An Integrated Approach for Shift Scheduling and Rostering Problems with Break Times for Inbound Call Centers
Table 11
Comparison of Model 2a and Model 2b for test problems.
Ins.
Inc. rate (%)
Model 2a (IP)
Model 2b (CP)
Obj.
Time (s)
No. of const.
No. of variab.
Obj.
Time (s) (fail lim.)
No. of const.
No. of variab.
1
10
123
27
Infeasible
No solution
15
127
27
Infeasible
No solution
20
129
27
Infeasible
No solution
25
134
27
Infeasible
No solution
26
141
27
13,536
139.66
331,764
444,186
13,536
0.34 (65.31)
39,846
17,034
30
142
27
13,632
131.67
331,764
444,186
13,632
0.39 (72.13)
40,074
17,146
2
10
173
38
Infeasible
No solution
15
186
38
17,856
222.32
409,314
541,283
17,856
0.75 (128.84)
70,969
30,992
3
10
223
51
Infeasible
No solution
15
240
51
Infeasible
No solution
20
243
51
Infeasible
No solution
23
257
51
24,672
367.77
500,964
656,034
24,672
0.96 (194.44)
124,906
56,210
25
257
51
24,672
362.65
500,964
656,034
24,672
1.04 (198.79)
124,906
56,210
4
10
316
66
Infeasible
No solution
15
330
66
Infeasible
No solution
20
342
66
Infeasible
No solution
25
350
66
Infeasible
No solution
26
357
66
34,272
566.91
606,714
788,439
34,272
1.20 (259.00)
213,933
99,108
30
372
66
35,712
559.43
606,714
788,439
35,712
1.26 (188.05)
222,033
103,128
5
10
344
78
Infeasible
No solution
15
360
78
Infeasible
No solution
19
371
78
35,616
778.32
691,314
894,363
35,616
2.65 (305.49)
262,823
121,604
20
371
78
35,616
834.24
691,314
894,363
35,616
2.49 (301.74)
262,823
121,604
6
10
338
78
Infeasible
No solution
15
358
78
Infeasible
No solution
19
367
78
35,232
856.23
691,314
894,363
35,232
2.67 (317.92)
259,342
120,184
20
367
78
35,232
861.55
691,314
894,363
35,232
2.55 (311.13)
259,342
120,184
7
10
413
90
Infeasible
No solution
15
433
90
Infeasible
No solution
20
448
90
Infeasible
No solution
22
459
90
44,064
1074.75
775,914
1,000,287
44,064
3.79 (313.65)
365,902
171,936
25
472
90
45,312
1133.63
775,914
1,000,287
45,312
4.05 (297.34)
375,418
176,668
8
10
413
109
Infeasible
No solution
15
433
109
Infeasible
No solution
20
448
109
Infeasible
No solution
22
459
109
44,064
1440.44
909,864
1,168,000
44,064
5.38 (416.09)
441,978
207,846
25
472
109
45,312
1616.64
909,864
1,168,000
45,312
4.59 (388.22)
453,470
213,566
9
10
611
135
Infeasible
No solution
15
640
135
Infeasible
No solution
20
667
135
64,032
2670.55
1,093,164
1,397,502
64,032
9.03 (504.03)
773,218
370,138
10
10
666
160
Infeasible
No solution
15
703
160
Infeasible
No solution
20
724
160
Infeasible
No solution
25
754
160
Infeasible
No solution
26
768
160
73,728
2967.78
1,269,414
1,618,177
73,728
12.44 (832.95)
1,045,410
503,232
30
789
160
75,744
3228.78
1,269,414
1,618,177
75,744
12.89 (826.12)
1,072,542
516,756
11
10
780
185
Infeasible
No solution
15
817
185
Infeasible
No solution
20
852
185
Timeout
No solution
25
889
185
Timeout
85,344
20.67 (930.82)
1,387,842
671,406
The results in bold are proved to be optimal. The increase rate (Inc. rate) corresponding to the lowest optimal value of the case. No integer solution found. Search terminated by limit, no solution found. Timeout (3600 seconds).
