A Mixed Integer Linear Formulation and a Grouping League Championship Algorithm for a Multiperiod-Multitrip Order Picking System with Product Replenishment to Minimize Total Tardiness

Table 4

Results on instances with 10 orders.

Instance	Periods	No. of picker	Capacity level	Optimal/best solution		GPSO					GLCA
				Objective function	Time (s)	Objective function			Average times (s)	GAP (%)	Objective function			Average times (s)	GAP (%)
						Min	Avg.	Max			Min	Avg.	Max
28	3	3	1	4	2.28	4	4	4	3.38	0	4	4	4	4.62	0
29			2	0	0.35	0	0	0	2.65	0	0	0	0	4.46	0
30			3	0	0.34	0	0	0	2.98	0	0	0	0	3.91	0
31		5	1	5	0.83	5	5	5	2.12	0	5	5	5	3.4	0
32			2	0	0.53	0	0	0	2.14	0	0	0	0	3.55	0
33			3	0	0.54	0	0	0	2.61	0	0	0	0	3.16	0
34		7	1	3	0.96	3	3	3	2.58	0	3	3	3	3.02	0
35			2	0	0.67	0	0	0	3.01	0	0	0	0	3.07	0
36			3	0	0.67	0	0	0	2.78	0	0	0	0	3.98	0
37	5	3	1	12	14.76	12	12	12	1.81	0	12	12	12	1.97	0
38			2	0	0.51	0	0	0	2.71	0	0	0	0	2.17	0
39			3	0	0.50	0	0	0	2.65	0	0	0	0	3.52	0
40		5	1	5	0.77	5	5	5	2.53	0	5	5	5	2.29	0
41			2	0	0.81	0	0	0	3.01	0	0	0	0	3.32	0
42			3	0	0.80	0	0	0	3.18	0	0	0	0	3.31	0
43		7	1	3	16.31	3	3	3	2.09	0	3	3	3	3.36	0
44			2	0	1.13	0	0	0	3.2	0	0	0	0	3.21	0
45			3	0	1.07	0	0	0	3.46	0	0	0	0	4.51	0
46	7	3	1	12	2.98	12	12	12	2.18	0	12	12	12	2.48	0
47			2	0	0.69	0	0	0	2.14	0	0	0	0	3.36	0
48			3	0	0.68	0	0	0	3	0	0	0	0	3.48	0
49		5	1	5	3.11	5	5	5	2.92	0	5	5	5	3.61	0
50			2	0	1.18	0	0	0	3.15	0	0	0	0	3.51	0
51			3	0	1.1	0	0	0	3.45	0	0	0	0	3.65	0
52		7	1	3	30.25	3	3	3	3.15	0	3	3	3	3.34	0
53			2	0	1.57	0	0	0	3.26	0	0	0	0	4.99	0
54			3	0	1.67	0	0	0	3.25	0	0	0	0	4.4	0
Avg.										0					0