The following tables show the summary of the evaluation results compared with Gurobi9.01 and Cplex12.9.
All project files and related mps/lp files can be found on the Github.
Time is the best arrival time, not exact solution time.
|
Weeks |
Employees |
Cplex Value |
Gurobi Value |
Schedule Nurse ⅢValue |
Cplex Time(sec) |
Gurobi Time(sec) |
Schedule Nurse Ⅲ (sec) |
Millar-2Shift-DATA1.1 |
2 |
8 |
0 |
0 |
0 |
0.41 |
0.4 |
0.167 |
Millar-2Shift-DATA1 |
2 |
8 |
0 |
0 |
0 |
0.4 |
0.25 |
0.174 |
SINTEF |
3 |
24 |
0 |
0 |
0 |
3.57 |
3.48 |
4 |
Ozkarahan |
1 |
14 |
0 |
0 |
0 |
0.03 |
0.02 |
0.13 |
Musa |
2 |
11 |
175 |
175 |
175 |
0.01 |
0.02 |
10 |
Gpost-B |
4 |
8 |
3 |
3 |
3 |
351 |
83 |
7.75 |
Gpost |
4 |
8 |
5 |
5 |
5 |
206 |
29.93 |
7 |
LLR |
1 |
27 |
301 |
301 |
301 |
5.04 |
5.77 |
4 |
Azaiez |
4 |
13 |
0 |
0 |
0 |
9 |
2.93 |
6 |
BCDT-Sep |
4 |
20 |
170 |
150 |
100 |
|
23138 |
965 |
BCV-4.13.1 |
4 |
13 |
10 |
10 |
10 |
5.17 |
0.78 |
14.35 |
QMC-1 |
4 |
19 |
13 |
13 |
13 |
5.2 |
3.62 |
8 |
WHPP |
2 |
30 |
1001 |
1001 |
5 |
6314 |
9874 |
21 |
Valouxis-1 |
4 |
16 |
20 |
20 |
20 |
900 |
282 |
11.5 |
ikegami-2Shift-DATA1 |
4 |
28 |
0 |
0 |
0 |
20.22 |
4.91 |
5 |
ikegami-3Shift-DATA1 |
4 |
25 |
2 |
2 |
2 |
1630 |
170 |
9.4 |
ikegami-3Shift-DATA1.1 |
4 |
25 |
3 |
3 |
3 |
|
378 |
11 |
ikegami-3Shift-DATA1.2 |
4 |
25 |
3 |
3 |
3 |
|
425 |
11.3 |
|
|
|
|
|
|
|
|
|
References
-
Asta, S., Özcan, E., and Curtois, T. A tensor based hyper-heuristic for nurse rostering. Knowledge-based systems, 2016. 98: p. 185-199.
-
Burke E.K. and T. Curtois. New Approaches to Nurse Rostering Benchmark Instances. European Journal of Operational Research, 2014. 237(1): p. 71-81. pdf.
-
Solos, Ioannis P., Ioannis X. Tassopoulos and Grigorios N. Beligiannis. A Generic Two-Phase Stochastic Variable Neighborhood Approach for Effectively Solving the Nurse Rostering Problem. Algorithms, 2013. 6: p. 278-308.
Cplex 12.9 NEOS 8h timeout
|
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
sprint_early_01 |
4 |
10 |
56 |
56 |
1.59 |
sprint_early_02 |
4 |
10 |
58 |
58 |
1.93 |
sprint_early_03 |
4 |
10 |
51 |
51 |
1.43 |
sprint_early_04 |
4 |
10 |
59 |
59 |
1.78 |
sprint_early_05 |
4 |
10 |
58 |
58 |
3.52 |
sprint_early_06 |
4 |
10 |
54 |
54 |
1.83 |
sprint_early_07 |
4 |
10 |
56 |
56 |
1.06 |
sprint_early_08 |
4 |
10 |
56 |
56 |
0.83 |
sprint_early_09 |
4 |
10 |
55 |
55 |
0.59 |
sprint_early_10 |
4 |
10 |
52 |
52 |
0.84 |
|
|
|
|
|
|
sprint_hidden_01 |
4 |
10 |
32 |
32 |
64.04 |
sprint_hidden_02 |
4 |
10 |
32 |
32 |
4.49 |
sprint_hidden_03 |
4 |
10 |
62 |
62 |
10.87 |
sprint_hidden_04 |
4 |
10 |
66 |
66 |
75 |
sprint_hidden_05 |
4 |
10 |
59 |
59 |
17.34 |
sprint_hidden_06 |
4 |
10 |
130 |
130 |
9.51 |
sprint_hidden_07 |
4 |
10 |
153 |
153 |
4.45 |
sprint_hidden_08 |
4 |
10 |
204 |
204 |
9.79 |
sprint_hidden_09 |
4 |
10 |
338 |
338 |
65.33 |
sprint_hidden_10 |
4 |
10 |
306 |
306 |
9.01 |
|
|
|
|
|
|
sprint_late_01 |
4 |
10 |
37 |
37 |
10.01 |
sprint_late_02 |
4 |
10 |
42 |
42 |
4.2 |
sprint_late_03 |
4 |
10 |
48 |
48 |
8.62 |
sprint_late_04 |
4 |
10 |
73 |
73 |
84.96 |
sprint_late_05 |
4 |
10 |
44 |
44 |
8.22 |
sprint_late_06 |
4 |
10 |
42 |
42 |
4.87 |
sprint_late_07 |
4 |
10 |
42 |
42 |
10.18 |
sprint_late_08 |
4 |
10 |
17 |
17 |
98.17 |
sprint_late_09 |
4 |
10 |
17 |
17 |
213 |
sprint_late_10 |
4 |
10 |
43 |
43 |
10.68 |
|
|
|
|
|
|
|
|
|
|
|
|
medium_early_01 |
4 |
31 |
240 |
240 |
37.3 |
medium_early_02 |
4 |
31 |
240 |
240 |
21.26 |
medium_early_03 |
4 |
31 |
236 |
236 |
22.54 |
medium_early_04 |
4 |
31 |
237 |
237 |
34.88 |
medium_early_05 |
4 |
31 |
303 |
303 |
71.86 |
|
|
|
|
|
|
medium_late_01 |
4 |
30 |
148 |
157 |
|
medium_late_02 |
4 |
30 |
18 |
18 |
761 |
medium_late_03 |
4 |
30 |
24 |
30 |
|
medium_late_04 |
4 |
30 |
33 |
35 |
|
medium_late_05 |
4 |
30 |
101 |
108 |
|
|
|
|
|
|
|
medium_hidden_01 |
4 |
30 |
37 |
119 |
|
medium_hidden_02 |
4 |
30 |
113 |
219 |
|
medium_hidden_03 |
4 |
30 |
|
35 |
|
medium_hidden_04 |
4 |
30 |
32 |
80 |
|
medium_hidden_05 |
4 |
30 |
58 |
119 |
|
|
|
|
|
|
|
long_early_01 |
4 |
49 |
197 |
197 |
13.05 |
long_early_02 |
4 |
49 |
219 |
219 |
48.9 |
long_early_03 |
4 |
49 |
240 |
240 |
9.73 |
long_early_04 |
4 |
49 |
303 |
303 |
20.5 |
long_early_05 |
4 |
49 |
284 |
284 |
22.95 |
|
|
|
|
|
|
long_late_01 |
4 |
50 |
88 |
238 |
|
long_late_02 |
4 |
50 |
88 |
233 |
|
long_late_03 |
4 |
50 |
73 |
232 |
|
long_late_04 |
4 |
50 |
191 |
222 |
|
long_late_05 |
4 |
50 |
72 |
83 |
|
|
|
|
|
|
|
long_hidden_01 |
4 |
50 |
377 |
435 |
|
long_hidden_02 |
4 |
50 |
86 |
94 |
|
long_hidden_03 |
4 |
50 |
9 |
47 |
|
long_hidden_04 |
4 |
50 |
13 |
22 |
|
long_hidden_05 |
4 |
50 |
31 |
42 |
|
References
- http://www.goal.ufop.br/nrp/
Gurobi 9.01 NEOS 8h timeout
|
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
sprint_early_01 |
4 |
10 |
56 |
56 |
0.68 |
sprint_early_02 |
4 |
10 |
58 |
58 |
0.79 |
sprint_early_03 |
4 |
10 |
51 |
51 |
0.69 |
sprint_early_04 |
4 |
10 |
59 |
59 |
1.11 |
sprint_early_05 |
4 |
10 |
58 |
58 |
1.14 |
sprint_early_06 |
4 |
10 |
54 |
54 |
0.54 |
sprint_early_07 |
4 |
10 |
56 |
56 |
0.67 |
sprint_early_08 |
4 |
10 |
56 |
56 |
1.02 |
sprint_early_09 |
4 |
10 |
55 |
55 |
0.64 |
sprint_early_10 |
4 |
10 |
52 |
52 |
1.03 |
|
|
|
|
|
|
sprint_hidden_01 |
4 |
10 |
32 |
32 |
37.69 |
sprint_hidden_02 |
4 |
10 |
32 |
32 |
7.22 |
sprint_hidden_03 |
4 |
10 |
62 |
62 |
4.72 |
sprint_hidden_04 |
4 |
10 |
66 |
66 |
32.3 |
sprint_hidden_05 |
4 |
10 |
59 |
59 |
86.36 |
sprint_hidden_06 |
4 |
10 |
130 |
130 |
7.23 |
sprint_hidden_07 |
4 |
10 |
153 |
153 |
4.41 |
sprint_hidden_08 |
4 |
10 |
204 |
204 |
37.5 |
sprint_hidden_09 |
4 |
10 |
338 |
338 |
27.8 |
sprint_hidden_10 |
4 |
10 |
306 |
306 |
5.17 |
|
|
|
|
|
|
sprint_late_01 |
4 |
10 |
37 |
37 |
11.63 |
sprint_late_02 |
4 |
10 |
42 |
42 |
6.17 |
sprint_late_03 |
4 |
10 |
48 |
48 |
7.93 |
sprint_late_04 |
4 |
10 |
73 |
73 |
40.04 |
sprint_late_05 |
4 |
10 |
44 |
44 |
4.45 |
sprint_late_06 |
4 |
10 |
42 |
42 |
1.6 |
sprint_late_07 |
4 |
10 |
42 |
42 |
3.87 |
sprint_late_08 |
4 |
10 |
17 |
17 |
10.94 |
sprint_late_09 |
4 |
10 |
17 |
17 |
12.84 |
sprint_late_10 |
4 |
10 |
43 |
43 |
3.38 |
|
|
|
|
|
|
|
|
|
|
|
|
medium_early_01 |
4 |
31 |
240 |
240 |
6.22 |
medium_early_02 |
4 |
31 |
240 |
240 |
13.65 |
medium_early_03 |
4 |
31 |
236 |
236 |
6.08 |
medium_early_04 |
4 |
31 |
237 |
237 |
15.3 |
medium_early_05 |
4 |
31 |
303 |
303 |
47.42 |
|
|
|
|
|
|
medium_late_01 |
4 |
30 |
157 |
157 |
3103 |
medium_late_02 |
4 |
30 |
18 |
18 |
285 |
medium_late_03 |
4 |
30 |
29 |
29 |
2902 |
medium_late_04 |
4 |
30 |
35 |
35 |
889 |
medium_late_05 |
4 |
30 |
107 |
107 |
827 |
|
|
|
|
|
|
medium_hidden_01 |
4 |
30 |
53 |
116 |
|
medium_hidden_02 |
4 |
30 |
195 |
220 |
|
medium_hidden_03 |
4 |
30 |
17 |
35 |
|
medium_hidden_04 |
4 |
30 |
53 |
83 |
|
medium_hidden_05 |
4 |
30 |
73 |
122 |
|
|
|
|
|
|
|
long_early_01 |
4 |
49 |
197 |
197 |
3.67 |
long_early_02 |
4 |
49 |
219 |
219 |
40.6 |
long_early_03 |
4 |
49 |
240 |
240 |
3.17 |
long_early_04 |
4 |
49 |
303 |
303 |
6.55 |
long_early_05 |
4 |
49 |
284 |
284 |
4.74 |
|
|
|
|
|
|
long_late_01 |
4 |
50 |
235 |
235 |
7471 |
long_late_02 |
4 |
50 |
229 |
229 |
4686 |
long_late_03 |
4 |
50 |
220 |
220 |
18139 |
long_late_04 |
4 |
50 |
221 |
221 |
14865 |
long_late_05 |
4 |
50 |
|
|
|
|
|
|
|
|
|
long_hidden_01 |
4 |
50 |
343 |
346 |
|
long_hidden_02 |
4 |
50 |
88 |
89 |
|
long_hidden_03 |
4 |
50 |
30 |
38 |
|
long_hidden_04 |
4 |
50 |
22 |
22 |
16032 |
long_hidden_05 |
4 |
50 |
41 |
41 |
15747 |
Scehdule Nurse Ⅲ
|
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
sprint_early_01 |
4 |
10 |
56 |
56 |
3.56 |
sprint_early_02 |
4 |
10 |
58 |
58 |
4.1 |
sprint_early_03 |
4 |
10 |
51 |
51 |
3.46 |
sprint_early_04 |
4 |
10 |
59 |
59 |
3.94 |
sprint_early_05 |
4 |
10 |
58 |
58 |
38 |
sprint_early_06 |
4 |
10 |
54 |
54 |
3.8 |
sprint_early_07 |
4 |
10 |
56 |
56 |
3.43 |
sprint_early_08 |
4 |
10 |
56 |
56 |
6.57 |
sprint_early_09 |
4 |
10 |
55 |
55 |
3.78 |
sprint_early_10 |
4 |
10 |
52 |
52 |
3.46 |
|
|
|
|
|
|
sprint_hidden_01 |
4 |
10 |
32 |
32 |
3.89 |
sprint_hidden_02 |
4 |
10 |
32 |
32 |
3 |
sprint_hidden_03 |
4 |
10 |
62 |
62 |
3.96 |
sprint_hidden_04 |
4 |
10 |
66 |
66 |
11.17 |
sprint_hidden_05 |
4 |
10 |
59 |
59 |
6.7 |
sprint_hidden_06 |
4 |
10 |
130 |
130 |
4.15 |
sprint_hidden_07 |
4 |
10 |
153 |
153 |
3.85 |
sprint_hidden_08 |
4 |
10 |
204 |
204 |
6.9 |
sprint_hidden_09 |
4 |
10 |
338 |
338 |
9.6 |
sprint_hidden_10 |
4 |
10 |
306 |
306 |
8.4 |
|
|
|
|
|
|
sprint_late_01 |
4 |
10 |
37 |
37 |
5.1 |
sprint_late_02 |
4 |
10 |
42 |
42 |
4.3 |
sprint_late_03 |
4 |
10 |
48 |
48 |
7.3 |
sprint_late_04 |
4 |
10 |
73 |
73 |
7.14 |
sprint_late_05 |
4 |
10 |
44 |
44 |
43 |
sprint_late_06 |
4 |
10 |
42 |
42 |
6.2 |
sprint_late_07 |
4 |
10 |
42 |
42 |
9.5 |
sprint_late_08 |
4 |
10 |
17 |
17 |
6.1 |
sprint_late_09 |
4 |
10 |
17 |
17 |
5.6 |
sprint_late_10 |
4 |
10 |
43 |
43 |
4.75 |
|
|
|
|
|
|
|
|
|
|
|
|
medium_early_01 |
4 |
31 |
240 |
240 |
74 |
medium_early_02 |
4 |
31 |
240 |
240 |
26 |
medium_early_03 |
4 |
31 |
236 |
236 |
98 |
medium_early_04 |
4 |
31 |
237 |
237 |
35 |
medium_early_05 |
4 |
31 |
303 |
303 |
186 |
|
|
|
|
|
|
medium_late_01 |
4 |
30 |
157 |
157 |
154 |
medium_late_02 |
4 |
30 |
18 |
18 |
13 |
medium_late_03 |
4 |
30 |
29 |
29 |
103 |
medium_late_04 |
4 |
30 |
35 |
35 |
16.9 |
medium_late_05 |
4 |
30 |
107 |
107 |
38 |
|
|
|
|
|
|
medium_hidden_01 |
4 |
30 |
106 |
111 |
28800 |
medium_hidden_02 |
4 |
30 |
213 |
219 |
28800 |
medium_hidden_03 |
4 |
30 |
34 |
34 |
310 |
medium_hidden_04 |
4 |
30 |
76 |
78 |
28800 |
medium_hidden_05 |
4 |
30 |
118 |
118 |
751 |
|
|
|
|
|
|
long_early_01 |
4 |
49 |
197 |
197 |
74.5 |
long_early_02 |
4 |
49 |
219 |
219 |
230 |
long_early_03 |
4 |
49 |
240 |
240 |
59 |
long_early_04 |
4 |
49 |
303 |
303 |
113 |
long_early_05 |
4 |
49 |
284 |
284 |
179 |
|
|
|
|
|
|
long_late_01 |
4 |
50 |
235 |
235 |
374 |
long_late_02 |
4 |
50 |
229 |
229 |
319 |
long_late_03 |
4 |
50 |
219 |
220 |
28800 |
long_late_04 |
4 |
50 |
221 |
221 |
409 |
long_late_05 |
4 |
50 |
83 |
83 |
300 |
|
|
|
|
|
|
long_hidden_01 |
4 |
50 |
346 |
346 |
380 |
long_hidden_02 |
4 |
50 |
89 |
89 |
384 |
long_hidden_03 |
4 |
50 |
38 |
38 |
419 |
long_hidden_04 |
4 |
50 |
22 |
22 |
92 |
long_hidden_05 |
4 |
50 |
41 |
41 |
61 |
Cplex 12.9 NEOS 8h timeout
Instance Name |
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
instance1 |
2 |
8 |
607 |
607 |
0.19 |
instance2 |
2 |
14 |
828 |
828 |
0.64 |
instance3 |
2 |
20 |
1001 |
1001 |
1.54 |
instance4 |
4 |
10 |
1716 |
1716 |
6.76 |
instance5 |
4 |
16 |
1143 |
1143 |
20.85 |
instance6 |
4 |
18 |
1950 |
1950 |
10.27 |
instance7 |
4 |
20 |
1056 |
1056 |
55.84 |
instance8 |
4 |
30 |
1300 |
1300 |
2423 |
instance9 |
4 |
36 |
memory out |
439 |
|
instance10 |
4 |
40 |
4631 |
4631 |
57.45 |
instance11 |
4 |
50 |
3443 |
3443 |
27.1 |
instance12 |
4 |
60 |
4040 |
4040 |
549 |
instance13 |
4 |
120 |
|
|
|
instance14 |
6 |
32 |
1278 |
1278 |
3928 |
instance15 |
6 |
45 |
memory out |
4313 |
|
instance16 |
8 |
20 |
3225 |
3225 |
2939 |
instance17 |
8 |
32 |
5746 |
5746 |
6852 |
instance18 |
12 |
22 |
4459 |
4459 |
13121 |
instance19 |
12 |
40 |
3145.7 |
3157 |
|
instance20 |
26 |
50 |
Not feasible |
|
|
Gurobi 9.01 NEOS 8h timeout
Instance Name |
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
instance1 |
2 |
8 |
607 |
607 |
0.36 |
instance2 |
2 |
14 |
828 |
828 |
0.63 |
instance3 |
2 |
20 |
1001 |
1001 |
1.55 |
instance4 |
4 |
10 |
1716 |
1716 |
16.64 |
instance5 |
4 |
16 |
1143 |
1143 |
42.73 |
instance6 |
4 |
18 |
1950 |
1950 |
11.52 |
instance7 |
4 |
20 |
1056 |
1056 |
30.57 |
instance8 |
4 |
30 |
1300 |
1300 |
3445 |
instance9 |
4 |
36 |
406 |
439 |
|
instance10 |
4 |
40 |
4631 |
4631 |
90.06 |
instance11 |
4 |
50 |
3443 |
3443 |
93.43 |
instance12 |
4 |
60 |
4040 |
4040 |
243 |
instance13 |
4 |
120 |
|
|
|
instance14 |
6 |
32 |
1278 |
1278 |
378 |
instance15 |
6 |
45 |
3826 |
3836 |
|
instance16 |
8 |
20 |
3225 |
3225 |
76.7 |
instance17 |
8 |
32 |
5746 |
5746 |
173 |
instance18 |
12 |
22 |
4459 |
4459 |
1351 |
instance19 |
12 |
40 |
3149 |
3149 |
4101 |
instance20 |
26 |
50 |
4769 |
4769 |
6371 |
Scehdule Nurse Ⅲ
Instance Name |
Weeks |
Employees |
LB |
UB |
Exact Solution Time(sec) |
instance1 |
2 |
8 |
607 |
607 |
3 |
instance2 |
2 |
14 |
828 |
828 |
1.76 |
instance3 |
2 |
20 |
1001 |
1001 |
2.81 |
instance4 |
4 |
10 |
1716 |
1716 |
1.59 |
instance5 |
4 |
16 |
1143 |
1143 |
7.89 |
instance6 |
4 |
18 |
1950 |
1950 |
4.17 |
instance7 |
4 |
20 |
1056 |
1056 |
16 |
instance8 |
4 |
30 |
1300 |
1300 |
217 |
instance9 |
4 |
36 |
406 |
439 |
28800 |
instance10 |
4 |
40 |
4631 |
4631 |
51.8 |
instance11 |
4 |
50 |
3443 |
3443 |
47 |
instance12 |
4 |
60 |
4040 |
4040 |
489 |
instance13 |
4 |
120 |
|
|
|
instance14 |
6 |
32 |
1278 |
1278 |
30 |
instance15 |
6 |
45 |
3829 |
3832 |
19564 |
instance16 |
8 |
20 |
3225 |
3225 |
33 |
instance17 |
8 |
32 |
5746 |
5746 |
28 |
instance18 |
12 |
22 |
4419 |
4466 |
28800 |
instance19 |
12 |
40 |
3148 |
3150 |
28800 |
instance20 |
26 |
50 |
4769 |
4769 |
23500 |
References
- Strandmark, P., Qu, Y. and Curtois, T. First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem. Computers & Operations Research, 2020. 120, p. 104945. (pdf)
- Demirović, E., Musliu, N., and Winter, F. Modeling and solving staff scheduling with partial weighted maxSAT. Annals of Operations Research, 2019. 275(1): p. 79-99.
- Smet P. Constraint reformulation for nurse rostering problems, in: PATAT 2018 twelfth international conference on the practice and theory of automated timetabling, Vienna, August, 2018, p. 69-80.
- Rahimian, E., Akartunalı, K., and Levine, J. A hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems. European Journal of Operational Research, 2017. 258(2): p. 411-423.
4Weeks
Instance |
Weeks |
Employees |
LB |
UB |
GAP |
n030w4 1 6-2-9-1 |
4 |
30 |
1615 |
1685 |
4.33% |
n030w4 1 6-7-5-3 |
4 |
30 |
1740 |
1840 |
5.75% |
n035w4 0 1-7-1-8 |
4 |
35 |
1250 |
1415 |
13.20% |
n035w4 2 8-8-7-5 |
4 |
35 |
1045 |
1145 |
9.57% |
n040w4 0 2-0-6-1 |
4 |
40 |
1335 |
1640 |
22.85% |
n040w4 2 6-1-0-6 |
4 |
40 |
1570 |
1865 |
18.79% |
n050w4 0 0-4-8-7 |
4 |
50 |
1195 |
1445 |
20.92% |
n050w4 0 7-2-7-2 |
4 |
50 |
1200 |
1405 |
17.08% |
n060w4 1 6-1-1-5 |
4 |
60 |
2380 |
2465 |
3.57% |
n060w4 1 9-6-3-8 |
4 |
60 |
2615 |
2730 |
4.40% |
n070w4 0 3-6-5-1 |
4 |
70 |
2280 |
2430 |
6.58% |
n070w4 0 4-9-6-7 |
4 |
70 |
1990 |
2125 |
6.78% |
n080w4 2 4-3-3-3 |
4 |
80 |
3140 |
3320 |
5.73% |
n080w4 2 6-0-4-8 |
4 |
80 |
3045 |
3240 |
6.40% |
n100w4 0 1-1-0-8 |
4 |
100 |
1055 |
1230 |
16.59% |
n100w4 2 0-6-4-6 |
4 |
100 |
1470 |
1855 |
26.19% |
n110w4 0 1-4-2-8 |
4 |
110 |
2210 |
2390 |
8.14% |
n110w4 0 1-9-3-5 |
4 |
110 |
2255 |
2525 |
11.97% |
n120w4 1 4-6-2-6 |
4 |
120 |
1790 |
2165 |
20.95% |
n120w4 1 5-6-9-8 |
4 |
120 |
1820 |
2220 |
21.98% |
Schedule Nurse Ⅲ
Instance |
Weeks |
Employees |
LB |
UB |
GAP |
n030w4 1 6-2-9-1 |
4 |
30 |
1670 |
1670 |
0.00% |
n030w4 1 6-7-5-3 |
4 |
30 |
1815 |
1815 |
0.00% |
n035w4 0 1-7-1-8 |
4 |
35 |
1360 |
1360 |
0.00% |
n035w4 2 8-8-7-5 |
4 |
35 |
1080 |
1080 |
0.00% |
n040w4 0 2-0-6-1 |
4 |
40 |
1536 |
1565 |
1.89% |
n040w4 2 6-1-0-6 |
4 |
40 |
1750 |
1750 |
0.00% |
n050w4 0 0-4-8-7 |
4 |
50 |
1296 |
1320 |
1.85% |
n050w4 0 7-2-7-2 |
4 |
50 |
1303 |
1315 |
0.92% |
n060w4 1 6-1-1-5 |
4 |
60 |
2455 |
2455 |
0.00% |
n060w4 1 9-6-3-8 |
4 |
60 |
2675 |
2675 |
0.00% |
n070w4 0 3-6-5-1 |
4 |
70 |
2371 |
2380 |
0.38% |
n070w4 0 4-9-6-7 |
4 |
70 |
2105 |
2115 |
0.48% |
n080w4 2 4-3-3-3 |
4 |
80 |
3292 |
3300 |
0.24% |
n080w4 2 6-0-4-8 |
4 |
80 |
3178 |
3190 |
0.38% |
n100w4 0 1-1-0-8 |
4 |
100 |
1170 |
1170 |
0.00% |
n100w4 2 0-6-4-6 |
4 |
100 |
1790 |
1790 |
0.00% |
n110w4 0 1-4-2-8 |
4 |
110 |
2322 |
2330 |
0.34% |
n110w4 0 1-9-3-5 |
4 |
110 |
2455 |
2455 |
0.00% |
n120w4 1 4-6-2-6 |
4 |
120 |
2020 |
2020 |
0.00% |
n120w4 1 5-6-9-8 |
4 |
120 |
2050 |
2050 |
0.00% |
Gurobi 9.01(NEOS 8hours)
Instance |
Weeks |
Employees |
LB |
UB |
GAP |
n030w4 1 6-2-9-1 |
4 |
30 |
|
1670 |
#VALUE! |
n030w4 1 6-7-5-3 |
4 |
30 |
1772 |
1840 |
3.84% |
n035w4 0 1-7-1-8 |
4 |
35 |
1122 |
1435 |
27.90% |
n035w4 2 8-8-7-5 |
4 |
35 |
841 |
1165 |
38.53% |
n040w4 0 2-0-6-1 |
4 |
40 |
1298 |
1610 |
24.04% |
n040w4 2 6-1-0-6 |
4 |
40 |
1545 |
1790 |
15.86% |
n050w4 0 0-4-8-7 |
4 |
50 |
|
|
#VALUE! |
n050w4 0 7-2-7-2 |
4 |
50 |
1070 |
1410 |
31.78% |
n060w4 1 6-1-1-5 |
4 |
60 |
1980 |
2995 |
51.26% |
n060w4 1 9-6-3-8 |
4 |
60 |
2099 |
3090 |
47.21% |
n070w4 0 3-6-5-1 |
4 |
70 |
1980 |
2995 |
51.26% |
n070w4 0 4-9-6-7 |
4 |
70 |
1342 |
2850 |
112.37% |
n080w4 2 4-3-3-3 |
4 |
80 |
2627 |
3695 |
40.65% |
n080w4 2 6-0-4-8 |
4 |
80 |
2679 |
3495 |
30.46% |
n100w4 0 1-1-0-8 |
4 |
100 |
805 |
1210 |
50.31% |
n100w4 2 0-6-4-6 |
4 |
100 |
1156 |
2315 |
100.26% |
n110w4 0 1-4-2-8 |
4 |
110 |
2013 |
2380 |
18.23% |
n110w4 0 1-9-3-5 |
4 |
110 |
2049 |
2500 |
22.01% |
n120w4 1 4-6-2-6 |
4 |
120 |
1376 |
3320 |
141.28% |
n120w4 1 5-6-9-8 |
4 |
120 |
1473 |
2765 |
87.71% |