementing economically viable solutions. This section presents the several processes in RSC is important for implementing is required required to to be be implemented. implemented. is economically viable solutions. section presents the is required to be implemented. viable solutions. This section the existing literature withThis coordination of decision The disassembly process is defined as a set of activities economically economically viabledealing solutions. This section presents presents the existing literature dealing with coordination of decision The disassembly process is defined as a set of activities existing literature dealing with coordination of decision making in RSC for EOL products. The disassembly process is defined asin aaorder set of oftoactivities activities for disassembling the EOL productas harvest existing literature dealing with coordination of decision The disassembly process is defined set making in RSC for EOL products. for precious disassembling thehazardous EOL product product in order order to to harvest harvest in RSC for EOL products. for disassembling the EOL in its and/or components. it making making in et RSC for EOLand products. ¨ ¨ for disassembling thehazardous EOL product in orderHowever, to harvest Ozceylan al. (2014) Ozceylan and Paksoy (2014) its precious and/or components. However, it ¨ ¨¨ its precious and/or hazardous components. However, it requires the support of other processes such as the colOzceylan et al. (2014) and Ozceylan and Paksoyby(2014) ¨ its precious and/or hazardous components. However, it Ozceylan et al. (2014) and Ozceylan and ¨ ¨decision integration worked onetstrategic–tactical comrequires the support of other processes such as the colOzceylan al. (2014) and Ozceylan and Paksoy Paksoyby(2014) (2014) requires support of other as the collection ofthe EOL products from processes suppliers, such the distribution worked on strategic–tactical decision integration requires the support of other processes such as the colworked on strategic–tactical decision integration combining network design of closed-loop supply chain by andcomthe lection of EOL products from suppliers, the distribution worked on strategic–tactical decision integration by comlection of EOL products from suppliers, the distribution distribution of disassembled components forsuppliers, recycling etc. Henceforth, bining network design of closed-loop supply chain and the lection of EOL products from the bining network design of closed-loop supply chain and the disassembly line balancing problem. These works dealt of disassembled disassembled components for recycling etc. Henceforth, Henceforth, network design of closed-loop supply chain anddealt the of recycling etc. this process has components to be treatedfor align with other activities in bining disassembly line balancing problem. These works of disassembled components for recycling etc. Henceforth, disassembly line balancing balancing problem. Thesesupply workschain’s dealt with the decisions of productproblem. flows between this process has to be treated align with other activities in disassembly line These works dealt this process has to be treated align with other activities in the reverse supply chain (RSC) of EOL product. decisions of product flows between supply chain’s this processsupply has to be treated align with other activities in with with the decisions of flows supply actorsthe and the number of disassembly workstations. the reverse reverse chain (RSC) of EOL EOL product. with the decisions of product product flows between between supply chain’s chain’s the supply chain (RSC) of product. actors and the number of disassembly workstations. the reverse supply chain (RSC) of EOL product. actors and the number of disassembly workstations. According to Fleischmann et al. (2000), the supply side actors and the number of disassembly workstations. far as our knowledge, none of previous works dealing According to isFleischmann Fleischmann et al. (2000), (2000), the the the supply side As According to al. supply side of such RSC exogenously et determined number as our knowledge, none of previous works dealing According to isFleischmann et al. (2000),since the the supply side As As far as knowledge, none works withfar products has considered the integration of colof such RSC exogenously determined since number As farEOL as our our knowledge, none of of previous previous works dealing dealing of such RSC exogenously since the number sources of is EOL productsdetermined is fairly large compared to with EOL products has considered the integration of colof such RSC is exogenously determined since the number with EOL products has considered the integration of collection and disassembly processes. The majority of works of sources of EOL products is fairly large compared to with EOL products has considered the integration of colof sources of EOL products is fairly large compared to the numberofofEOL supply points isin fairly a forward supply chain. lection and disassembly processes. The majority of works of sources products large compared to lection and disassembly processes. The majority of works focused on the disassembly line balancing for minimizing the number number of supply supply points intoaa be forward supply chain. lection and disassembly processes. The majority of works the of points in forward supply chain. This paramount difference has taken into account focused on the the disassembly required line balancing balancing fora minimizing minimizing the of supply points forward chain. focused on disassembly line for the number of workstations to reach given cycle Thisnumber paramount difference hasinto toaand be taken supply into account account on the disassembly required line balancing fora minimizing This paramount difference has be taken into while coordinating the collection disassembly process focused the number of workstations to reach given cycle This paramount difference has to be taken into account the number of workstations required to reach a given cycle time (Batta¨ ıa and Dolgui, 2013; Bentaha et al., 2013, while coordinating the collection and disassembly process the number of workstations required to reach a given cycle while coordinating the collection and disassembly process of EOL product. time (Batta¨ ıa and Dolgui, 2013; Bentaha et al., 2013, while coordinating the collection and disassembly process time (Batta¨ ıa and Dolgui, 2013; Bentaha et al., 2013, 2014a,b). However, there is a number of studies addressing of EOL EOL product. product. time (Batta¨ ıa and Dolgui, 2013; Bentaha et al., 2013, of there is a number of studies and addressing of EOL product. 2014a,b). However, there is of addressing this pointHowever, in forward supply chain. Chandra Fisher This paper is organized as follows. Section 2 analyzes 2014a,b). 2014a,b). However, there is aa number number of studies studies and addressing this point in forward supply chain. Chandra Fisher This paper is organized as follows. Section 2 analyzes this point in forward supply chain. Chandra and Fisher (1994) initiated the work on coordination of production This paper is organized as follows. Section 2 analyzes the existing literature related to the integrated function this point in forward supply chain. Chandra and Fisher This paper is organized as follows. Section 2 analyzes (1994) initiated the work on coordination of production the existing literature related to the integrated function (1994) initiated the work on coordination of production and distribution planning where there is an inventory the existing literature related to the integrated function on RSC corresponding to disassembly process. Section 3 (1994) initiated the work on coordination of production the existing literature related to the integrated function distribution planning where there is an inventory on RSC RSC corresponding corresponding to disassembly disassembly process. Section 33 and and distribution planning where there is an This work has drawn attention in on to Section describes the mathematical model forprocess. the coordinating and distribution planning where there of is researchers an inventory inventory on RSC corresponding to disassembly process. Section 3 between. between. This work has drawn attention of researchers in describes the mathematical model for the coordinating between. This work has drawn attention of researchers in the last two decades (Boudia and Prins, 2009; Bard and describes the mathematical model for the coordinating formulation proposed. The decoupled formulation is prebetween. Thisdecades work has drawnand attention of researchers in describes theproposed. mathematical model forformulation the coordinating the last two (Boudia Prins, 2009; Bard and formulation The decoupled is prethe last two decades (Boudia and Prins, 2009; Bard and Nananukul, 2010; Armentano et al., 2011; Amorim et al., formulation proposed. The decoupled formulation is presented in section 4. An illustrative example and the results the last two decades (Boudia and Prins, 2009; Bard and formulation proposed. The decoupled formulation is preNananukul, 2010; Armentano et al., 2011; Amorim et al., sented in section section 4. An An illustrative example and the the results 2012). 2010; sented in 4. example and results of numerical experiments are provided in section 5. Section Nananukul, 2010; Armentano Armentano et et al., al., 2011; 2011; Amorim Amorim et et al., al., sented in section 4. An illustrative illustrative example and the results Nananukul, 2012). of numerical numerical experiments are provided provided in section section 5. Section Section 2012). of experiments are in 5. 2012). of This numerical experiments are provided in section 5. Section Adapting the work of Chandra and Fisher (1994), this work has been funded by the government of R´ egion Adapting work of Chandra and Fisher this work has been funded by the government of R´ eegion Adapting the work and (1994), this work aimsthe to coordinate the collection and (1994), disassembly Rhˆ one–Alpes, France. This work has been funded by the government of R´ gion This Adapting the work of of Chandra Chandra and Fisher Fisher (1994), this This work has been funded by the government of R´ e gion work aims to coordinate the collection and disassembly Rhˆ o ne–Alpes, France. work aims to coordinate the collection and disassembly Rhˆ o ne–Alpes, France. work aims to coordinate the collection and disassembly Rhˆ one–Alpes, France. Copyright © 2015 IFAC Copyright © 2015 IFAC Copyright Copyright © © 2015 2015 IFAC IFAC 10.1016/j.ifacol.2015.06.061. 76 76 76 76.

(25) INCOM 2015 May 11-13, 2015. Ottawa, Canada. Decision variables:. processes in a RSC through an inventory in order to minimize the total cost. The scheme of the RSC considered is depicted in Fig. 1. Specifically, the collection process adapts the capacitated vehicle routing problem while the disassembly process deals with the determination of the number of products disassembled. The inventory is used to balance those processes.. Yit It Pt SOat xijt. 3. FORMULATION. load of the vehicle after visiting i at period t; inventory of EOL product’s items at period t; number of products disassembled at period t; stockout of component a at period t; 1 if j is visited after i directly at period t ; 0 otherwise.. Mixed Integer Programming (MIP) M in {CD · Pt + CH · It + CPa · SOat t∈T a∈A CF · x1jt + Cij · xijt }; +. A number of EOL items of a given product is dispersed in a number of suppliers. The term ”item” is used in order to distinguish with ”product” because the model considers one type of product only. A fleet of capacitated vehicles is used to pick them up into a capacitated inventory. The number of vehicles available is assumed unlimited. The vehicle is allowed to not visit all suppliers but once a supplier visited, the whole number of EOL products has to be picked up.. i∈N j∈N. j∈N,j>1. s.t.. . j∈N,i=j. . Each item is assumed to posess all corresponding components released by disassembly. The capacity of disassembly line is obtained by dividing the working hours in a period with the cycle time. The unsold components are discarded while the inventory of EOL products incurs the holding cost. The penalty cost is induced by the unfulfilled demands.. xijt ≤ 1, ∀i ∈ N \ {1} , ∀t ∈ T ;. xivt =. i∈N,i=v. (1). . j∈N,j=v. xvjt , ∀v ∈ N, ∀t ∈ T ;. Yit ≤ C − (C − Sit ) · x1it , ∀i ∈ N \ {1} , ∀t ∈ T ; Yjt ≥ Yit + Sjt − C + C · xijt + (C − Sjt − Sit ) · xjit , ∀i ∈ N , ∀j ∈ N \ {1} , i = j, ∀t ∈ T ; It = It−1 + Sit · xijt − Pt , ∀t ∈ T ;. (2) (3) (4) (5) (6). j∈N i∈N,i=j. na · Pt + SOat ≥ qat , ∀a ∈ A, ∀t ∈ T ; xijt · Sit ≤ Yit ≤ xijt · C,. j∈N,i=j. Fig. 1. Reverse Supply Chain Considered. 0 ≤ It ≤ IC, ∀t ∈ T ;. 0 ≤ Pt ≤ DC, ∀t ∈ T ;. SOat ≥ 0, ∀a ∈ A, ∀t ∈ T ;. xijt ∈ {0, 1}, ∀i ∈ N, ∀j ∈ N, ∀t ∈ T ;. qat I0 Sit C IC DC CD. demand of component a at period t; initial inventory level; number of items available at supplier i at period t; vehicle capacity; inventory capacity; disassembly line capacity; disassembly cost of a product. CH CPa CF Cij. holding cost for EOL product; penalty cost for component a; fixed vehicle cost; traveling cost from i to j;. (9) (10) (11) (12). The objective function (1) minimizes the total cost by considering the cost of disassembly, the unfulfilled demands, the inventory level of EOL products and the collection cost. The constraints (2)–(5) correpond to the collection of items while the constraints (6) bridge them with the contraints (7) corresponding to the demand of components. The constraints (2) set a single departure from a supplier. The constraints (3) guarantee that a vehicle has to leave a node after visiting it. The constraints (4) calculate the load after visiting the first supplier. Meanwhile, the constraints (5) are the well-known subtour avoidance constraints. The constraints (6) balance between the inventory level, the number of products collected and the number of products disassembled. For determining the number of demands unfulfilled, the constraints (7) are required. The constraints (8)–(12) define the domain as well as the nature of decision variables.. Parameters: set of component index: a = {1, 2, · · · , A}; set of nodes i, j = {1, 2, · · · , N } where 1 is depot; planning horizon t = {1, 2, · · · T }; number of component a in the product;. (8). ∀i ∈ N, ∀t ∈ T ;. The demand of components, the availability of EOL product in suppliers, the initial inventory level and the distance between the depot and the suppliers are deterministic and given. Because the items are collected into an inventory, multi-period is considered into the problem. The problem of coordination between the collection and disassembly process is formulated as follows:. A N T na. j∈N,i=j. (7). 4. DECOUPLED FORMULATION This section presents the formulations of disassembly and distribution without coordination. The disassembly 77.

(26) INCOM 2015 May 11-13, 2015. Ottawa, Canada scheduling determines the number of products disassembled as well as the inventory level. Using this information, the collection is planified. The decision variable Collectiont is introduced to determine the number of items intended for being collected in the collection scheduling. MIP of Disassembly Scheduling M in {CD · Pt + CH · It + CPa · SOat }; (13) t∈T. s.t.. capacity: infinitive, 200 % of average demands and 118 % of average demands. The value of 200 % and 118 % come from the assumption that the average demands in all periods are equal to 50 % and 85 % of disassembly capacity (based on the data used in Chandra and Fisher (1994)). The supplies in all periods were generated using uniform distribution between 9 and 11. The vehicle capacity was determined as two times the average supply in all nodes and periods. The disassembly and holding costs were 10 and 1, respectively. The fixed vehicle cost was fixed to 10 and the vehicle running cost was equal to 1. The penalty cost was fixed to 4 for each unfulfilled demand.. a∈A. It = It−1 + Collectiont − Pt , ∀t ∈ T ; Constraints (7), (9)–(11) Collectiont ≥ 0, ∀t ∈ T ;. (14) (15). The following formulation presents the collection scheduling: MIP of Collection Scheduling { Cij · xijt + M in t∈T i∈N j∈N . +. a∈A. s.t.. Collectiont ≥ na ·. . i∈N,i=j. . j∈N,j>1. CF · x1jt. CPa · SOat };. . . j∈N i∈N,i=j. Sit · xijt , ∀t ∈ T ;. Table 1. Benefit of coordinated strategy N. T. A. Demand. 5. 5. 5. 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110%. 10. (16) 10. 5 10. (17) 20. Sit · xijt + SOat ≥ qat , ∀a ∈ A, ∀t ∈ T ; (18). 5 10. 10. Constraints (2)–(5), (8) and (12) The objective function (16) aims to minimize the collection and the penalty costs. The collection cost consists of distance cost and fixed vehicle cost. The penalty cost is induced when the amount of items targeted in disassembly scheduling is not respected. The number of products collected is less than Collectioni since it is only the amount demanded is disassembled (Constraints 17). Constraints (18) are required for calculating the penalty cost for stockout of component.. 5. 5 10. 10. 5 10. 20. 5 10. 25. 5. 5. 5. NUMERICAL EXPERIMENTS 10. Numerical experiments were carried out in order to test our model as well as to observe the impact of certain parameters on the results and computational time. To this aim, 108 instances were generated using different number of nodes, number of periods, number of components, the relative percentages of demands-supplies and the value of the disassembly capacity.. 10. 5 10. 20. 5 10. For the number of nodes, 5, 10 and 25 nodes were considered where the first node is depot. The system run in 5, 10 and 20 periods. Concerning the number of components, we have two types of products consisting of 5 and 10 components, respectively.. Cost reduction (in %) Unconsd* Less Consd* Consd* 47 47 47 24 24 24 64 64 64 7 7 7 47 47 47 13 13 13 65 65 65 8 8 8 47 47 47 20 20 20 66 66 66 9 9 9 45 45 45 24 24 24 63 63 63 11 11 11 47 47 47 23 23 23 65 65 65 16 16 16 48 48 47 22 22 22 65 65 64 15 16 15 49 49 49 18 18 18 66 66 66 10 10 10 49 49 49 12 14 14 67 66 67 11 13 11 48 47 48 11 11 10 66 65 65 5 8 3 *consd = constrained. The model was implemented in java JDK 7 using ILOG TM R CPLEX 12.6 on a PC with processor IntelCore i7 CPU 2.9 GHz and 4 Go RAM under Windows 7 Professional. Each instance was executed within 10 minutes. Table 1 and 2 show the results obtained.. The coordinates of nodes are generated using uniform distribution between 0 and 100. The supplies are generated uniformly between 9 and 11 for each suppliers (the depot has no supply). The demands are generated using uniform distribution between 40 % - 60 % and 90 % - 110 % of the supplies. The instances are divided into three categories namely unconstrained, less constrained and constrained where each category has different value of the disassembly. Based on the results presented in Table 1, we can conclude that the model with coordiantion allows reducing the total cost from 7 % to 66 %. Fig. 2–4 provides the difference between the corresponding costs for the converged instances shown in Table 2. 78.

(27) INCOM 2015 May 11-13, 2015. Ottawa, Canada. Table 2. Average solver gap and computation time N. T. A. Demand. Solver gap. 5. 5. 5. 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110% 40%-60% 90-110%. Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal Optimal 3% Optimal 4% 13% 13% 14% 14% Optimal 3% Optimal 5% 12% 14% 14% 15% 20% 18% 22% 20%. 10 10. 5 10. 20. 5 10. 10. 5. 5 10. 10. 5 10. 20. 5 10. 25. 5. 5 10. 10. 5 10. 20. 5 10. Computation time (in seconds) 0 0 0 0 0 0 0 0 2 4 3 4 0 5 1 8 16 600 24 600 603 603 600 604 25 600 85 602 601 605 612 610 605 605 619 613. Fig. 3. Difference of Penalty Costs. Fig. 4. Difference of Transportation Costs transportation cost but their penalty and holding costs are lower resulting in lower total costs. According to the results presented in Table 2, the computation time is more than 1 second for instances with 5 customers and 10 periods. About 44 % of the instances requires more than 10 minutes to converge starting from the instances having 5 components and 10 periods. 6. CONCLUSIONS This work proposed a coordinated optimisation model for collection and disassembly activites in Reverse Supply Chains. The coordination is based on the balance between the number of products collected, the inventory level and the number of products disassembled with aim of fulfilling the demands of components. The results of numerical experiments showed that the coordinated strategy allowed the decision makers to reduce the total cost. In our future research work, the uncertainty of the availability of EOL products at suppliers as well as of the number of components in products will be considered since such phenomena are major in reverse supply chains.. Fig. 2. Difference of Disassembly Costs The values are obtained by substracting the costs of the coordinated and uncoordinated strategy.. REFERENCES Amorim, P., G¨ unther, H.O., and Almada-Lobo, B. (2012). Multi-objective integrated production and distribution planning of perishable products. International Journal of Production Economics, 138(1), 89–101. Armentano, V., A.L. Shiguemoto, and Løkketangen, A. (2011). Tabu search with path relinking for an integrated productiondistribution problem. Computers & Operations Research, 38(8), 1199–1209.. Comparing the costs, the disassembly and penalty cost of the coordinated strategy are lower. However, for all instances, the coordinated strategy has more important holding costs than the uncoordinated strategy. For the majority of the instances having 90 % - 110 % demands of supplies, the transportation cost of the coordinated strategy is lower. Some instances have no difference in 79.

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