Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Table 3

Comparison of the MIP, T&B, and ICBD methods based on the number of unsolved instances, average gap, and execution time.

		# uns				% gap			Time
		MIP	T&B	ICBD		MIP	T&B	ICBD	MIP	T&B	ICBD
20	2	0	0	0		0	0	0	0.95	0.89	1.07
	3	0	0	0		0	0	0	2.52	2.14	1.87
	4	0	0	0		0	0	0	8.17	9.01	4.27
	5	0	0	0		0	0	0	31.12	31.05	11.65
30	2	0	0	0		0	0	0	3.48	2.79	3.06
	3	0	0	0		0	0	0	17.27	34.62	10.99
	4	0	1	0		0	0.01	0	145.81	233.14	83.26
	5	0	0	0		0	0	0	365.14	287.38	85.61
40	2	0	0	0		0	0	0	10.85	3.41	4.93
	3	0	0	0		0	0	0	66.68	30.9	16.09
	4	0	0	0		0	0	0	466.00	348.09	111.52
	5	2	8	2		0.15	0.67	0.05	1463.93	1446.89	743.84
50	2	0	0	0		0	0	0	40.54	5.69	9.96
	3	0	1	0		0	0.01	0	257.40	280.30	103.89
	4	3	4	1		0.11	0.11	0.02	1545.20	1212.69	648.19
	5	18	16	11		1.87	1.22	0.53	2993.74	2542.33	2031.87
60	2	0	0	0		0	0	0	82.51	24.34	19.72
	3	1	3	1		0.02	0.03	0.01	844.00	737.04	247.40
	4	7	9	3		0.29	0.28	0.06	2306.63	1446.28	929.21
	5	26	21	13		3.18	1.08	0.68	3473.69	2798.76	2488.82
	Sum	57	63	31	Average	0.28	0.17	0.07	706.28	573.89	377.86