Developing a fuzzy linear programming model for locating recovery facility in a closed loop supply chain

Figures & data

Figure 1 Recovery system for conceptual closed loop supply chain.

Table 1 Different sizes of test problems in the literature.

Reference	No. of manufacturers	No. of DCs	No. of customers	No. of collection centres	No. of remanufacturing centres	Disposal centres
Jayaraman, Guide, and Srivastava (1999)	–	–	100	40	30	–
Gen, Altiparmak, and Lin (2006)	20	30	500	–	–	–
Aras, Aksen, and Karaarslan (2008)	–	–	120	35	–	–
Yeh (2005)	3	–	–	80	20	–
Jayaraman, Patterson, and Rolland (2003)	30	40	100	40	30	–

Table 2 Designed small size test problems.

Problem no.	No. of suppliers	No. of manufacturers	No. of distribution centres	No. of customers	No. of collection centres	No. of remanufacturing centres	Disposal	No. of products
1	3	2	4	5	3	2	3	1
2	3	2	4	5	3	2	3	2
3	5	2	4	5	4	2	3	1
4	5	2	4	7	4	2	3	2
5	5	2	4	7	4	2	3	3

Table 3 Designed medium size test problems.

Problem no.	No. of suppliers	No. of manufacturers	No. of DCs	No. of customers	No. of collection centres	No. of remanufacturing centres	Disposal	No. of products
1	10	3	7	7	7	5	4	1
2	10	3	7	7	7	5	4	2
3	10	3	7	7	7	5	4	3
4	10	6	8	10	8	6	5	1
5	10	6	8	10	8	6	5	2
6	10	6	8	10	8	6	5	3
7	10	7	9	15	9	7	7	1
8	10	7	9	15	9	7	7	2
9	10	7	9	15	9	7	7	3

Table 4 Levels of parameters for GA.

Population size	Crossover rate	Mutation rate
70	0.7	0.1
150	0.7	0.2
200	0.8	0.1

Figure 2 Adjustment of mutation and crossover rates by MINITAB.

Figure 3 Analysis of population size.

Table 5 Results for small size test problem.

Problem number	GA objective function	LINGO objective function	GA time	LINGO time	Error
1	1252640	1181491	365.17	1	0.06
2	1355365	1226598	578.26	5	0.1
3	2028732	1794968	410.08	42	0.13
4	3852185	1831084	654.33	780	1.1
5	7734957	3465977	1012.6	815	1.23

Table 6 Results for medium size test problem.

Problem number	GA objective function	LINGO objective function	GA time	LINGO time	error
1	1634129	–	1467.3	>10,800	–
2	1895608	–	1630.09	>10,800	–
3	1845281	–	1427.3	>10,800	–
4	1899429	–	1511.08	>10,800	–
5	2403157	–	1741.7	>10,800	–
6	2134252	–	1917.06	>10,800	–
7	2726481	–	2113.09	>10,800	–
8	2859374	–	2284.2	>10,800	–
9	3098100	–	2165.01	>10,800	–

Figure 4 Comparison of objective function answers for small size test problems.

Figure 5 Comparison of solution times for small size test problems.

Figure 6 Comparison of objective function answers for medium size test problems.

Figure 7 Comparison of solution times for medium size test problems.

Table 7 Selected problems for design of optimised configuration.

No.	No. of suppliers	No. of manufacturers	No. of DCs	No. of customer	No. of collection centres	No. of remanufacturing centres	No. of disposals	Product no.
3	10	3	7	7	7	7	7	3
6	10	6	8	10	8	6	5	3
8	10	7	9	15	9	7	7	3

Table 8 Optimised configuration for selected problems.

No.	No. of suppliers	No. of manufacturers	No. of DCs	No. of customers	No. of collection centres	No. of remanufacturing centres	No. of disposals	Product no.
3	10	3	4	7	5	2	2	3
6	10	6	6	10	2	3	2	3
8	10	7	3	15	5	4	4	3

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