A Modified Column Generation to Solve the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

Table 1

Data for problems.

Instance	Number of customers	Number of different type vehicles	Capacity	Fixed cost	Variable cost	Available number of vehicles of kind th
1	10	1	20	20	1	1
		2	30	40	1.1	1
		3	40	70	1.3	2
		4	70	200	1.7	1
2	15	1	30	60	1	1
		2	60	100	1.1	1
		3	80	250	1.5	1
		4	150	300	2	1
3	20	1	20	70	1	1
		2	35	120	1.1	2
		3	50	200	1.2	2
		4	120	250	2	3
4	25	1	25	50	1	2
		2	35	80	1.1	2
		3	50	200	1.2	3
		4	120	250	1.7	3
5	30	1	25	35	1	3
		2	35	50	1.1	2
		3	50	75	1.2	4
		4	120	150	1.7	4
6	35	1	50	60	0.7	1
		2	120	75	1	2
		3	160	200	1.1	3
7	40	1	60	20	1	3
		2	140	50	1.7	2
		3	200	120	2	1
8	45	1	50	20	1	2
		2	150	35	1.4	1
		3	200	50	1.4	1
		4	300	120	1.7	1
9	50	1	20	20	1	4
		2	30	35	1.1	2
		3	40	50	1.2	4
		4	70	120	1.7	4
		5	120	225	2.5	2
		6	200	400	3.2	1
10	50	1	120	100	1	4
		2	160	1500	1.1	2
		3	300	3500	1.4	1
11	50	1	50	100	1	4
		2	100	250	1.6	3
		3	160	450	2	2
12	50	1	40	100	1	2
		2	80	200	1.6	4
		3	140	400	2.1	3
13	55	1	20	10	1	2
		2	50	35	1.3	2
		3	100	100	1.9	2
		4	150	180	2.4	1
		5	250	400	2.9	1
		6	400	800	3.2	1
14	60	1	20	10	1	2
		2	50	35	1.3	2
		3	100	100	1.9	2
		4	150	180	2.4	1
		5	250	400	2.9	1
		6	400	800	3.2	1
15	65	1	20	10	1	1
		2	50	35	1.3	2
		3	100	100	1.9	2
		4	150	180	2.4	2
		5	250	400	2.9	1
		6	400	800	3.2	1
16	70	1	20	10	1	3
		2	50	35	1.1	3
		3	100	100	1.2	2
		4	150	180	1.4	2
		5	250	400	1.9	1
		6	400	800	2.2	1
17	75	1	20	10	1	4
		2	50	35	1.3	4
		3	100	100	1.9	2
		4	150	180	2.4	2
		5	250	400	2.9	1
		6	400	800	3.2	1
18	80	1	20	10	1	5
		2	50	35	1.3	6
		3	100	100	1.9	2
		4	150	180	2.4	2
		5	250	400	2.9	1
		6	400	800	3.2	1
19	85	1	20	10	1	5
		2	50	35	1.3	6
		3	100	100	1.9	3
		4	150	180	2.4	2
		5	250	400	2.9	1
		6	400	800	3.2	1
20	90	1	20	10	1	5
		2	40	25	1.2	5
		3	80	45	1.5	2
		4	100	80	2.0	2
21	95	1	20	10	1	5
		2	30	35	1.3	5
		3	70	55	1.7	3
		4	100	85	1.9	2
		5	150	135	2.3	2
22	100	1	100	500	1	4
		2	150	1200	1.4	4
		3	300	1900	1.7	5