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 3

Results on instances with 5 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
1	3	3	1	2	0.81	2	2	2	0.09	0	2	2	2	0.04	0
2			2	0	0.22	0	0	0	0.1	0	0	0	0	0.22	0
3			3	0	0.23	0	0	0	0.24	0	0	0	0	0.46	0
4		5	1	0	0.29	0	0	0	1.27	0	0	0	0	2.39	0
5			2	0	0.31	0	0	0	0.85	0	0	0	0	2.03	0
6			3	0	0.30	0	0	0	0.83	0	0	0	0	1.45	0
7		7	1	0	0.40	0	0	0	1.32	0	0	0	0	2.82	0
8			2	0	0.43	0	0	0	0.85	0	0	0	0	1.91	0
9			3	0	0.43	0	0	0	1.35	0	0	0	0	1.93	0
10	5	3	1	2	0.79	2	2	2	0.78	0	2	2	2	0.9	0
11			2	0	0.31	0	0	0	3.46	0	0	0	0	4.27	0
12			3	0	0.31	0	0	0	1.67	0	0	0	0	3.52	0
13		5	1	0	0.45	0	0	0	3.67	0	0	0	0	3.21	0
14			2	0	0.47	0	0	0	1.74	0	0	0	0	2.67	0
15			3	0	0.45	0	0	0	1.80	0	0	0	0	2.43	0
16		7	1	0	0.63	0	0	0	1.34	0	0	0	0	3.36	0
17			2	0	0.62	0	0	0	2.34	0	0	0	0	3.32	0
18			3	0	0.64	0	0	0	2.32	0	0	0	0	4.65	0
19	7	3	1	2	0.57	2	2	2	1.32	0	2	2	2	2.67	0
20			2	0	0.41	0	0	0	2.14	0	0	0	0	2.45	0
21			3	0	0.43	0	0	0	2.95	0	0	0	0	3.51	0
22		5	1	0	0.61	0	0	0	2.12	0	0	0	0	3.36	0
23			2	0	0.66	0	0	0	2.72	0	0	0	0	3.59	0
24			3	0	0.65	0	0	0	2.35	0	0	0	0	2.36	0
25		7	1	0	0.87	0	0	0	3.36	0	0	0	0	3.36	0
26			2	0	0.91	0	0	0	2.36	0	0	0	0	3.54	0
27			3	0	0.81	0	0	0	2.40	0	0	0	0	3.14	0
Avg.										0					0