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 6

Results on instances with 50 orders.

Instance	Periods	No. of picker	Capacity level	Optimal/best solution		GPSO				GLCA				GAP (%)
				Objective function	Time (s)	Objective function			Average times (s)	Objective function			Average times (s)
						Min	Avg.	Max		Min	Avg.	Max
82	3	3	1		1500	46	46	46	15.5	46	46	46	15.6	0
83			2		1500	46	46	46	40.7	46	46	46	39.7	0
84			3		1500	23	27.5	35	75.3	23	23	23	74.8	19.6
85		5	1		1500	40	40	40	43.3	40	40	40	36.4	0
86			2		1500	20	20	20	80.4	20	20	20	69.7	0
87			3		1500	5	8.75	11	145.2	5	5	5	145.9	75
88		7	1		1500	37	37	37	45.5	37	37	37	45	0
89			2		1500	8	8.75	11	64	8	8	8	66.8	9.4
90			3		1500	0	0.75	3	86.5	0	0	0	60.15	+
91	5	3	1		1500	80	80	80	25.3	80	80	80	24.2	0
92			2		1500	46	47.5	49	54.5	46	46	46	57.2	3.3
93			3		1500	26	31.75	36	102.3	23	23	23	112	38
94		5	1		1500	100	100	100	43.8	100	100	100	43.1	0
95			2		1500	20	20	20	104.7	20	20	20	115.5	0
96			3		1500	5	6.5	9	252.4	5	5	5	228.2	30
97		7	1		1500	66	66	66	109.9	66	66	66	101.4	0
98			2		1500	8	8	8	163.6	8	8	8	155.8	0
99			3		1500	0	0	0	138	0	0	0	128.45	0
100	7	3	1		1500	115	115	115	56.6	115	115	115	51.1	0
101			2		1500	46	47.5	50	59.9	46	46	46	66	3.3
102			3		1500	25	27.25	31	130.4	23	23	23	135.1	18.5
103		5	1		1500	100	100	100	71.6	100	100	100	76.1	0
104			2		1500	20	20	20	164.3	20	20	20	149.1	0
105			3		1500	5	5	5	273.2	5	5	5	266.4	0
106		7	1		1500	66	66	66	72.6	66	66	66	77.7	0
107			2		1500	8	8	8	195.4	8	8	8	176.3	0
108			3		1500	0	0	0	172.3	0	0	0	157.95	0
Avg.														>7.3

no feasible solution found.