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ISSN: 1995-0772 EISSN: 1998-1090 2016 December10(17):pages 36-49

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A Mathematical Model for Optimizing the Closed Loop Supply Chain for multiple products with Varying Demand in a Product Life Cycle 1A.

Sasikumar, 2K. Natarajan, 3M. Ramasubramaniam

1Associate

Professor, Department of Mechanical Engineering, Karpagam Institute of Technology, Anna University ,Tamilnadu, India. Department of Mechanical Engineering, P.S.G .College of Technology, Anna University, Tamilnadu, India. 3Associate Professor, Center for Logistics and Supply chain, Loyola Institute of Business Administration, Chennai, Tamilnadu, India. 2Professor,

Received 2 September 2016; Accepted 2 December 2016; Published 31 December 2016 Address For Correspondence: A. Sasikumar, Associate Professor, Department of Mechanical Engineering, Karpagam Institute of Technology, Anna University, Tamilnadu, India Copyright © 2016 by authors and American-Eurasian Network for Scientific Information (AENSI Publication). This work is licensed under the Creative Commons Attribution International License (CC BY).http://creativecommons.org/licenses/by/4.0/

ABSTRACT Background: To interlink the Product Life cycle (PLC) curve of a multiple product with three different scenarios of demand and returns in a closed loop supply chain (CLSC) network. Objective: The purpose of this model is to find the optimal inventory positioning for three different scenario of demand for multiple product at different stages of CLSC during different stages of product lifecycle. For this a network consists of manufacturer, distributor, retailer, customers and for returns repair, collection site, repair site, disassembly site, recycling site and disposal site are considered and a model is developed for maximizing the profit in a CLSC system. Results: The results of the analysis show that the manufacturer can take appropriate decisions at all the stages of PLC by considering various product recovery options. Conclusion: To ensure the profitability of supply chain it is important for companies to focus on designing and implementing suitable policy interventions. As a recommendation, we propose to devise suitable buy-back or revenue-sharing contract arrangements with distributor which would incentivize them suitably to hold more inventories in the earlier stages of product introduction. Similar arrangements can be considered for implementation of the high demand products in the retailer stages as well.

KEYWORDS: INTRODUCTION The Closed Loop Supply Chain (CLSC) is a process in which the manufacturer not only ensures supply of finished products but also systematically accepts the shipped products or parts from the point of consumptions for possible repair, recycle, remanufacture and proper disposal. A CLSC effectively manages resources by appropriate allocation of parts and products for remanufacturing, recycling or disposal sites. Thus, CLSC is of practical interest for supply chain managers and executives. The shorter lifespan of PLC also influences where the inventory is positioned across the CLSC. This is further complicated because of sporadic end-of-life, end-ofuse and commercial returns in such CLSC networks. Returns of the product may occur in different forms in the quantity and quality and it can be categorized into three types. First its commercial returns of the product which can be repaired, refurbished in the repair site. Second is the end- of- use returns which after disassembly of the ToCite ThisArticle: A. Sasikumar, K. Natarajan, M. Ramasubramaniam., A Mathematical Model for Optimizing the Closed Loop Supply Chain for multiple products with Varying Demand in a Product Life Cycle. Advances in Natural and Applied Sciences. 10(17);Pages: 36-49

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A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

products the usable parts can be hold in the part inventory and finally end-of-life returns whose parts can be recycled and possibly can be disposed. Consequently, optimal product parts mix and inventory positioning is of paramount importance in a CLSC especially under PLC. In this paper, we propose a mathematical model to maximize the profit of CLSC by determining the optimal inventory of multiple product and cost associated at various sites with the three different demand (High, Medium and Low) and returns variations along the four stages of PLC. 2. Literature review: The research in CLSC field is contemporary and has received due consideration in the recent past. Though it is possible to review a large body of research in this area of research, due to the brevity of the paper we consider only the literature that are closely connected with our work. A number of authors have addressed the profitability problem in a CLSC. In a case based approach in a battery recycling industry, [6] developed a model in multi echelon, multi product, multi period in a CLSC network. The model considers only recycling of end-oflife products. [13] proposed a model by configuring a different remanufacturing process to find optimal quantity of products and parts in the CLSC network. The performance of the model is analyzed for multiple products within a single period and validated through computational testing. In another case study research, [11] in a truck tyre remanufacturing shows that for maximizing the profit in CLSC, the decisions related to the number of facilities, their location, and the allocation of the corresponding product flows are important. For the same industry and also including plastic goods manufacturing, [7] integrated the multi echelon distribution inventory model for forward and reverse network by minimizing the cost to increase profitability. Addressing the uncertainty in the returns, [12] integrated the forward and reverse supply chain with proper allocation-location model for the warehouse. In this model, they have considered only single product, single period with constant demand and uncertain in returns. Extending the model, [8] developed a model to maximize the expected profit of the manufacturer by determining the production quantities of a new product, the quantities of remanufactured product and the acquisition prices of the used product within capacity constraints. While the type of returns and uncertainties associated with them are important, the problem becomes complex when we consider the product life cycle. There is some research which throws light on this aspect. [3] investigated inventory control policies in a manufacturing/remanufacturing system with PLC assuming demand rate and return rate as a random variable. The result of this investigation shows that different inventory control policies should be adopted during different phase of the PLC. In addition to this, the inventory policy characterization for single product over the entire PLC with various set up costs is studied by [15]. In the study, the optimal or near-optimal policy characterization with practical structure is determined for every life cycle stage under several setup cost configurations. They devise policies which control the parameters in CLSC under deferred sales in a PLC situation. Along with the issue of PLC, capacity planning issues also have been addressed [10]. The result of the study shows that collection and remanufacturing capacity policies are insensitive to the total product demand. When we focus on multi period, multiple product context, [5] developed a model to find the number of processing centers and disassembly centers to be opened for minimizing the fixed cost. To maximize the profit, a CLSC network structure by [9] consists of three echelons in the forward direction, (suppliers, facilities and distribution centers) and two echelons, in the reverse direction (disassembly, and redistribution centers) with demand as stochastic was developed without considering Product life cycle. In real situation for recovery options, parts of a product will play a vital role at the various sites. By considering the parts in multi product and multi period, [4] proposed a model to guarantee the optimal values of transportation amounts of manufactured and disassembled products in a CLSC while determining the location of plants and retailers. Recently author [1] presented a model for optimization of uncertainty parameters in a multi product, multi echelon CLSC with multi period. This model illustrate the optimal location and allocation of products/parts at each facility, number of products to be remanufactured, number of parts to be purchased from external suppliers and inventory level of products/parts in order to maximize the profit of the organization. Most of the integrated models found in CLSC devise optimal inventory, policies, location of various sites and selection of suppliers for multi product multi period without considering PLC. In summary, there have been a lot of related contributions that are worth noting in managing a CLSC. However, the review brings forth that though the problems of PLC in CLSC has been researched, there is a requirement for a more comprehensive treatment of PLC and study its impact during the CLSC design stage. Hence, an attempt was made by us [2] to interlink the PLC with CLSC network for single product, single part and for time period of 16. An example was illustrated in the model to show that the decision variable involved in inventory positioning at various sites depend on the different stages of PLC. To this extent of our model, the three different scenarios of demand (High, Medium and Low) of multiple products are considered taking into account the PLC.

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3. Problem Definition: From Industry point of view, there are various types of possible CLSC network configurations available. Among these, we propose a generalized form of CLSC framework. In this study, the framework of reverse logistics consists of a manufacturer, distributor, retailer, collection site, repair site, disassembly site, disposal site and multiple recycling sites as shown in the Figure 1. After using the products, some of the customers return the used products. The returned products are collected during different stages of PLC at collection site and are segregated into two types of returns. First, commercial returns of the returns products which are sent to the repair site for refurbishing and small repair. Second, the end of life returns which are taken to the disassembly sites for disassembling the product into parts. The unused parts can be disposed to the disposed site and the endof-use parts can be sent to multiple recycling sites for processing and the good parts are taken to part inventory at different stages of PLC. Here the end period inventory of a product at manufacturer, distributor and retailer are considered so that it could be the initial inventory for subsequent periods. In addition, unit inventory holding cost, shipment cost, set up cost and capacity constraints of repair site, disassembly site and recycling site are taken into account. If the demand and inventory of the products are more than units returned, manufacturer should produce new products at the manufacturing site. The main objective of the model is maximization of profit by determining the optimal quantity and inventory of multiple products and parts during different stages of PLC. To maintain model parsimony, the framework of [14] is considered without external suppliers. Further, we assume that if the demand of the product during different stages of PLC is more than the returned products, manufacturer has the capacity to produce new products.

Fig. 1: Proposed framework of CLSC 4. Model Formulations and Assumptions: The Indices, Parameters and its associated decision variables and the mathematical model formation of the proposed CLSC are specified below. For computation purpose, the various input data are taken from the literature [14]. The assumptions involved in this model are as follows: • The CLSC is assumed to be centralized at manufacturer. Hence the manufacturer is responsible for the entire cost of the supply chain network. • Reverse Logistics industry can use its experience or the historical data of product to predict the stage length of PLC. In this paper, without loss of generality, different stages of a PLC are demarcated according to the demand and return. Each stage is described as follows: (1) Introduction: Demand remains at a low and the returns are rarely seen and can be ignored. (2) Growth: Demand begins to increase linearly and some returns will emerge as percentage of the demand. (3) Maturity: Demand remains in a steady state, without increase or decrease but the percentage of returned products will be more than the previous stage. (4) Decline: Demand starts to decrease linearly with greater percentage of returns. • The lead time of delivery for various sites is ignored. • The process involved in the repair site, disassembly site, and multiple recycling site of return product is done immediately. • If the quantity of the product is not enough to meet the requirements by the manufacturer, then manufacturer should produce products inside the manufacturing site. • Maximum capacity of manufacturer, disassembly, repair, and multiple recycling sites are known. • The capacity of collection site is unlimited. • The initial inventory of the manufacturer is known for all products.

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

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• The final period of the inventory of manufacturer, distributor and retailer are also known so that it will act as opening inventory for next period. Indices t Set of period t =1, 2,T j Set of products, j= 1, 2, J i Set of parts, i = 1, 2,I l Set of recycling site l=1,2..L. Decision Variables Xjt Units of Product j to be repaired at period t Pjt Units of Product j obtained from part inventory at period t Yjt Units of Product j in collection site at period t Zjt Units of returned Product j to be disassembled at period t Mfgjt Units of Product j manufactured in the manufactured site at period t Eit Units of Part i that are obtained in the disassembly site at period t Rit Units of end-of-use return of part i at period t Git Units of part i to be disposed at period t Filt Units of Part i to be recycled in recycling site l at period t InvMjt Inventory of Product j at the manufacturing site at period t InvRjt Inventory of Product j at the retailer at period t InvDjt Inventory of Product j at the distributor at period t ShipMDjt Shipment of Product from manufacturer to distributor of product j at period t ShipDRjt Shipment of Product from distributor to retailer of product j at period t Uilt Binary variable for set up of recycling site l for part i at period t Vit Binary variable for set up of disassembly site at period t Wjt Binary variable for set up of repair site at period t Parameters Sj Unit selling price for the product j aj Resource usage to produce one unit of product j yj Unit direct manufacturing cost of Product j ej Resource usage to repair one unit of product j Cj Max Capacity of repair site for product j Djt Demand for product j at period t dj Unit repair cost of Product j fj Set-up cost of disassembly site for product j gj Set-up cost of repair site for product j Bi Max capacity of disassembly site to disassemble part i hi Unit disassembly cost for part i mi Unit disposal cost for part i ri Resource usage to disassemble one unit of part i qij Unit requirements for part i to produce one unit of product j nil Unit recycling cost for part i in recycling site l oil Set-up cost of recycling site l for part i sil Resource usage to recycle one unit of part i in recycling site l Oil Max capacity of Recycling site l to recycle part i HRjt Unit Inventory holding cost at retailer of Product j at period t HDjt Unit Inventory holding cost at Distributor of Product j at period t HMjt Unit Inventory holding cost at Manufacturer of Product j at Period t SHjt Unit Shipment cost of product at period t I Inventory of a product j at Manufacturing site at period t=1 F1 Inventory of a product j at retailer at the end Period t F2 Inventory of a Product j at distributor at the end Period t F3 Inventory of a Product j at Manufacturer at the end Period t MD Max capacity of truck to travel from Manufacturer to Distributor DR Max capacity of truck to travel from Distributor to Retailer z Max percent of commercial returns M A big number Nt Max percent of total returns M1 Max percent of end-of-use returns M2 Max percent of end-of-life returns L Max number of recycling sites A Max capacity of the manufacturer plant

Max Z

  S j ( X jt  Pjt  Mfg jt )   y j Mfg jt    hi Eit  J

T

J

j 1 t 1

T

I

j 1 t 1

T

i 1 t 1

   f j V jt    d j X jt    mi (Git )   g j (W jt ) J

T

j 1 t 1

J

T

j 1 t 1

I

T

i 1 t 1

J

T

j 1 t 1

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

40

I

T

L

I

T

L

J

T

  nil Fitl    oilU itl   HR jt ( InvR jt ) i 1 t 1 l 1

i 1 t 1 l 1

j 1 t 1

  HD jt ( InvD jt )   HM jt InvM jt    SH jt ShipMDjt  ShipDRjt  J

T

J

j 1 t 1

T

j 1 t 1

J

T

(1)

j 1 t 1

Subject to

 q P   R   F J

j 1

L

ij

L

F l 1

ilt

jt

it

l 1

ilt

 Git  Rit  Eit

(2) (3)

 q Z   E J

j 1

ij

jt

it

Pjt  X jt  Mfg jt

Rit  M 1 Eit L

F l 1

ilt

(4) (5) (6)

 M 2 Eit

Git  (1  M1  M 2 ) Eit Mfg jt  I InvR jt  F1 InvD jt  F2 InvM jt  F3

InvR jt 1  ShipDRjt 1  D jt  InvR jt InvD jt 1  ShipMDjt 1  ShipDRjt  InvD jt Mfg jt  InvM jt 1  ShipMDjt  InvM jt InvM jt 1  Pjt 1  X jt 1  Mfg t 1 ShipMDjt  MD

ShipDRjt  DR X jt  Z jt  Y jt

(7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)

 a Mfg   A J

j 1

j

jt

ri Eit  Bi

sil Filt  OilUilt e j X jt  C j

X jt  zYjt Z jt  1  z Y jt Y jt  ND jt

(20) (21) (22) (23) (24) (25) (26)

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

41

I

T

L

U i 1 t 1 l 1

ilt

L (27)

Z jt  MV jt

(28)

X jt  M 1W jt Uilt , Vjt , Wjt Є { 0, 1} Xjt , Pjt , Yjt , Zjt , Mfgjt , Eit , Filt , Rit, Git ,InvMjt, InvRjt, InvDjt, ShipMDjt, ShipDRjt

(29) (30) ≥0

(31)

The objective function (1) maximizes the total profit for the manufacturer. The first term represents the total selling profit of the product. It includes the repaired product with new product and shortage of the product to be produced in the manufacturing site during different stages of PLC. Second term represents the unit direct manufacturing cost multiplied by the amount of manufactured item in the manufactured site at different stages of PLC. Third and fourth terms of the expression represent the unit disassembly cost and set up cost for disassembly site at different stages of PLC. The fifth, sixth and seventh term represents the unit repair cost, disposal cost and set up cost for repair in the repair site. The next two terms include the cost related to unit recycling cost and set up cost of recycling at recycling site. The last four terms of the expression represents the inventory cost associated with the retailer, distributor, manufacturer and shipment cost from the manufacturer to distributor and from distributor to retailer respectively. Constraint (2) ensures that the number of recycled parts is equal to the number of manufactured parts and number of end–of-use parts. The relationship between number of disassemble parts equal to the summation of number of recycling parts and end-of-use parts and disposal parts are presented in constraint (3). Constraint (4) ensures the relationship between parts and products in disassembly site. The sum of parts from part inventory and the products from repair site is equal to manufacturing product is represented in constraint (5). Constraints (6) to (8) show the percent of end-of-use returns and end-of-life returns. Initial inventory at manufacturer site at period 1 is represented in constraints (9). Final inventory of the product at the end period of retailer, distributor and manufacturer are considered in the constraints (10) to (12). The inventory and shipment restriction at period t and previous period t-1 for retailer, distributor and manufacturer are enforced from the constraints (13) to (16). Capacity constraints of truck from manufacturer to distributor and from distributor to retailer are ensured in the constraints (17) and (18). Besides, constraint (19) represents that the collected products is sent to repair or disassembly site. Constraints (20) to (23), reflects the maximum capacity of manufacturer, disassembly, recycling and repair sites. Constraints (24) and (25) represent maximum percent of commercial returns. The maximum percentage of total returns at the collecting site at various stages of PLC is considered in constraint (26). Besides, the capacity limitation of recycling is represented in constraint (27). The constraints (28) and (29) ensure the units of returned products to be disassembled and repaired at different stages of PLC. Finally, the decision variables are defined in the constraints (30) and (31). The proposed model is in the form of Mixed Integer linear programming problem and solved by IBM ILOG CPLEX OPL studio. The results obtained from the model are validated through computational testing and sensitivity analysis. 5. Computational Results: In this section, for testing the model, numerical examples are considered with appropriate input parameters. Here the total duration of PLC is chosen as t= 14 periods. Among these, the first 2 periods is for introduction stage, next 5 periods is for growth stage and the remaining 4 periods for maturity and last 3 periods is for decline stage. In this analysis, the number of product, number of parts and number of recycle are chosen as 3. The 3 products are having the same mode of working with different specifications and the unit requirements of three parts of these products are different. Based on the assumptions for different stages of PLC, the three demand scenarios high (1500), medium (1000) and low (500) of three different products and percentage of return product are quoted as zero return at introduction stage. In growth stage, demand scenario is increased linearly with 500 for all products with 30 percent returns. During the maturity stage, demand scenario high (4000), medium (3500) and low (3000) is assumed steady with 50 percent of returns. During the decline stage, demand is assumed to decrease linearly with 500 for all products with 70 percent of returns. Apart from these parameters, the ending inventory during the final period for manufacturer, distributor and retailers are known. The end period inventories F1=100, F2= 200, F3= 300 of retailer, distributor, manufacturer and shipments capacity are quoted. Among the returns, 60 percent of products are sent to repair site and 40 percent are sent to the disassembly site. After disassembly of product into parts in the disassembly site, 20 percent of parts are assumed as End-of – use returns and is sent to the part inventory and another 30 percent of parts are considered as End-of-life returns.

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These End-of –life returns parts are sent to recycling site. Remaining 50 percent of parts are sent to the disposed sites. The other required input parameters are written in Appendix-I. In this paper, the optimal solution of the mixed integer program is got by IBM ILOG CPLEX OPL studio (version 12.5) The decision variables for the quantity of the multiple products at repair sites, part inventory and new product to be manufactured for different stages of PLC is shown in the Table.2. Number of parts obtained in the disassembly, parts to end of use returns, parts for disposal and to be recycled for different stage of PLC is shown in the Table.3. The inventory at retailer, distributor and manufacturer for different stages of PLC is shown in the Table.4. The various cost associated with the objective function are summarized in the Table.5. (a & b). 6. Sensitivity Analysis: A sensitivity analysis is performed to validate the proposed model by taking the average values of each product and parts at different stages of PLC with various combinations of decision variables. First part of the analysis focuses on a simple demand and return combination as shown in Appendix. Figure 2 is the average demand and returns at different stages of PLC under this condition. Here there are no returns in the introduction stages. The decision variable, number of products to be manufactured at manufacture site is higher than the part inventory and commercial return of the product at repair site of all three different demand scenarios are illustrated in the Figure 3.It is noticeable that the 60 percent of collected products are sent to repair site and 40 percent sent to disassembly, the manufacturer produces new product for all the demand scenarios. Hence, the manufacturer can take appropriate decision by considering commercial returns and part inventory. The analysis of parts at various sites with three demand scenarios of all the products is illustrated in Figure 4. It reveals that the number of parts at the disassembly site are considerably higher than the number of recycled and end of use returns. The inventory at manufacturer, retailer and distributor is illustrated in Figure.5. This indicates the average inventory of product at distributor is more than the inventory of retailer and manufacturer for all the stages of the PLC. It has been observed that the average inventory of distributor is linearly decreasing for all demand scenario of the product throughout the product life cycle. The average inventory at retailer is increasing from introduction to growth stage for all demand scenarios of the product after which there is a decrease in inventory levels throughout the life cycle of the product. But the manufacturer inventory is lower than the inventory of retailer and distributor. It is noted that the inventory is increasing from a high demand scenario of product to low demand scenario of product. Hence the manager has to watch closely, the inventory status of low demand product at the manufacturing sites throughout the PLC. The cost parameters involved in keeping the inventory at retailer, distributor and manufacturer are important. The cost incurred during the different stages of PLC is shown in Figure.6. The following inference is made from the figure: (1) Introduction stage: The average cost of inventory at distributor is high when compared with inventory cost at manufacturer and retailer for all demand scenario of the product. (2) Growth stage: The average inventory cost of retailer is more for the high demand product than the cost of other scenario of product at distributor and manufacturer. (3) Maturity stage: Average inventory cost of retailer is more for the high demand product than the cost of distributor. When compared to retailer and distributor, the average inventory cost at manufacturer is negligible. (4) Decline stage: Inventory cost of distributor is high for high demand products and it is reduced for other scenario of demand, but inventory cost at manufacturer for high demand products is less and increase for other scenario of demand. There is no inventory cost at retailer. As a result of the above observations, to maximize the profit, manufacturing companies need to focus on reducing the average inventory cost of distributor at introduction stage and for high demand product at decline stage and decrease the average inventory cost of retailer at growth stage and for high demand product at maturity stage of the PLC. Table 2: The decision variables for the quantity of Product at Repair site, Part Inventory and Manufacturing sites Returns Per Product from repair Product from Part Stages Demand iod site Inventory

Growth

Introdu ction

t

1 2 3 4

Djt HIG H 150 0 150 0 200 0 250 0

ME DIU M 100 0 100 0 150 0 200 0

LO W

Yt HIG H

MED IUM

LO W

Xt HIG H

500

0

0

0

500

0

0

0

600

450

750

600

100 0 150 0

LO W

0

ME DIU M 0

0

Product to be manufactured in manufacturing site Mfgt HIG ME LO H DIU W M 0 0 0

0

0

0

0

90

60

LO W

Pt HIG H

0

ME DIU M 0

0

0

0

0

270

180

300 360 450

120 360

450

270

0

360

240

480

360

480 120

150

0

90 600

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

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5 6 7 8 9

Maturity

10 11 12

Decline

13 14

300 0 350 0 400 0

250 0 300 0 350 0

200 0 250 0 300 0

400 0 400 0 400 0 400 0 350 0 300 0

350 0 350 0 350 0 350 0 300 0 250 0

300 0 300 0 300 0 300 0 250 0 200 0

350 0

200 0

150 0

600 900 105 0 120 0 120 0 117 5 110 0

450

750 750 900

630

122 5 120 0 112 5 100 0 775

1175 1100

625 0

675

240

585

220

600

225

195

465

200

165

840

630

0

135

155

20

55

280

210

325

0 130 0

Intro ducti on

Table 3: The decision variables for the quantity of Part at Disassembly site, Disposal site and Recycling sites Pe Parts to be Recycled Sta Products obtained Parts obtained in Parts from end- Parts to be rio ges in disassembly site disassembly site of-use returns disposed d t Zjt Ett Rtt Gtt Fit HI ME LO HI ME L HI ME LO HI ME L HI Re ME Re GH DIU W G DIU O G DI W G DI O G cy DI cy M H M W H UM H UM W H cle UM cle sit sit e e 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 5

Growth

6 7 8 9

Maturity

10 11 12

Decline

13 14

240 300 360 420 480 480 470 440 370 250 0 650

180 240 300 360 420 490 470 440 390 270 40 560

120 180 240 300 360 490 480 450 400 310 110 420

10 20 13 80 17 40 21 00 24 60

102 0 138 0 174 0 210 0 246 0

12 00 15 60 19 20 22 80 26 40

29 20 28 50 26 70 23 30 17 00 37 0 31 20

293 0 284 0 266 0 234 0 164 0 340

29 10 28 30 26 00 22 90 16 00 19 0 34 90

317 0

20 4 27 6 34 8 42 0 49 2 58 4 57 0 53 4 46 6 34 0 74

Growth

276 348 420 492 586 568 532 468 336

24 0 31 2 38 4 45 6 52 8 58 2 56 6 53 0 45 8 32 0 38

68 62 4

Table 4: Inventory at Retailer, Distributor and Manufacturer Stages Period Inventory at Retailer t InvRjt HIGH MEDIU LOW M 1 0 0 0 2 10000 4500 0 3 10500 5500 1000 4 10500 6000 2000 5 10000 6000 2500 6 9000 5500 2500 7 7500 4500 2000

Int ro du cti on

204

634

69 8

51 0 69 0 87 0 10 50 12 30 14 60 14 25 13 35 11 65 85 0 18 5 15 60

Inventory at Distributor InvDjt HIGH MEDIU M 18500 19000 16500 16000 15000 14500 13500 13000 12000 11500 10500 10000 9000 8500

510

60 0 78 0 96 0 11 40 13 20

30 6 41 4 52 2 63 0 73 8

3

306

3

3

414

3

3

522

3

1

630

3

1

738

3

879

3

3

852

3

2

798

3

3

702

3

2

504

3

3

102

3

158 5

17 45

87 6 85 5 80 1 69 9 51 0 11 1 93 6

1

170

14 55 14 15 13 25 11 45 80 0 95

3

951

3

690 870 105 0 123 0 146 5 142 0 133 0 117 0 840

LOW 17000 15000 13500 12000 10500 9000 7500

980

940

960

880

900

780

800

540

620

80

220

112 0

840

500

0

975

980

740

125 60

720

880

185 405

840

940

220

555

600

960 235

675

375

1400

245

235 660

720

960 245

720

660

105 0

180

240 705

480

840 210

735

705

100 162 5

150

240 735

600 720

180

540

720

275

120

210

720

1225

975

450

630

1050

150 180

540

900

925

360

540

L O W

0 0

Re cy cle sit e 0 0

36 0 46 8 57 6 68 4 79 2

2

87 3 84 9 79 5 68 7 48 0 57

2

10 47

2

Inventory at Manufacturer InvMjt HIGH MEDIU LOW M 4980 5580 4380 3380 3980 4580 2860 3340 3820 2460 2820 3180 2180 2420 2660 2020 2140 2260 1980 1980 1980

2 2 2 2

2 2 2 2 2

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

Decl ine

Maturit y

44

8 9 10 11 12 13 14

6000 4500 3000 1500 500 0 0

3500 2500 1500 500 0 0 0

1500 1000 500 0 0 0 0

7500 6000 4500 3000 1500 0 200

Growth

Introdu ction

Table 5(a): Various cost associated at different sites Per Disassembly cost of Disassembly cost of Stages iod Product Parts t HIG MED LOW HI ME LO H IUM GH DIU W M 1 0 0 0 0 0 0 0

0

0

0

0

0

0

3

5

5

4

408 0 552 0 696 0 840 0 984 0

5100

600 0 780 0 960 0 114 00 132 00

153 0 207 0 261 0 315 0

116 80 114 00 106 80 932 0 680 0 148 0 124 80

1465 0 1420 0 1330 0 1170 0 8400

4

5

5

4

5

5

5

4

6

5

5

4

7

5

5

4

8

5

5

4

Maturity

10 11 12

Decline

13 14

5

5

5

4

5

5

4

5

5

4

5

0

4

5

5

4

5

4

6900 8700 1050 0 1230 0

1700

145 50 141 50 132 50 114 50 800 0 950

1585 0

174 50

Intro ducti on Growth Maturity

9 10 11 12 13 14

3000 0 2250 0 1500 0 7500 2500 0 0

0

369 0 438 0 427 5 400 5 349 5 255 0 555

0

2040 2760 3480 4200 4920 5860 5680 5320 4680 3360

240 0 312 0 384 0 456 0 528 0 582 0 566 0 530 0 458 0 320 0 380

680

Table 5(b): Various cost associated at different sites Peri Stages Inventory cost at Retailer Repair cost od t HIG MEDI LOW HIGH MEDI H UM UM 1 0 0 0 0 0 2 5000 22500 0 0 0 0 3 5250 27500 5000 365 545 0 4 5250 30000 10000 455 725 0 5 5000 30000 12500 545 905 0 6 4500 27500 12500 635 1085 0 7 3750 22500 10000 725 1265 0 8

6000 4500 3000 1500 500 0 0

Disposal cost of Parts HI ME LO GH DIU W M 0 0 0

2

9

Decl ine

7000 5500 4000 2500 1000 0 0

468 0

1940 1880 1760 1500 1000 0 300

1960 1900 1780 1560 1100 180 300

Inventory cost at Manufacture HIG ME LO H DIU W M 876 9960 111 0 60 676 7960 916 0 0 572 6680 764 0 0 492 5640 636 0 0 436 4840 532 0 0 404 4280 452 0 0 3960 396 396 0 0

Inventory cost at Distributor HIG ME LO H DIU W M 570 555 510 00 00 00 495 480 450 00 00 00 450 435 405 00 00 00 405 390 360 00 00 00 360 345 315 00 00 00 315 300 270 00 00 00 255 225 270 00 00 00

388 0 376 0 352 0 300 0 200 0

225 00 180 00 135 00 900 0 450 0

3920

360

392 0 384 0 364 0 324 0 248 0 920

600

600

3800 3560 3120 2200

0

6340

698 0

1960 1920 1820 1620 1240 460 300

210 00 165 00 120 00 750 0 300 0 0

180 00 135 00 900 0 450 0 150 0 0

0

0

0

600

600

Recycling cost LOW

HIGH

MEDIU M 0 0

Recyc le site 0 0

LOW

0 0

Recyc le site 0 0

0 0

Recyc le site 0 0

0 0 184

616

3

922

3

1085

2

274

832

3

1246

3

1409

2

364

1048

3

1570

3

1733

2

454

1264

1

1894

3

2057

2

544

1480

1

2218

3

2381

2

17500

7500

725

1475

739

1756

1

2641

3

2624

2

12500

5000

710

1415

724

1714

3

2560

3

2552

2

7500

2500

665

1325

679

2408

2

2398

3

2390

2

2500 0 0 0

0 0 0 0

560 380 0 980

1175 815 125 1685

604 469 169 634

1402 1535 226 1876

3 2 3 3

2110 1516 310 2857

3 3 3 3

2066 1445 176 3146

2 2 2 2

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

4000 3500 3000 2500 2000 1500 1000 500 0

Introduction Growth

DEMAND

Decline

LOW

MEDIUM

LOW

MEDIUM

HIGH

Maturity

HIGH

Number of Product

45

RETURNS

900 800 700 600 500 400 300 200 100 0

Introduction

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

MEDIUM

LOW

Growth

HIGH

Number of Products

Fig. 2: Average Demand and Returns of Three different Demand scenarios of Product at different stages of PLC

Maturity Decline

PRODUCT FROM PRODUCT FROM PRODUCT TO BE PRODUCT REPAIR SITE PART INVENTORY MANUFUTERED IN OBTAINED IN MANUFACTURING DISASSEMBLEY SITE SITE Fig. 3: Average commercial returns of the product at repair site, part inventory and product obtained in the disassembly site along with product to be manufactured at manufacturing site at different stages of PLC 3000 2500 2000 1500 1000

Introduction

500

Growth

PARTS OBTAINED IN DISASSEMBLEY SITE

PARTS FROM END-OF-USE RETURNS

PARTS TO BE RECYCLED

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

0

Maturity Decline

PARTS TO BE DISPOSED

Fig. 4: Disassembly parts as end –of –life returns, end-of –use returns and disposed parts at different stages of PLC

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

18000 16000 14000 12000 10000 8000 6000 4000 2000 0

Introduction Growth

INVENTORY AT RETAIER

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

Maturity

HIGH

Number of Products

46

Decline

INVENTORY AT INVENTORY AT DISTRIBUTOR MANUFACTURER

Fig. 5: Inventory at Manufacturer, Retailer and Distributor at different stages of PLC

60000 50000 40000 30000 20000 10000 0

Introduction

Maturity

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

Growth

HIGH

Average Inventory Cost

The other cost parameters associated with the returns of three demand scenarios of products and parts are illustrated in the Figure.7. Average disassembly cost of parts, average disposal cost, average commercial return of the product and average recycling cost at various stages of PLC are then compared. In this analysis, the cost involved at disassembly sites for parts are more when compared to the other cost probably due to the high inventory. Industries should focus on how to control the disassembly cost of parts and the percentage of end of life returns(recycling cost) and end of use returns(part inventory) so that the disposal costs for all scenarios of product are reduced.

Decline

Inventory cost at Inventory cost at Inventory cost at Retailer Distributor Manufacture 14000 12000 10000 8000 6000 4000 2000 0

Introduction Growth

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

HIGH

LOW

MEDIUM

Maturity

HIGH

Average cost occured at Various site

Fig. 6: Inventory cost incurred at Manufacturer, Distributor and Retailer at various stages of PLC

Decline

Disassembly Disassembly Disposal Reapair cost Recycling cost of cost of Parts cost of Parts cost Product

Fig. 7: Disassembly, Disposal, Repair and Recycling cost incurred at various stages of PLC

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

47

7. Conclusions and Future Research: This paper analyzes the relationship between the demand and return of product in a CLSC during each stages of the product life cycle. The main contribution of the paper is to find the optimal inventory positioning for three different scenarios of demand for multiple product at different stages of CLSC during four stages of product life cycle. The proposed mathematical model is solved by IBM ILOG CPLEX OPL studio. To analyze the performance of the model, a numerical example is considered with a linear function of demand and various percentages of returns during different stages of PLC. The computational result of the decision variables at different sites of the CLSC for the period length of 14 is analyzed. To validate the results, sensitivity analysis is performed under different scenarios of demand and returns. The results of the analysis show that the manufacturer can take appropriate decisions at all the stages of PLC by considering various product recovery options. Based on the sensitivity analysis, it is important for companies to focus on designing and implementing suitable policy interventions to ensure profitability of the supply chain. As a recommendation, we propose to devise suitable buy-back or revenue-sharing contract arrangements with distributor which would incentivize them suitably to hold more inventories in the earlier stages of product introduction. Similar arrangements can be considered for implementation of the high demand products in the retailer stages as well. Further, since the disassembly stage is facing higher cost runs, it is recommended that this stage is properly integrated within the entire supply chain. Also, process improvement methodologies could be adopted to make this stage more efficient. Similar policies can be devised for managing the recycling and repair sites. Some of the assumptions in this paper can be relaxed for future research. The present study has a limitation that the inventory policies are not characterized. As a next step, fixed order quantity and periodic review policies can be included in the study. Further, lead time can be included at various sites of the CLSC and the return of product from customer to retailer, retailer to distributor, and distributor to manufacturer can be adopted in the model. Uncertainty in the demand rate and return rate also deserve further investigation when considering the PLC in CLSC. Apart from this, it is observed that the current model is computationally intensive even for small scale problems. For large scale implementations, the computational times are expected to be prohibitive. Thus, metaheuristic algorithms like Very Large Scale Neighborhood Search, Genetic Algorithm and Particle Swam optimization may be proposed for solving this problem Appendix Table 5: Product related parameters j

1

2

3

Sj

700

670

675

aj

1

2

2

yj

30

35

30

ej

1

2

1

Cj

9000

10000

8500

dj

1

2

1

fj

5

5

4

gj

5

5

4

Table 6: Part related parameters i

1

2

3

Bi

9000

10000

10000

hi

4

5

5

mi

3

4

4

ri

1

1

1

Table 7: Djt Demand for Product j at period t t/j 1 2 3

1 1500 1000 500

2 1500 1000 500

3 2000 1500 1000

4 2500 2000 1500

5 3000 2500 2000

6 3500 3000 2500

7 4000 3500 3000

8 4000 3500 3000

9 4000 3500 3000

10 4000 3500 3000

11 4000 3500 3000

12 3500 3000 2500

13 3000 2500 2000

14 2500 2000 1500

48

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

Table 8: Njt Returns for product j at period t Introduction Growth t/j 1 2 3 4 1 0.0 0.0 0.3 0.3 2 0.0 0.0 0.3 0.3 3 0.0 0.0 0.3 0.3

5 0.3 0.3 0.3

6 0.3 0.3 0.3

Maturity 8 9 0.5 0.5 0.5 0.5 0.5 0.5

7 0.3 0.3 0.3

10 0.5 0.5 0.5

Decline 12 0.7 0.7 0.7

11 0.5 0.5 0.5

13 0.7 0.7 0.7

14 0.7 0.7 0.7

Table 9: qij. Unit requirements for part i to produce one unit of Product j i/j

1

2

3

1

2

1

3

2

1

3

2

3

3

2

1

Table 10: Recycling site- related Parameters. nil(Unit recycling cost for part i in recycling site l) i/l

1

2

3

1

2

4

4

2

3

4

3

3

2

3

4

oil (Set-up cost of recycling site l for part i) i/l

1

2

3

1

4

4

5

2

4

4

5

3

5

4

4

sil (Resource usage to recycle on unit part i in recycling site l ) i/l

1

2

3

1

1

1

1

2

1

1

1

3

1

1

1

Oil (Max. Capacity of recycling site l to recycle part i) i/l

1

2

3

1

9000

10000

10000

2

10000

9500

9000

3

8500

10000

8500

Table 11: Inventory related costs and shipments cost HRjt(Unit Inventory cost at Retailer of Product j at Period t) t/j 1 2 3 4 5 6 7 1 5 5 5 5 5 5 5 2 5 5 5 5 5 5 5 3 5 5 5 5 5 5 5 HDjt(Unit Inventory cost at Distributor of Product j at Period t) 1 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 HMjt(Unit Inventory cost at Manufacturer of Product j at Period t) 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 SHil(Unit shipment cost of Product at period t) 1 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

8 5 5 5

9 5 5 5

10 5 5 5

11 5 5 5

12 5 5 5

13 5 5 5

14 5 5 5

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

2 2 2

2 2 2

2 2 2

2 2 2

2 2 2

2 2 2

2 2 2

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

3 3 3

A. Sasikumar et al., 2016/Advances in Natural and Applied Sciences. 10(17) December 2016, Pages: 36-49

49

Table 12: Other parameters I

1000

z

0.6

F1

100

M

10000

F2

200

M1

0.2

F3

300

M2

0.3

MD

1000

L

100

DR

2500

A

250000

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