Table 12.

Performance of the heuristic algorithms for large instances of the TCMCRP

Instance	Obj. CPLEX	Avg. Obj. (ILS)	Avg. Obj. (VNS)	Avg. Obj. (TS)	Avg. time (TS)	Instance	Obj. CPLEX	Avg. Obj. (ILS)	Avg. Obj. (VNS)	Avg. Obj. (TS)	Avg. time (TS)
1	40	40	40	40	51.69	42	–	65	65	65	108.47
2	37	37	37	37	59.82	43	–	58	58	58	79.15
3	–	37	37	37	62.11	44	–	61.5	62	62	81.19
4	41	41	41	41	55.04	45	–	63	63	63	98.35
5	40	40	40.6	42	58.21	46	75	75	75	75	45.77
6	–	39	39	39	56.61	47	72	72	72	72	64.68
7	–	40	40	40	59.54	48	58	71	71	75	67.84
8	–	39	39	39	56.30	49	73	73	73	73	59.97
9	–	39	39	39	57.91	50	73	73	73	73	65.24
10	36	36	36	36	41.86	51	–	71	71	71	66.42
11	41	41	41	41	43.83	52	75	75	75	75	56.92
12	33	36	37	37	46.99	53	–	72	72	72	65.39
13	39	39	39	39	44.38	54	–	67	67	67	64.76
14	43	43	43	43	46.87	55	–	27	27	27	134.17
15	–	44	44	44	51.37	56	–	29	29	29	123.58
16	40	40	40	40	38.80	57	–	28	28	28	148.83
17	–	40	40	40	44.35	58	–	30	30	30	235.21
18	–	38	38	38	41.83	59	–	31	31	31	149.97
19	43	43	43	43	32.93	60	–	28.5	30	30	168.48
20	38	43	43	43	25.76	61	–	30	30	30	151.52
21	43	36	36	36	33.36	62	–	30	30	30	172.51
22	41	40	39	41	29.23	63	–	30	30	30	143.45
23	37	39	39	37.8	27.91	64	27	27	27	27	113.68
24	37	40	37	40	38.62	65	–	27	27	27	111.39
25	41	43	43	41.8	31.07	66	–	30	30	30	137.35
26	40	39	39	40	31.56	67	–	28	28	28	116.41
27	–	40	39	41	25.39	68	–	29	29	29	104.40
28	58	58	58	58	119.81	69	–	27	25.5	27	100.56
29	54	54	54	54	121.73	70	–	26	26	26	118.94
30	–	58	58	58	149.92	71	–	30	30	30	96.77
31	58	58	57	58	100.45	72	–	29	29	29	143.71
32	–	58	58	58	115.17	73	27	27	27	27	76.56
33	–	56. 8	56.6	57	114.68	74	26	26	26	26	58.93
34	–	57	57	57	123.46	75	–	30	30	30	62.97
35	–	58	58	59	122.05	76	30	30	30	30	76.56
36	–	58.6	58.8	60	114.36	77	–	27	27	27	55.06
37	62	63	63	63	84.07	78	–	28	28	28	60.30
38	64	64	64	64	103.12	79	19	21.5	22	26	84.69
39	–	65	65	65	88.53	80	–	29	29	29	58.97
40	63	63	63	63	80.20	81	–	28	28	28	66.77
41	–	61	61	61	103.00

Instance	Obj. CPLEX	Avg. Obj. (ILS)	Avg. Obj. (VNS)	Avg. Obj. (TS)	Avg. time (TS)	Instance	Obj. CPLEX	Avg. Obj.(ILS)	Avg. Obj. (VNS)	Avg. Obj. (TS)	Avg. time (TS)
82	–	82	82	83	268.10	109	–	204	205	205	612.85
83	–	84	84	84	348.76	110	–	200	200	200	628.25
84	–	83	83	83	425.76	111	–	212.5	211	214	650.92
85	–	82	82	82	292.54	112	–	195	195	195	556.26
86	–	83	81	83	356.49	113	–	207	207	207	588.06
87	–	80	80	80	435.97	114	–	204	204	204	655.70
88	–	78	78	78	285.89	115	–	206	206	208	498.43
89	–	82	82	82	313.02	116	–	206	206	206	652.08
90	–	81	81	81	416.23	117	–	212.5	212.5	216	647.54
91	76	76	76	76	208.18	118	–	187	187	187	430.56
92	–	76	76	76	239.70	119	–	181.4	181.5	183	412.39
93	–	78	78	78	341.14	120	–	175	175	175	434.29
94	–	77	77	77	207.87	121	–	182.6	183.4	184	381.11
95	–	78	77	78	246.38	122	–	176	176	176	427.44
96	–	77	77	77	319.33	123	–	183	181.5	183	423.03
97	–	76	76	76	207.59	124	–	177	176.6	177	361.37
98	–	73	73	73	253.26	125	–	182	182	182	432.76
99	–	81	81	81	263.51	126	–	174	174	174	437.62
100	63	63	63	63	152.86	127	–	176	175	176	205.59
101	–	67	67	67	156.37	128	–	187	187	187	262.79
102	–	68	68	68	140.16	129	–	183	187	187	282.10
103	65	65	65	65	151.75	130	–	179	179	179	252.82
104	–	67	67	67	202.37	131	–	179	179	179	263.21
105	–	68	68	68	194.93	132	–	180	181	184	284.48
106	–	68	68	68	120.83	133	–	180	180	180	255.53
107	–	66	66	66	162.23	134	–	183	183	183	267.43
108	–	67	67	67	182.30	135	–	171.5	172	176	283.86

Bold values show best results