A performance comparison and evaluation of metaheuristics for a batch scheduling problem in a multi-hybrid cell manufacturing system with skilled workforce assignment

Omer Faruk Yilmaz; Mehmet Bulent Durmusoglu

doi:10.3934/jimo.2018007

Article Contents

2018, Volume 14, Issue 3: 1219-1249. Doi: 10.3934/jimo.2018007

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A performance comparison and evaluation of metaheuristics for a batch scheduling problem in a multi-hybrid cell manufacturing system with skilled workforce assignment

Omer Faruk Yilmaz^1, , and
Mehmet Bulent Durmusoglu^2,

1.
Department of Industrial Engineering, Yalova University, Yalova, Turkey
2.
Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

* Corresponding author: Omer Faruk Yilmaz
* Corresponding author: Omer Faruk Yilmaz

Received: July 31, 2016

Revised: May 31, 2017

Early access: January 2018

Published: June 2018

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Abstract

This paper focuses on the batch scheduling problem in multi-hybrid cell manufacturing systems (MHCMS) in a dual-resource constrained (DRC) setting, considering skilled workforce assignment (SWA). This problem consists of finding the sequence of batches on each cell, the starting time of each batch, and assigning employees to the operations of batches in accordance with the desired objective. Because handling both the scheduling and assignment decisions simultaneously presents a challenging optimization problem, it is difficult to solve the formulated model, even for small-sized problem instances. Three metaheuristics are proposed to solve the batch scheduling problem, namely the genetic algorithm (GA), simulated annealing (SA) algorithm, and artificial bee colony (ABC) algorithm. A serial scheduling scheme (SSS) is introduced and employed in all metaheuristics to obtain a feasible schedule for each individual. The main aim of this study is to identify an effective metaheuristic for determining the scheduling and assignment decisions that minimize the average cell response time. Detailed computational experiments were conducted, based on real production data, to evaluate the performance of the metaheuristics. The experimental results show that the performance of the proposed ABC algorithm is superior to other metaheuristics for different levels of experimental factors determined for the number of batches and the employee flexibility.

Keywords:

Mathematics Subject Classification: Primary: 90B35, 90C10; Secondary: 90C27.

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Figure 1. Batch-flow and one-piece flow

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Figure 2. Average cell response time (Solution decoding)

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Figure 3. Multi-Hybrid Cell Manufacturing System for the illustrative example

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Figure 4. Crossover operator

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Figure 5. Box-plot of RPD values with respect to the algorithms (for nine employees)

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Figure 6. Box-plots of RPD values obtained by the algorithms for each level of NBEC (for nine employees)

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Figure 7. Box-plots of RPD values obtained by the algorithms for each level of NESL (for nine employees)

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Figure 8. Box-plots of RPD values obtained by the ABC algorithm for each level of NESL (for nine employees)

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Table 1. Illustrative example data for the problem

$i$	$cx_i$	$cn_i$	$q_i$	$r_{im}$	$e_{zim}$	$r_{im}$	$e_{zim}$	$r_{im}$	$e_{zim}$	$r_{im}$	$e_{zim}$	$o_i$	$a_i$
1	66	35	5	5	15	0	10	0	5	15	20	16	4
2	86	30	10	0	20	0	15	5	5	0	30	16	4
3	80	30	5	15	15	5	5	0	30	20	10	20	5
4	55	20	10	10	10	0	5	0	20	20	0	20	5

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Table 2. Maximum and minimum number of employees

$i$	$W_i$ (Maximum)	$W1_i$ (Minimum)
1 (Cell1)	2	1
2 (Cell1)	3	1
3 (Cell2)	3	1
4 (Cell2)	3	1

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Table 3. The batch list representation scheme (Encoding scheme)

position numbers	1	2	3	4
batch list	2	4	1	3
batch-employee assignment	1-3	1-2	2	1-3
employee-machine assignment	(1-2) (3-4)	(2-3) (1-4)	(1-2-3-4)	(3-4) (1-2)

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Table 4. The cell cycle times and the first lead times

$i$	$cn_i$	employee1	employee2	employee3	$cy_i$	$FT_i$
1 (Cell1)	35	-	66	-	66	86
2 (Cell1)	30	43	43	-	43	91
3 (Cell2)	30	50	-	25	50	120
4 (Cell2)	20	35	20	-	35	85

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Table 5. Cell cycle times, batch sizes, operation times and total walking times

$i$	$cx_i$	$cn_i$	$q_i$	$e_{zim}$	$e_{zim}$	$e_{zim}$	$r_{im}$	$e_{zim}$	$e_{zim}$	$e_{zim}$	$e_{zim}$	$o_i$
1	957	450	5	16	150	MO	MO	450	155	108	62	16
2	622	468	4	16	150	110	358	MO	160	108	62	16
3	915	432	10	15	144	MO	MO	432	148	105	55	16
4	590	455	5	15	144	100	355	MO	152	105	58	16
5	887	420	15	15	140	MO	MO	420	145	96	55	16
6	555	438	8	15	140	88	350	MO	145	96	55	16
7	741	319	15	12	135	MO	MO	319	130	84	45	16
8	508	355	5	12	135	75	280	MO	138	84	48	16
9	626	250	10	9	120	MO	MO	250	117	71	44	15
10	436	272	10	9	120	60	212	MO	117	71	44	15
11	472	155	15	8	108	MO	MO	155	88	66	32	15
12	363	186	9	8	108	26	160	MO	102	66	38	15
13	525	182	12	8	115	MO	MO	182	95	71	40	14
14	414	210	8	8	115	50	160	MO	112	71	44	14
15	617	226	14	11	131	MO	MO	226	102	85	48	14
16	469	258	8	11	131	58	200	MO	120	85	50	14
17	755	318	10	14	145	MO	MO	318	115	94	55	14
18	541	360	5	14	145	80	280	MO	134	94	60	14
19	940	431	5	18	153	MO	MO	431	139	118	65	16
20	653	490	15	18	153	120	370	MO	155	118	73	16
21	1070	485	10	25	168	MO	MO	485	163	135	78	16
22	739	545	8	25	168	135	410	MO	175	135	85	16
23	1202	528	10	34	185	MO	MO	528	188	161	90	16
24	857	607	5	34	185	147	460	MO	211	161	103	16

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Table 6. Experimental factors and their levels

Factor	Level
Number of Batches on Each Cell (NBEC)	1	NB
(Problem size factor)	2	[5$\times$ NB]
	3	[10$\times$ NB]
Number of Employees for each Skill Level		Junior	Normal	Senior
(NESL)	1	33%	33%	33%
	2	66%	33%	00%
	3	66%	00%	33%
	4	100%	00%	00%
	5	00%	66%	33%
	6	33%	66%	00%
	7	00%	100%	00%
	8	33%	00%	66%
	9	00%	33%	66%
	10	00%	00%	100%

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Table 7. The coefficient of skill levels

	Junior	Normal	Senior
Skill level coefficients	0.63	1	1.29

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Table 8. The promising values of the parameters for the metaheuristics

Algorithm	Notation	Values		Combination
			NBEC=1	NBEC=2	NBEC=3
GA	$PS$	20, 40, 60, 80,100	40	60	80
	$pcross$	0.2, 0.4, 0.6, 0.8	0.8	0.6	0.6
	$pmutation$	0.1, 0.2, 0.3, 0.4	0.3	0.2	0.2
ABC	$NFS$	20, 40, 60, 80,100	40	40	60
	$\lambda$	2, 4, 6, 8, 10	2	4	4
	$limit$	2, 4, 6, 8, 10	6	6	4
SA	$initialtemp$	$10^3\times$(1, 3, 5, 7)	1	3	5
	$coolingrate$	0.9, 0.95, 0.99	0.99	0.99	0.99
	$epoch$	5, 10, 15, 20	10	15	15

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Table 9. The tuned values of the parameters for the metaheuristics

Algorithm	Notation	Combination
		NBEC=1	NBEC=2	NBEC=3
GA	$PS$	30, 40, 50	50, 60, 70	70, 80, 90
	$pcross$	0.7, 0.8, 0.9	0.5, 0.6, 0.7	0.5, 0.6, 0.7
	$pmutation$	0.25, 0.3, 0.35	0.15, 0.2, 0.25	0.15, 0.2, 0.25
ABC	$NFS$	30, 40, 50	30, 40, 50	50, 60, 70
	$\lambda$	1, 2, 3	3, 4, 5	3, 4, 5
	$limit$	5, 6, 7	5, 6, 7	3, 4, 5
SA	$initialtemp$	750, 1000,1250	2500,3000, 3500	4000,5000, 6000
	$coolingrate$	0.98, 0.99	0.98, 0.99	0.98, 0.99
	$epoch$	8, 10, 12	13, 15, 17	13, 15, 17

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Table 10. The maximum computational times

	ABC	GA	SA
NBEC=1	14.87	12.68	9.16
NBEC=2	53.40	46.07	38.73
NBEC=3	98.25	95.53	83.68

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Table 11. Median of RPD values and computational time of algorithms for 9 employees

NESL$\times$NBEC				RPD
NESL$\times$NBEC	LB	SA	GA	ABC	ABCWLS	GAWLS	CPU
1$\times$1	23580	17.66	16.96	18.82	18	17, 14	15
2$\times$1	18989	19.34	20.01	16.08	20.04	21.39	15
3$\times$1	22263	17.99	18.97	16.62	18.83	19.05	15
4$\times$1	23196	20.22	19.23	17.4	18.55	20.13	15
5$\times$1	22223	16.05	17.66	18.19	18.99	18.25	15
6$\times$1	22097	18.05	19.18	16.02	17.39	21.05	15
7$\times$1	20685	20.57	18.87	18.53	18.32	19.08	15
8$\times$1	24351	19.93	21.03	16.56	17.36	21.58	15
9$\times$1	19621	17.45	18.6	18.57	18.92	20.4	15
10$\times$1	23961	20.42	20.57	15.97	20.02	21.16	15
Medians		18.768	19.108	17.276	18.642	19.923	15
1$\times$2	123093	34.99	30.13	26.88	27.85	32.15	51.2
2$\times$2	116383	33.24	31.81	29.88	28.44	32.73	51.2
3$\times$2	125259	28.87	27.55	29.16	29.28	29.71	51.2
4$\times$2	114564	30.38	28.49	28.59	29.36	29.73	51.2
5$\times$2	108065	28.37	30.16	29.74	29.65	32.76	51.2
6$\times$2	121750	30.88	30.67	29.75	30.49	32.6	51.2
7$\times$2	119274	31.85	31.92	27.21	31.93	33.58	51.2
8$\times$2	118577	30.56	29.65	28.24	32.1	29.16	51.2
9$\times$2	104521	29.57	30.03	25.62	32.12	30.22	51.2
10$\times$2	111100	29.45	29.11	29.65	31.03	35.54	51.2
Medians		30.816	29.952	28.472	30.225	31.818	51.2
1$\times$3	242399	36.45	35.13	34.05	36.48	39.72	96.9
2$\times$3	249240	40.28	39.55	36.66	36	41.11	96.9
3$\times$3	238045	39.79	36.61	34.87	36.76	39.92	96.9
4$\times$3	246187	37.21	38.62	35.04	38.24	39.51	96.9
5$\times$3	229842	36.44	35.87	36.48	39.46	41.09	96.9
6$\times$3	228375	36.34	36.01	36.14	38.63	39.45	96.9
7$\times$3	211540	37.34	36.91	35.92	39.04	38.87	96.9
8$\times$3	225562	40.26	40.27	36.21	37.61	41.78	96.9
9$\times$3	232299	39.72	38.53	33.32	36.2	42.21	96.9
10$\times$3	237518	39.76	37.6	34.73	36.86	41.06	96.9
Medians		38.359	37.51	35.342	37.528	40.472	96.9

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Table 12. Median of RPD values and computational time of algorithms for 15 employees

NESL$\times$ NBEC				RPD
NESL$\times$ NBEC	LB	SA	GA	ABC	ABCWLS	GAWLS	CPU
7$\times$1	20685	3.68	3.45	3.11	3.53	3.65	15
7$\times$2	119274	5.11	4.9	4.65	5.07	5.15	51.2
7$\times$3	228375	6.32	5.98	5.6	5.92	6.44	96.9

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Table 13. Three-way ANOVA: RPD versus NBEC, NESL, and Algorithms

Source	F	Sig. ($p$)	Partial eta squared
NBEC	132.802	0.000	0.708
NESL	1.186	0.395	0.155
Algorithms	22.228	0.002	0.626
Interactions
NBEC*NESL	1.324	0.199	0.362
NBEC*Algorithms	1.284	0.266	0.226
NESL*Algorithms	0.814	0.748	0.337

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