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 5

Results on instances with 20 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
55	3	3	1	15	1500	13	13	13	6.9	15.4	13	13	13	6.2	15.4
56			2	4	1500	2	2.6	4	10.6	53.8	2	2	2	11.5	100
57			3	0	1120.2	0	0	0	10.7	0	0	0	0	8.95	0
58		5	1	12	1500	10	10	10	9.6	20	10	10	10	10.5	20
59			2	3	1500	0	0	0	9.3	+	0	0	0	8.2	+
60			3	2	1500	0	0	0	18.9	+	0	0	0	15.9	+
61		7	1	19	971.2	19	19	19	14.7	0	19	19	19	14.3	0
62			2	2	1500	0	0	0	20.6	+	0	0	0	20.75	+
63			3	4	1500	0	0	0	24.5	+	0	0	0	22.7	+
64	5	3	1	28	1500	24	24	24	11.1	16.7	24	24	24	11.8	16.7
65			2	3	1500	2	2	2	25	50	2	2	2	26.2	50
66			3	5	1500	0	0	0	14.5	+	0	0	0	14	+
67		5	1	31	1500	30	30	30	22.5	3.3	30	30	30	22.6	3.3
68			2	2	1500	0	0	0	21.7	+	0	0	0	20.85	+
69			3	1	1500	0	0	0	30.9	+	0	0	0	33.8	+
70		7	1	20	1500	19	19	19	30	5.3	19	19	19	33.1	5.3
71			2	5	1500	0	0	0	32	+	0	0	0	34.55	+
72			3	4	1500	0	0	0	62.6	+	0	0	0	55.9	+
73	7	3	1	37	1321.6	37	37	37	25.1	0	37	37	37	22	0
74			2	3	1500	2	2	2	28.6	50	2	2	2	29.8	50
75			3	5	1500	0	0	0	32.2	+	0	0	0	27.4	+
76		5	1	34	1500	30	30	30	43.6	13.3	30	30	30	37.3	13.3
77			2	4	1500	0	0	0	26.0	+	0	0	0	24.25	+
78			3	6	1500	0	0	0	50.7	+	0	0	0	45.9	+
79		7	1	22	1500	19	19	19	50	15.8	19	19	19	43.5	15.8
80			2	4	1500	0	0	0	32.3	+	0	0	0	28.7	+
81			3	3	1500	0	0	0	79.0	+	0	0	0	73.65	+
Avg.															>22.3