An Integrated Approach for Shift Scheduling and Rostering Problems with Break Times for Inbound Call Centers

Table 12

Comparison of our model and other models in [8] for benchmark instances.

					Ejection Chain		Branch and Price		Gurobi 5.6.3		Our Proposed CP Model
Ins.	W	St.	Sh.	LB	10 min.	60 min.	Sol.	Time (s)	Sol.	Time (s)	Sol.	Time (s)	First Time (s)
#1	2	8	1	607	607	607	607	0.27	607	1.62	607	0.75	0.75
#2	2	14	2	828	923	837	828	0.13	828	5.22	828	62.69	62.69
#3	2	20	3	1001	1003	1003	1001	0.45	1001	13.54	1001	158.33	158.33
#4	4	10	2	1716	1719	1718	1716	1.50	1716	158.99	1716	518.48	518.48
#5	4	16	2	1143	1439	1358	1160	25.61	1143	1520.24	1180	3600.15	722.62
#6	4	18	3	1950	2344	2258	1952	10.46	1950	440.93	2014	3600.59	3588.83
#7	4	20	3	1056	1284	1269	1058	93.73	1056	2152.48	1091	3600.50	3196.73
#8	4	30	4	1281	2529	2260	1308	3600.00	1323	3599.83	1522	3601.76	3581.42
#9	4	36	4	247	474	463	439	76.99	439	3599.85	452	3602.85	3164.02
#10	4	40	5	4631	4999	4797	4631	113.44	4631	244.20	4666	3604.51	3572.05
#11	4	50	6	3443	3967	3661	3443	19.11	3443	109.92	3455	3610.79	3507.97
#12	4	60	10	4040	5611	5211	4046	1336.4	4040	2303.84	4409	3676.93	2998.03
#13	4	120	18	1346	8707	3037	Out of Memory		3109	3600.55	Out of Memory
#14	6	32	4	1277	2542	1847	Out of Memory		1280	3600.13	1345	3606.70	3531.89
#15	6	45	6	3806	6049	5935	Out of Memory		4964	3600.00	4548	3625.62	3317.59
#16	8	20	3	3211	4343	4048	3323	265.02	3233	3599.99	3332	3601.62	3580.48
#17	8	32	4	5726	7835	7835	Out of Memory		5851	3600.00	5911	3607.98	3569.21
#18	12	22	3	4351	6404	6404	Out of Memory		4760	3599.99	4668	3604.73	3587.60
#19	12	40	5	2945	6522	5531	Out of Memory		5420	3605.90	4900	3626.12	3404.58
#20	26	50	6	4743	23531	9750	Out of Memory		-	3600.05	Out of Memory
#21	26	100	8	20868	38294	36688	Out of Memory		-	3600.21	Out of Memory
#22	52	50	10	-	-	516686	Out of Memory		-	3600.19	Out of Memory
#23	52	100	16	-	-	54384	Out of Memory		-	3600.43	Out of Memory
#24	52	150	32	?	-	156858	Out of Memory		Out of Memory		Out of Memory

Known optimal solutions are in bold.
W= Number of Weeks, St.= Number of Staff, Sh.= Number of Shift Type, LB=Best Known Lower Bound.