MILP Model and a Rolling Horizon Algorithm for Crane Scheduling in a Hybrid Storage Container Terminal

Table 1

Computational results for small-scale instances.

No.	n	CPLEX		IGA		RHA		Gap^1	Gap^2
		1	8	5.99	168.16	6.09	50.15				6.09	3.38	-1.67	0.09	93.27
2	8	8.43	107.48	8.53	49.38	8.53	2.97	-1.13	0.00	93.99
3	8	7.28	98.24	7.42	52.12	7.41	3.19	-1.73	0.14	93.89
4	8	8.88	79.36	9.09	46.27	9.10	2.77	-2.48	-0.11	94.02
5	8	6.75	147.35	6.83	53.99	6.83	3.52	-1.08	0.00	93.48
6	8	8.15	198.83	8.28	47.59	8.26	2.80	-1.28	0.25	94.12
Average		7.58	133.24	7.71	49.92	7.70	3.10	-1.56	0.06	93.79
7	14	13.86	3083	15.07	174.36	14.31	9.15	-3.18	5.06	94.75
8	14	13.95	2809	14.79	167.79	14.25	7.95	-2.16	3.62	95.26
9	14	14.16	2987	15.02	171.09	14.60	9.88	-3.14	2.77	94.23
10	14	11.72	3108	13.09	157.08	12.19	10.11	-4.01	6.88	93.56
11	14	14.46	2968	16.26	176.76	14.98	9.12	-3.57	7.88	94.84
12	14	12.05	2876	12.74	170.07	12.47	11.27	-3.44	2.12	93.38
Average		13.37	2971.83	14.49	169.53	13.80	9.58	-3.25	4.72	94.34
13	20	18.46	18000	21.54	346.66	19.35	21.12	-4.81	10.18	93.91
14	20	26.74	16001	32.44	340.99	28.58	19.67	-6.85	11.91	94.23
15	20	31.77	15283	33.39	332.07	32.70	20.84	-2.94	2.07	93.72
16	20	20.80	17854	23.17	345.02	22.14	18.30	-6.41	4.48	94.70
17	20	37.89	14354	43.83	344.16	40.06	19.30	-5.72	8.61	94.39
18	20	31.30	14532	36.50	352.40	33.09	21.92	-5.69	9.35	93.78
Average		27.83	16004.00	31.81	343.55	29.32	20.19	-5.40	7.77	94.12
19	24	48.72	18000	54.33	504.98	46.11	44.84	5.36	15.13	91.12
20	24	46.73	18000	47.65	518.91	42.42	47.27	9.23	10.98	90.89
21	24	56.13	18000	59.38	505.72	52.14	48.35	7.11	12.19	90.44
22	24	56.66	18000	57.83	498.56	55.07	51.84	2.80	4.77	89.60
23	24	43.42	18000	44.43	522.57	39.41	48.44	9.22	11.30	90.73
24	24	44.19	18000	46.65	511.85	42.59	50.63	3.61	8.71	90.11
Average		49.31	18000.00	51.71	510.43	46.29	48.56	6.22	10.51	90.48
25	28	122.39	18000	142.24	702.98	113.57	119.67	7.20	20.15	82.98
26	28	118.42	18000	116.60	681.32	102.88	106.94	13.13	11.77	84.30
27	28	105.11	18000	104.30	682.48	97.45	112.43	7.29	6.57	83.53
28	28	149.28	18000	156.44	680.04	139.27	120.50	6.71	10.98	82.28
29	28	121.37	18000	123.49	676.77	104.94	104.81	13.53	15.02	84.51
30	28	140.07	18000	149.61	724.38	125.47	121.95	10.42	16.13	83.16
Average		126.11	18000.00	132.11	691.33	113.93	114.38	9.71	13.44	83.46
Average								1.14	7.30	91.24

Obj: objective function value; CPU: computation time (second).
Gap¹ = (-)/ (%).
Gap² = (-)/ (%).
= (-)/ (%).