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

Table 7

Occupied rectangular area in the heuristic Min Occupied Rectangular area.

Instance	Class	Number of customers	Number of items	CPLEX		SA		% gap
				Cost	Time (s)	Cost	Time (s)
P3	2	3	6	130.25	0.31	130.25	9.46	0.00
	3	3	6	130.25	0.38	130.25	15.96	0.00
	4	3	7	130.25	0.44	130.25	21.46	0.00
	5	3	12	130.25	0.84	130.25	34.86	0.00
P4	2	4	8	201.55	0.54	201.55	9.28	0.00
	3	4	7	188.10	0.58	188.10	15.07	0.00
	4	4	11	201.55	1.81	201.55	20.67	0.00
	5	4	13	201.55	2.21	201.55	39.76	0.00
P5	2	5	10	222.35	2.34	222.35	9.56	0.00
	3	5	9	237.52	1.97	237.52	22.05	0.00
	4	5	12	222.35	5.53	222.35	22.77	0.00
	5	5	17	222.35	15.08	222.35	44.13	0.00
P6	2	6	11	257.31	9.99	257.31	10.08	0.00
	3	6	11	257.31	8.60	257.31	18.83	0.00
	4	6	16	257.31	28.48	257.31	21.25	0.00
	5	6	18	257.31	34.61	257.31	25.92	0.00
P7	2	7	12	308.36	20.75	317.51	14.33	2.97
	3	7	12	308.36	39.11	318.81	12.73	3.39
	4	7	19	308.36	137.70	326.82	17.81	5.99
	5	7	23	308.36	440.71	317.51	12.84	2.97
P8	2	8	13	345.48	44.89	345.48	11.40	0.00
	3	8	15	371.76	146.19	371.76	12.43	0.00
	4	8	22	345.48	653.90	345.48	15.17	0.00
	5	8	26	345.48	2207.99	345.48	20.63	0.00
P9	2	9	15	406.73	473.62	406.73	8.42	0.00
	3	9	17	397.47	986.25	397.47	9.44	0.00
	4	9	24	394.97	3600.24	394.9	11.43	0.00
	5	9	30	429.88	3600.26	406.73	11.30	−5.39
P10	2	10	17	–	–	446.9	10.46	–
	3	10	29	453.43	3600.20	453.13	9.81	−0.07
	4	10	25	477.25	3600.33	430.86	14.39	−9.72
	5	10	33	–	–	430.86	17.55	–
Average					655.53		17.23	0.004