Mathematical Model and Simulated Annealing Algorithm for the Two-Dimensional Loading Heterogeneous Fixed Fleet Vehicle Routing Problem

Table 6

Comparison of results of CPLEX and SA on small-scale unrestricted 2L-HFFVRP of classes 2–5.

Instance	Class	Number of customers	Number of items	CPLEX		SA		% gap
				Cost	Time (s)	Cost	Time (s)
P3	2	3	6	130.25	0.43	130.25	17.42	0.00
	3	3	6	130.25	0.32	130.25	32.17	0.00
	4	3	7	130.25	0.34	130.25	30.95	0.00
	5	3	12	130.25	0.55	130.25	38.95	0.00
P4	2	4	8	201.55	0.67	201.55	20.56	0.00
	3	4	7	188.10	0.54	188.10	27.06	0.00
	4	4	11	201.55	0.52	201.55	34.36	0.00
	5	4	13	201.55	0.46	201.55	39.67	0.00
P5	2	5	10	222.35	0.49	222.35	21.37	0.00
	3	5	9	237.52	0.54	237.52	12.98	0.00
	4	5	12	222.35	0.66	222.35	28.92	0.00
	5	5	17	222.35	1.71	222.35	32.52	0.00
P6	2	6	11	257.31	0.93	257.31	12.53	0.00
	3	6	11	257.31	1.17	257.31	24.44	0.00
	4	6	16	257.31	2.17	257.31	23.63	0.00
	5	6	18	257.31	3.37	257.31	16.13	0.00
P7	2	7	12	308.36	2.84	317.51	27.03	2.97
	3	7	12	308.36	3.69	318.81	12.44	3.39
	4	7	19	308.36	8.65	318.81	19.92	3.39
	5	7	23	308.36	13.38	317.51	22.64	2.97
P8	2	8	13	345.48	2.86	345.48	11.63	0.00
	3	8	15	371.76	8.27	371.76	13.86	0.00
	4	8	22	345.48	15.68	345.48	31.64	0.00
	5	8	26	345.48	46.06	345.48	17.40	0.00
P9	2	9	15	406.73	6.54	406.73	9.28	0.00
	3	9	17	397.47	64.76	397.47	26.43	0.00
	4	9	24	394.97	75.75	394.97	11.27	0.00
	5	9	30	394.97	996.45	397.46	6.98	0.63
P10	2	10	17	446.91	223.98	446.91	11.13	0.00
	3	10	29	442.88	3600.04	453.13	11.74	2.31
	4	10	25	422.04	2444.98	430.86	15.11	2.09
	5	10	33	430.86	3600.09	439.00	12.25	1.89
Average					347.78		21.08	0.61