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ScienceDirect Procedia CIRP 29 (2015) 656 – 661

The 22nd CIRP conference on Life Cycle Engineering

Network Design and Optimization for Multi-product, Multi-time, Multiechelon Closed-loop Supply Chain under Uncertainty Anil Jindal*, Kuldip Singh Sangwan, and Sachin Saxena Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan – 333031, India * Corresponding author. Tel.: +91-1596-515-852; fax: +91-1596-244-183. E-mail address: [email protected], [email protected]

Abstract This paper proposes the network design and optimization of a multi-product, multi-time, multi-echelon capacitated closed-loop supply chain in an uncertain environment. The uncertainty related to ill-known parameters like product demand, return volume, fraction of parts recovered for different product recovery processes, purchasing cost, transportation cost, inventory cost, processing, and set-up cost at facility centers is handled with fuzzy numbers. A fuzzy mixed-integer linear programming model is proposed to decide optimally the 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 to the organization. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and the degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example. © © 2015 2015 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the International Scientific Committee of the Conference “22nd CIRP conference on Life Cycle (http://creativecommons.org/licenses/by-nc-nd/4.0/). Engineering. Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering Keywords: Closed-loop supply chain; Product recovery; Fuzzy MILP; Reverse Logistics

1. Introduction Closed-loop supply chain (CLSC) is an environmentally and economically sound way to achieve many of the goals of sustainable development [1]. It has many benefits over the traditional supply chain [2], but it also complicates the management and control of traditional supply chain [3]. It is further complicated by the uncertainty in quantity, quality and timing of the return [4-5]. This uncertainty affects the percentage of products/parts recovered from different product recovery options like reuse, refurbish, recycle, and disposal, which further affect the inventory level of products and parts as well as the processing and set-up cost at various facility centres. Therefore, in this uncertain environment, determining the number of products to be remanufactured; the number of parts to be directly purchased; inventory level of product and parts; and the location and allocation of external supplier(s), collection centre(s), disassembly centre(s), refurbishing centre(s), recycling centre(s), and disposal centre(s) is challenging to maximize the profit to the organization.

This paper proposes the network design and optimization of a multi-product, multi-time and multi-echelon capacitated CLSC in an uncertain environment. The uncertainty related to ill-known parameters is handled with triangular fuzzy numbers. The proposed CLSC network is presented by a fuzzy mixed-integer linear programming model to decide optimally the location and allocation of parts at each facility, inventory level of parts, number of products to be remanufacturer, and number of parts to be purchased from external suppliers in order to maximize the profit of organization. The proposed framework is tested by solving an illustrative CLSC network problem using the methodology proposed by Jiménez et al. [6]. The advantage of the methodology is that it allows working with the concept of feasibility degree to find an optimal solution between two conflicting objectives, i.e. to improve the objective function value and the degree of satisfaction of constraints simultaneously. The paper is organized as follows. The next section presents the literature review. The proposed CLSC framework

2212-8271 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering doi:10.1016/j.procir.2015.01.024

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Anil Jindal et al. / Procedia CIRP 29 (2015) 656 – 661

is introduced in section 3 and the mathematical model for the proposed framework is given in section 4. The solution methodology is discussed in section 5 and section 6 is devoted to an illustrative example to test the model. Finally, in Section 7 conclusions are presented. 2. Literature review In recent years there has been a growing awareness of the importance of incorporating CLSC activities along with the traditional indicators [7]. Lee and Dong [8] discussed that reverse logistics network has a strong influence on the forward logistics and vice versa, therefore, the design of the forward and reverse logistics network should be integrated. Various strategic and operational aspects of CLSC have been investigated in the last decade. Beamon and Fernandes [9] proposed a single product, multi-time capicated location and allocation model. Kim et al. [10] developed a multiperiod, multi-product mixed integer programming model with crisp parameters. However, in the framework only refurbishment and disposal of parts is considered and the repair, reuse and recycle of products/parts is not considered. Kannan et al. [11] compared the results of genetic algorithm and particle swarm optimization for the design of multiproduct and multi-time CLSC model. Mutha and Pokharel [12] presented location-allocation model to optimize the cost by considering the modular product structure with different disposal and recycling fractions for each module. However, the model assumed deterministic demands by historical average. Özceylan and Paksoy [7] proposed a mixed-integer mathematical model for the location of plant and retailers in CLSC network. Amin and Zhang [13] proposed a two phase multi-objective model to maximize profit and weights of suppliers, and to minimize defect rates. Shi et al. [5] proposed a mathematical model based on Lagrangian relaxation method to investigate a CLSC network in which demand and return are uncertain. Özceylan and Paksoy [7] proposed a multiechelon, multi-time period MILP model to minimize the total cost. The uncertainty in percentage of products recovered is handled with scenario analysis. Özceylan and Paksoy [14] proposed a fuzzy multi-objective model to take into account the fuzziness in the capacity, objectives, demand constraints, and reverse rates. From the above literaure review it can be observed that most of the CLSC models are single time period models [1519] and a few are multi-time period models [7, 9-10, 12]. Therefore, there is a need to develop a multi-product, multitime, multi-echelon capacitated CLSC framework and optimization model including product acquisition cost, transportation cost, purchasing cost, inventory cost, processing and set-up costs simultaneously considering the uncertainty in ill-know parameters. 3. Proposed closed loop supply chain framework A generalized CLSC framework is presented for handling multi-product, multi-time, multi-echelon returns in which forward flow, reverse flow and their mutual interactions are considered simultaneously (Figure 1). The proposed framework is an extension of the previous work [20], which is

a single time period model without considering the inventory level of products and parts and the related inventory costs. It is assumed that the remanufactured products have same quality as the brand-new products and can be sold with the same price [9-10]. Secondly that only parts of products can be disposed off or recycled and not the whole product [21]. The objective of the model is to maximize the profit to the organization by optimally determining the number of parts to be purchased from external supplier(s) and the number of products to be remanufactured under capacity constraints; location and allocation to different facility centres and inventory level of parts to meet the product demand. ~ D jt

~ D jt

Pjt Manufacturer

Distributor

Customers

Retailer

K~j External Suppliers (k)

Sikt

Part Inventory

J~

Ajmt

j

Cjmt

Filt Refurbishing Centers (l) Forward Logistics Reverse Logistics

Finlt

~

Oi

Rjmnt

Disassembly Centers (n)

Yint

~

E Recycle Center

i

I~i

Collection and Repair Centers (m) with Product inventory

Wint

Disposal Center

Fig. 1 The proposed closed loop supply chain framework 4. The proposed fuzzy mixed-integer linear programming model (Fuzzy MILP) The proposed Fuzzy MILP model represents the proposed framework in mathematical terms for optimization. Indices j i k m n l t

set of products, j = 1, 2,…..J set of parts, i = 1, 2,…..I set of suppliers, k = 1, 2,…..K set of collection/repair centres, m = 1, 2,…..M set of disassembly centres, n = 1, 2,…..N set of refurbishing centres, l = 1, 2,…..L set of time periods, t = 1, 2,…..T

Decision variables units of product j to be produced at time t Pjt units of product j to be collected at collection centre Cjmt m at time t units of product j reused from collection centre m at Ajmt time t units of product j disassembled at site n from Rjmnt collection centre m at time t (PI)jmt inventory level of product j at collection centre m at time t (PrI)it inventory level of part i at time t units of part i purchased from supplier k at time t Sikt units of part i obtained at disassembly site n at time t Tint units of parts i refurbished at site l from disassembly Finlt centre n at time t units of part i refurbished at refurbishing centre l at Filt time t units of part i disposed from disassembly centre n at Wint time t units of part i recycled from disassembly centre n at Yint time t binary variable for set-up of collection facility for Bjmt

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Anil Jindal et al. / Procedia CIRP 29 (2015) 656 – 661

Vjnt Uilt

product j at m at time t binary variable for set-up of disassembly site for product j at n at time t binary variable for set-up of refurbishing site for part i at l at time t

Parameters ~ demand of product j to be produced at time t D jt ~ ( PF ) j

profit by selling the product j

qij

units of part i in product j

( MP) jt plant capacity to produce product j at time t ~ (CC ) jm unit cost of collection and inspection for product j at collection centre m ~ ( SC ) jm set-up cost for collection of product j at centre m

( MC) jmt capacity of collection centre m for product j at time t ~ ( DC ) in unit cost of disassembly for part i at disassembly centre n ~ ( SD) jn set-up cost for disassembly of product j at centre n

and reused products. Equation (3), (4) and (5) represents the flow balance constraint at collection centre, disassembly centre and refurbishing centre respectively. While equation (6), (7) and (8) calculate the number of parts at disassembly centres, number of parts at refurbishing centres and number of products at disassembly centres respectively. Constraints (9), (10), (11), and (12) provide the maximum limit on the number of products collected, number of products reused, number of parts refurbished and number of parts to be recycled respectively. Constraints (13), (14), (15) and (17) ensure the capacity limit for collection centre, disassembly centre, refurbishing centre and plant respectively. Constraint (16) ensures the maximum and minimum capacity of the external suppliers. The constraints (18) and (19) are related to binary and general integer values of the decision variables. All the decision variables are positive numbers. Objective Function Maximize ~ ~ ¦¦ ( PF j ) * ( Pjt  ¦ A jmt )  ¦¦¦ ( RP ) i * Yint t

m

j

t

n

i

( MD) jnt capacity of disassembly centre n for product j at time

~ ~  ¦¦¦ ( PC ) ik * S ikt  ¦¦¦ (CC ) jm * C jmt

t ~ ( RC ) il unit cost of refurbishing for part i at centre l ~ ( SR ) il set-up cost for refurbishing of part i at centre l ( MR) ilt capacity of refurbishing centre l for part i at time t ~ (UC ) jm unit cost of repair for product j from collection centre

~ ~  ¦¦¦ ( SC ) jm * B jmt  ¦¦¦ (UC ) jm * A jmt

m ~ unit cost of disposal for part i (WDC ) i ~ ( RP ) i unit profit of recycling for part i ~ ( RF ) jm unit cost of refund to customers for product j ~ ( PC ) ik unit purchasing cost for part i from supplier k

~ (Pr I C ) it unit inventory cost of part i at time t ~ ( PI C ) jmt unit inventory cost of product j at collection centre m

at time t maximum and minimum purchase ( MXS) k , (MNS) k order from supplier k ~ (TCD) jmn unit cost of transportation from collection centre m to disassembly centre n for product j ~ (TCR) inl unit cost of transportation from disassembly centre n to refurbishing centre l for part i ~ (TCU ) jm unit cost of transportation from collection/repair centre m to distributor for product j Maximum percentage of product j returned K~ j Maximum percentage of product j reused J~ j

~ Oi ~ Ei

Maximum percentage of part i refurbished Maximum percentage of part i recycled

It should be noted that parameters with a tilde (~) at the top are indicated by the triangular fuzzy numbers. Equation (1) represents the objective function i.e. to maximize the profit of the organization. Constraint (2) ensures that demand for each product is satisfied with the sum of newly produced products

t

k

i

t

m

j

t

n

i

t

l

i

t

n

i

t

j

m

t

j

m

t

j

m

t

m

t

j

m

j

~ ~  ¦¦¦ ( DC ) in * Tint  ¦¦¦ ( SD ) jn * V jnt t

n

j

~ ~  ¦¦¦ ( RC ) il * Filt  ¦¦¦ ( SR ) il * U il t

l

i

~ ~  ¦¦¦ (WDC ) i * Wint  ¦¦¦ ( RF ) jm * C jmt t

m

j

~ ~  ¦¦¦¦ (TCD) jmn * R jmnt  ¦¦¦¦ (TCR) inl * Finlt n

t

i

n

l

~ ~  ¦¦¦ (TCU ) jm * A jmt  ¦¦ (Pr I C ) it * (Pr I ) it ~  ¦¦¦ ( PI C ) jmt * ( PI ) jmt

t

i

(1)

Subject to ~ D jt

Pjt  ¦ A jmt

(2)

j, t

m

C jmt  ( PI ) jm,t 1

A jmt  ¦ R jmnt  ( PI ) jmt

j, m, t

(3)

n

Yint  Wint  ¦ Finlt

Tint

(4)

i, n, t

l

¦q

ij

¦F  ¦S

* Pjt  (Pr I ) it

ilt

j

l

¦¦ q

Tint

m

ij

 (Pr I ) i ,t 1

i, t

(5)

i, n, t

R jmnt

(6)

j

¦F

Filt

ikt

k

inlt

(7)

i, l , t

n

¦R

R jnt

jmnt

j, n, t

(8)

j, t

(9)

m

¦C

jmt

~ dK~j * D jt

m

A jmt d J~j * C jmt

¦F

inlt

j, m, t

~

(10)

i, n, t

(11)

i, n, t

(12)

d Oi * Tint

l

~ Yint d E i * Tint

C jmt d (MC ) jmt * B jmt

j, m, t

(13)

659

Anil Jindal et al. / Procedia CIRP 29 (2015) 656 – 661

¦R

jmnt

d ( MD) jnt *V jnt

(14)

j, n, t

m

¦F

inl

d ( MR) ilt *U il

(15)

i, l

n

( MNS ) k d ¦ S ikt d ( MXS ) k

(16)

k , t

i

(17)

Pjt d (MP) jt

j, t

B jmt ,V jnt ,U ilt

{0,1}

i, j, m, n, l , t

(18)

Pjt , C jmt , A jmt , R jmnt , R jnt , S ikt , Tint , Finlt , Filt ,Wint , Yint , PI jmt , Pr I it

I

(19)

j, m, n, l , i, k , t

5. Solution methodology In this paper the methodology proposed by Jiménez et al. [6] and Pishvaee and Razmi [22] is used to find out the optimal solution. The various steps of the solution methodology are: 5.1. Convert the fuzzy MILP model to crisp MILP model A number of methods are proposed in the literature to deal with possibilistic programming models [6, 23-24]. Among these methods the Jiménez et al. [6] method is selected to deal with proposed fuzzy MILP model. The advantage of this method is that it allows the decision makers (DMs) to find a balanced solution between two conflicting objectives, i.e. to improve the objective function value and to improve the degree of satisfaction of constraints. The crisp equivalent of objective function is shown below: Maximize § PF j  2 u PF

¦¦ ¨¨ t

j

©

pes

mos j

 PF

opt j

4

· § ¸ * ( Pjt  ¦ A jmt )  ¦¦¦ ¨ RPi ¨ ¸ m t n i © ¹

pes

 2 u RPi 4

mos

 RPi · ¸¸ * Yint ¹ opt

opt § CC pes  2 u CC mos · § PC pes  2 u PC ikmos  PC ikopt · jm  CC jm ¸ * C jmt ¸¸ * S ikt  ¦¦¦ ¨ jm  ¦¦¦ ¨¨ ik ¨ ¸ 4 4 t k i © t m j © ¹ ¹ opt opt § SC jmpes  2 u SC mos · § UC pes  2 u UC mos · jm  UC jm jm  SC jm ¸ * B jmt  ¦¦¦ ¨ jm ¸ * A jmt  ¦¦¦ ¨ ¨ ¸ ¨ ¸ 4 4 t m j t m j © ¹ © ¹ opt § SD pes  2 u SD mos · § DC pes  2 u DCinmos  DCinopt · jn  SD jn ¸ * V jnt ¸¸ * Tint  ¦¦¦ ¨ jn  ¦¦¦ ¨¨ in ¨ ¸ 4 4 t n i © t n j © ¹ ¹

§ WDCi  2 u WDC  ¦¦¦ ¨¨ 4 t n i ©

mos i

§ RF  WDC · ¨ ¸¸ * Win  ¦¦¦ ¨ t j m © ¹ opt i

pes jm

 2 u RF 4

mos jm

 RF

opt jm

· ¸ * C jmt ¸ ¹

opt pes pes mos opt § TCD jmn ·  2 u TCD mos § · jmn  TCD jmn ¸ * R jmnt  ¦¦¦¦ ¨ TCRinl  2 u TCRinl  TCRinl ¸ * Finlt  ¦¦¦¦ ¨ ¨ ¸ ¨ ¸ 4 4 t j m n © t i n l © ¹ ¹ opt mos opt pes § TCU jmpes  2 u TCU mos ·  TCU § Pr ICit  2 u Pr ICit  Pr ICit · jm jm ¨ ¸ ¨  ¦¦¦ *A  ¨ ¸¸ * (Pr I ) it ¨ ¸ jmt ¦¦ 4 4 t i © t j m © ¹ ¹ opt pes § PIC jmt ·  2 u PIC mos jmt  PIC jmt ¸ * ( PI ) jmt  ¦¦¦ ¨ ¨ ¸ 4 t j m © ¹

5.2. Calculate the decision vector complying the expectations of decision maker In order to get a decision vector that complies with the expectations of the DM, the model is solved for each value of degree of feasibility (α) to obtain a set of acceptable solution ~z D . The decision vector complying the expectation of decision maker is given by the following equation (20).



P G~ ( z )

­ °° ® ° °¯

1 ª z G º « » ¬G  G ¼ 0

if

ztG

decrea sin g G  z  G if

(20)

zdG

5.3. Compute the optimum solution The next step is to compute the degree of satisfaction of the fuzzy goal G~ for each α – acceptable solution, i.e. the z D to the fuzzy membership degree of each fuzzy number ~ set G~ . There are several methods to do this, but the index proposed by Yager [25] is used here as shown in equation (21).



f

K G~ ( z (D ))

³P

~ z (D )

( z ).P G~ ( z )dz

f

(21)

f

³P

~ z (D )

( z )dz

Now to find the balance solution between the feasibility degree and the degree of satisfaction, the membership degree of each α–acceptable optimal solution is calculated using tnorm algebraic product (equation 22). So the best solution is one which has the greatest membership degree.

P D~ ( x* )

max ^ D K G~ (~ z (D ))`

(22)

6. Illustrative example

The crisp equivalents of constraints given by equation number 2, 9, 10, 11, and 12 are as follows. The other constraints remain as such. · § D jtpes  2 u D mos  D opt jt jt ¸ ¨ ¸ ¨ 4 ¹ ©

jmt

f

§ RC pes  2 u RC ilmos  RC ilopt · § SR pes  2 u SRilmos  SRilopt · ¸¸ * Filt  ¦¦¦ ¨¨ il ¸¸ * U ilt  ¦¦¦ ¨¨ il 4 4 t l i © t l i © ¹ ¹ pes

ª § K jpes  K mos · § K opt  K mos ·º j j ¸  1  D ¨ j ¸» * d «D ¨ ¸ ¨ ¸» 2 2 m «¬ ¨© ¹ © ¹¼ pes mos opt mos ª § D jt  D jt · § D jt  D jt ·º ¸  1  D ¨ ¸» j , t «D ¨ ¸ ¨ ¸» 2 2 «¬ ¨© ¹ © ¹¼ ª § J jpes  J mos · § J opt  J mos ·º j j ¸  1  D ¨ j ¸» * C jmt A jmt d «D ¨ j, m, t ¨ ¸ ¨ ¸» 2 2 ¹ © ¹¼ ¬« © ª § O pes  Omos · § Oopt  Omos ·º ¦l Finlt d ««D ¨¨ i 2 i ¸¸  1  D ¨¨ i 2 i ¸¸»» * Tint i, n, t ¹¼ © ¹ ¬ © ª § E i pes  E imos · § E iopt  E imos ·º ¸¸» * Tint ¸¸  1  D ¨¨ Yint d «D ¨¨ i, n, t 2 2 ¹¼» © ¹ ¬« ©

¦C

Pjt  ¦ A jmt m

j, t

This section presents an example to illustrate how the proposed model works in a multi-time, multi-product, multiechelon CLSC framework under an uncertain environment. Inventory of products is maintained at the collection centres, and part inventory is done at part inventory centre. Both the initial inventory and minimum inventory of products and parts is 10 and 25 respectively. The maximum purchase order for each supplier is 8000, 9000 and 9000, and the minimum purchase order for each supplier is 100. It is further assumed

660

Anil Jindal et al. / Procedia CIRP 29 (2015) 656 – 661

that K~ j (maximum percentage of product j returned) = (0.50, ~ 0.60, 0.70), J j (maximum percentage of product j reused) = ~ (0.10, 0.20, 0.30), Oi (maximum percentage of part i ~ refurbished) = (0.65, 0.70, 0.75), and E i (maximum percentage of part i recycled) = (0.10, 0.15, 0.20). The rest of input parameters can be had from Jindal and Sangwan [20]. The proposed model is solved using IBM ILOG Optimization Studio 12.2 on intel core i5 processor machine. The model contains 476 constrains, 303 variables, 252 integers, and 1667 non-zeros. To find the optimum value of degree of feasibility, all the α-acceptable optimal solutions are calculated (with the minimum α = 0.4, as specified by the decision maker) as shown in Table 1. Table 1 α-acceptable optimal solution Possibility distribution of the objective value, ~ z D

α = 0.4 α = 0.5 α = 0.6 α = 0.7 α = 0.8 α = 0.9

877060, 934931, 992790 851470, 910855, 970230 815180, 873699, 932210 775800, 832222, 888630 735590, 788663, 841720 694710, 743159, 791600

0.84 0.77 0.66 0.53 0.40 0.27

0.334 0.383 0.393 0.373 0.322 0.241

α=1

654960, 697597, 740160

0.13

0.131

K G~ ( z (D )) P D~ xD

After that the decision maker establishes an aspiration level G~ whose membership function is as follows (using equation 20). P G~ ( z )

if

z t 992790

decrea sin g

992790 d z d 654960

if

z d 654960

In order to find the balance solution between the feasibility degree and the degree of satisfaction, compatibility index and membership degree of each α–acceptable optimal solution is calculated using equation (21) and (22) respectively. These values are shown in last two columns of Table 1. It is observed that α = 0.6 is the optimum feasibility degree, which corresponds to the highest membership degree of 0.393. With a feasibility degree (α) of 0.6, Table 2 provides the number of products to be manufacturer to meet the customer demand, with a probabilistic profit of USD (815180, 873699, 932210). Table 3 and Table 4 shows the number of products to be collected and reused at the various collection/repair centres respectively. It can be observed from these tables that for product 1 all the products are collected at collection centre 1 and 2 only. Similarly for product 2 all the collection is done at collection centre 2 and 3 only. Table 5 shows the number of products disassembled at each disassembly centres, while Table 6 and Table 7 shows the number of parts disposed and recycled from each disassembly centre respectively. The number of parts refurbished at each refurbishing centre is shown in Table 8. Table 9 shows the number of parts purchased from each external supplier to fulfil the production demand. Table 9 shows that all of part1, part2 and part3 is purchased from supplier1, supplier 3 and supplier2 respectively. The product inventory and part inventory are shown in Table 10 and Table 11 respectively. The optimum flow of products and parts at period-1 is shown in Figure 2.

Pjt

Period 1

Period 2

Period 3

j=1

1365

1183

1456

j=2

1274

1092

1365

Table 3 Number of products collected at each collection centre Period 1

Cjmt

Period 2

Period 3

m=1 m=2 m=3 m=1 m=2 m=3 m=1 m=2 m=3

j=1

300

400

146

250

350

135

400

500

2

j=2

190

300

300

179

250

250

46

400

400

Table 4 Number of products reused from each collection centres Period 1

Ajmt

Feasibility degree, α

1 ­ ° z  654960 ® ° 992790  654960 0 ¯

Table 2 The number of products to be manufactured at different time periods

Period 2

Period 3

m=1 m=2 m=3 m=1 m=2 m=3 m=1 m=2 m=3

j=1

48

64

23

40

56

21

64

80

0

j=2

30

48

48

28

40

40

7

64

64

Table 5 Number of products disassembled at each disassembly centre Period 1

Rjnt

Period 2

Period 3

n=1

n=2

n=1

n=2

n=1

n=2

j=1

211

500

168

450

158

600

j=2

264

400

171

400

211

500

Table 6 Number of parts disposed from each disassembly Period 1

Wint

Period 2

Period 3

n=1

n=2

n=1

n=2

n=1

n=2

i=1

213

385

149

368

167

473

i=2

250

473

179

447

195

578

i=3

167

315

119

298

130

385

Table 7 Number of parts recycled from each disassembly centre Period 1

Yint

Period 2

Period 3

n=1

n=2

n=1

n=2

n=1

n=2

i=1

176

319

123

304

137

391

i=2

206

391

147

369

160

478

i=3

137

261

98

246

107

319

Table 8 Number of parts at each refurbishing centre Period 1

Filt

Period 2

Period 3

l=1

l=2

l=1

l=2

l=1

i=1

2321

0

2005

0

2481

l=2 0

i=2

5

2800

0

2425

196

2800

i=3

0

1870

0

1617

0

1997

Table 9 Number of parts purchased from each external suppliers Sikt

Period 1

Period 2

Period 3

k=1

k=2

k=3

k=1

k=2

k=3

k=1

k=2

i=1

4231

0

0

3637

0

0

4526

0

k=3 0

i=2

0

0

5112

0

0

4400

0

0

5467

i=3

0

3408

0

0

2933

0

0

3645

0

Table 10 Product inventory at each collection centre PIjmt

Period 1

Period 2

Period 3

m=1 m=2 m=3 m=1 m=2 m=3 m=1 m=2 m=3

j=1

10

10

10

10

10

10

10

10

10

j=2

10

10

10

10

10

10

10

10

10

Anil Jindal et al. / Procedia CIRP 29 (2015) 656 – 661 Table 11 Part inventory at different time periods Period 1

Period 2

Period 3

i=1

25

25

25

i=2

25

25

25

i=3

25

25

25

1500, 1400

Distributor

1500, 1400

Retailer

48 ,3

0 1 1, 26 9, 39 31

Part1, Part2, Part3

Recycling Center

38

5, 4

73

6, 2

52

123,1

,31

300

Collection Center (m =2)

300

, ,0

Disassembly Center (n =2)

0,1836,1224

176,206,137

33

146,

41 ,0

96

Refurbishing Center (l =2)

400,

4, 6 96

4

14

70

External Supplier (k =3)

Collection Center (m =1)

60

0,0

0,

11

211,1

10 0,

8 0,1

0,5

Disassembly Center (n =1)

825,5,0 46

8 40

Refurbishing Center (l =1)

80

2,0

8

0, 0, 3

,4

21 ,5, 0

0,2

External Supplier (k =2)

8

23

23

0

,4

External Supplier (k =1)

,0,0 4230

64

Part Inventory

Customers

300, 190

1365,1274

Manufacturer

48

213,250,167

Collection Center (m =3)

5

Disposal Center

Product1, Product2

Fig. 2 Optimum flow of products and parts at first period 7. Conclusions In this paper a multi-product, multi-time, multi-echelon capacitated CLSC framework is proposed in an uncertain environment. The model considers multi-collection centres, multi-disassembly centres, multi-refurbishing centres, and multi-external suppliers to take care of purchasing cost, transportation cost, inventory cost, processing cost, set-up cost, and capacity constraints simultaneously. The uncertainties related to ill-known parameters are represented by triangular fuzzy numbers. A fuzzy MILP model is proposed to represent the proposed framework in mathematical terms for optimization. The proposed solution methodology is able to generate a balance solution between the feasibility degree and the degree of satisfaction. The effectiveness of the developed fuzzy optimization model as well as the usefulness of the proposed solution approach is investigated by solving an illustrative example. The proposed closed-loop supply chain framework and mathematical model can be customized for various industries. However, for the large size real business problems efficient heuristics need to be developed. References [1] Winkler, H. Closed-loop production systems—A sustainable supply chain approach. CIRP Journal of Manufacturing Science and Technology 2011; 4 (3): 243-246. [2] Talbot, S., Lefebvre, E., and Lefebvre, L.-A. Closed-loop supply chain activities and derived benefits in manufacturing SMEs. Journal of Manufacturing Technology Management 2007; 18 (6): 627-658. [3] Guide, V. D. R., Jr., Jayaraman, V., Srivastava, R., and Benton, W. C. Supply-chain management for recoverable manufacturing systems. Interfaces 2000; 30 (3): 125-142. [4] Pochampally, K. K. and Gupta, S. M. A multiphase fuzzy logic approach to strategic planning of a reverse supply chain network. Electronics

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