Abstract
We use a binary integer programming model to formulate and solve a nurse scheduling problem (NSP) which maximally satisfies nurse preferences. In a practical application of a VA hospital, besides considering the scheduling of two types of nurses (registered nurses and licensed practical nurses), two other types of employees (nursing assistants and health care techs), one nurse manager, and a clinical nurse leader are also included in our model. Most of these employees are working full-time. In addition, we distinguish the schedule of weekdays and weekends with different requirements and different preferences for employees. Besides the requirements for each shift, we consider requirements for specific employees in some shifts in practical situations. The seven shifts each day do not necessarily have the same length in our model. Vacation time of employees is also considered in our model. Thus, the requirements for nurse scheduling are complicated and the objective is to maximize the satisfaction of preferred schedules of all these employees, including both nurses and other staffs. The presented model is complex, but efficiently solvable, satisfying the set of requirements in a particular application in a VA hospital.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abernathy, W., Baloff, N., Hershey, J., Wandel, S.: A three-stage manpower planning and scheduling model-a service-sector example. Oper. Res. 21(3), 693–711 (1973)
Beliën, J., Demeulemeester, E.: A branch-and-price approach for integrating nurse and surgery scheduling. Eur. J. Oper. Res. 189(3), 652–668 (2008)
Burke, E.K., Bb N.N., De Causmaecker, P.: Fitness evaluation for nurse scheduling problems. Proceedings of the 2001 IEEE Congress on Evolutionary Computation, Seoul, Korea, pp. 1139–1146 (2001)
Burke, E., De Causmaecker, P., Berghe, G., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7, 441–499 (2004)
Cheang, H., Lim, A., Rodrigues, B.: Nurse rostering problems-a bibliographic survey. Eur. J. Oper. Res. 151, 447–460 (2003)
Chern, C.-C., Chien, P.-S., Chen, S.-Y.: A heuristic algorithm for the hospital health examination scheduling problem. Eur. J. Oper. Res. 186(3), 1137–1157 (2008)
ILOG CPLEX 11.0 Users Manual, 2007.
Duenas, A., Tutuncu, G.Y., Chilcott, J.B.: A genetic algorithm approach to the nurse scheduling problem with fuzzy preferences. IMA J. Manag. Math. 20, 369–383 (2009)
Ferland, J., Berrada, I., Nabli, I., Ahoid, B., Michelon, P., Gascon, V., Gagne, E.: Generalized assignment type goal programming problem: application to nurse scheduling. J. Heuristics 7, 391–413 (2001)
De Grano, M.L., Medeiros, D.J., Eitel, D.: Accommodating individual preferences in nurse scheduling via auctions and optimization. Health Care Manage Sci. 12, 228–242 (2009)
Gutjahr, W.J., Rauner, M.S.: An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria. Comput. Oper. Res. 34(3), 642–666 (2007)
Jaumard, B., Semet, F., Vover, T.: A generalized linear programming model for nurse scheduling. Eur. J. Oper. Res. 107, 1–18 (1998)
Mohan, S.: Scheduling part-time personnel with availability restrictions and preferences to maximize employee satisfaction. Math. Comput. Model. 48(11–12), 1806–1813 (2008)
Pardalos, P.M., Resende, M.: Handbook of Applied Optimization, Oxford University Press (2002).
Topaloglu, S., Selim, H.: Nurse scheduling using fuzzy modeling approach Fuzzy Sets and Systems, Corrected Proof, Available online 15 Oct 2009 (in press).
Tsai, C.-C., Li, S.H.A.: A two-stage modeling with genetic algorithms for the nurse scheduling problem. Expert Syst. Appl. 36(5), 9506–9512 (2009)
Vanhoucke, M., Maenhout, B.: On the characterization and generation of nurse scheduling problem instances. Eur. J. Oper. Res. 196(2), 457–467 (2009)
Warner, D.M.: Scheduling nursing personnel according to nursing preference: A mathematical programming approach. Oper. Res. 24:842–856, 1976
Wright, P.D., Bretthauer, K.M., Cote, M.J.: Reexamining the nurse scheduling problem: staffing ratios and nursing shortages. Decis. Sci. 37(1), 29–70 (2006)
Acknowledgment
This material is based upon work supported by the Office of Systems Redesign, Department of Veteran Affairs. This research has been partially supported by CAO funds.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
Appendix 1: Results of Nurse Scheduling with One Preference Shift in a Week
 | Preferences | Assignments | Satisfication | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Weeks | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
Type 1 (RN) | ||||||||||||
1 | 6 | 6 | 3 | 1 | 6 | 6 | 3 | 1 | Y | Y | Y | Y |
2 | 1 | 1 | 6 | 6 | 1 | 1 | 6 | 6 | Y | Y | Y | Y |
3 | 6 | 3 | 3 | 3 | 6 | 3 | 3 | 1 | Y | Y | Y | N |
4 | 1 | 3 | 6 | 3 | 1 | 3 | 6 | 3 | Y | Y | Y | Y |
5 | 1 | 6 | 3 | 1 | 1 | 6 | 1 | 1 | Y | Y | N | Y |
6 | 6 | 1 | 1 | 6 | 6 | 1 | 1 | 6 | Y | Y | Y | Y |
7 | 6 | 6 | 1 | 1 | 6 | 6 | 1 | 1 | Y | Y | Y | Y |
8 | 3 | 1 | 6 | 6 | 3 | 1 | 6 | 6 | Y | Y | Y | Y |
9 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | Y | Y | Y | Y |
10 | 6 | 1 | 6 | 3 | 6 | 1 | 6 | 3 | Y | Y | Y | Y |
11 | 3 | 3 | 6 | 1 | 3 | 3 | 6 | 1 | Y | Y | Y | Y |
12 | 3 | 3 | 6 | 3 | 3 | 3 | 6 | 3 | Y | Y | Y | Y |
13 | 6 | 6 | 6 | 3 | 6 | 6 | 6 | 3 | Y | Y | Y | Y |
14 | 3 | 3 | 1 | 6 | 3 | 3 | 1 | 6 | Y | Y | Y | Y |
15 | 6 | 6 | 1 | 1 | 6 | 6 | 1 | 1 | Y | Y | Y | Y |
16 | 3 | 1 | 1 | 6 | 3 | 1 | 1 | 6 | Y | Y | Y | Y |
17 | 3 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | Y | Y | Y | Y |
18 | 3 | 3 | 1 | 1 | 3 | 3 | 1 | 1 | Y | Y | Y | Y |
19 | 1 | 1 | 6 | 6 | 1 | 1 | 6 | 6 | Y | Y | Y | Y |
20 | 1 | 6 | 1 | 6 | 1 | 6 | 1 | 6 | Y | Y | Y | Y |
21 | 6 | 3 | 6 | 6 | 6 | 3 | 6 | 6 | Y | Y | Y | Y |
22 | 3 | 3 | 3 | 1 | 3 | 3 | 3 | 1 | Y | Y | Y | Y |
23 | 6 | 1 | 6 | 3 | 6 | 1 | 6 | 3 | Y | Y | Y | Y |
24 | 6 | 3 | 3 | 1 | 6 | 3 | 1 | 1 | Y | Y | N | Y |
25 | 3 | 1 | 3 | 3 | 3 | 1 | 6 | 3 | Y | Y | N | Y |
26 | 3 | 1 | 3 | 1 | 3 | 1 | 1 | 1 | Y | Y | N | Y |
27 | 1 | 6 | 3 | 3 | 1 | 6 | 3 | 3 | Y | Y | Y | Y |
28 | 3 | 1 | 1 | 6 | 3 | 3 | 3 | 6 | Y | N | N | Y |
29 | 1 | 1 | 3 | 3 | 1 | 1 | 6 | 3 | Y | Y | N | Y |
Type 2 (LPN) | ||||||||||||
1 | 4 | 4 | 2 | 3 | 1 | 4 | 2 | 3 | N | Y | Y | Y |
2 | 5 | 5 | 2 | 5 | 5 | 5 | 4 | 5 | Y | Y | N | Y |
3 | 4 | 6 | 2 | 2 | 4 | 6 | 1 | 6 | Y | Y | N | N |
4 | 1 | 5 | 2 | 7 | 1 | 5 | 2 | 7 | Y | Y | Y | Y |
5 | 6 | 3 | 3 | 5 | 6 | 3 | 3 | 5 | Y | Y | Y | Y |
6 | 5 | 4 | 2 | 4 | 5 | 6 | 1 | 4 | Y | N | N | Y |
7 | 6 | 7 | 1 | 1 | 6 | 7 | 4 | 5 | Y | Y | N | N |
8 | 4 | 2 | 4 | 5 | 4 | 1 | 4 | 3 | Y | N | Y | N |
9 | 2 | 2 | 5 | 2 | 6 | 1 | 5 | 4 | N | N | Y | N |
10 | 5 | 5 | 6 | 7 | 5 | 5 | 6 | 7 | Y | Y | Y | Y |
11 | 2 | 7 | 4 | 2 | 2 | 6 | 4 | 6 | Y | N | Y | N |
Type 3 (NA) | ||||||||||||
1 | 7 | 5 | 2 | 2 | 7 | 5 | 1 | 7 | Y | Y | N | N |
2 | 7 | 5 | 5 | 5 | 1 | 5 | 5 | 6 | N | Y | Y | N |
3 | 2 | 7 | 2 | 5 | 2 | 7 | 4 | 6 | Y | Y | N | N |
4 | 2 | 5 | 7 | 5 | 2 | 5 | 7 | 7 | Y | Y | Y | N |
Type 4 (HCT) | ||||||||||||
1 | 7 | 2 | 5 | 2 | 3 | 3 | 5 | 7 | N | N | Y | N |
2 | 7 | 2 | 2 | 2 | 7 | 2 | 6 | 1 | Y | Y | N | N |
3 | 5 | 4 | 3 | 5 | 5 | 4 | 3 | 6 | Y | Y | Y | N |
Appendix 2: Results of Assignments with Respect to Each Day with One Preference Shift in a Week (Employees Who Do Not Appear in this Table Mean They Do Not Need to Work in that Corresponding Week)
Week 1 | |||||||
---|---|---|---|---|---|---|---|
(ID.Shift) | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 RN | |||||||
1.6 | 1 | 1 | Â | Â | Â | Â | 1 |
2.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
3.6 | Â | Â | Â | Â | Â | Â | 1 |
4.1 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
5.1 | 1 | Â | 1 | 1 | 1 | 1 | 1 |
6.6 | 1 | 1 | 1 | Â | 1 | Â | Â |
7.6 | Â | Â | 1 | 1 | 1 | Â | 1 |
8.3 | Â | 1 | 1 | 1 | 1 | Â | Â |
9.1 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
10.6 | 1 | 1 | Â | Â | 1 | 1 | Â |
11.3 | 1 | Â | Â | 1 | 1 | 1 | Â |
12.3 | 1 | Â | 1 | Â | 1 | Â | 1 |
13.6 | 1 | Â | 1 | 1 | Â | 1 | 1 |
14.3 | Â | 1 | 1 | 1 | Â | Â | 1 |
15.6 | Â | 1 | 1 | 1 | Â | Â | 1 |
16.3 | 1 | 1 | Â | 1 | 1 | 1 | Â |
17.3 | 1 | 1 | Â | 1 | 1 | Â | Â |
18.3 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
19.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
20.1 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
21.6 | 1 | 1 | 1 | Â | Â | 1 | Â |
22.3 | 1 | 1 | Â | Â | Â | 1 | 1 |
23.6 | 1 | 1 | Â | 1 | 1 | 1 | Â |
24.6 | Â | 1 | 1 | 1 | 1 | 1 | Â |
25.3 | Â | Â | 1 | 1 | 1 | 1 | 1 |
26.3 | 1 | Â | 1 | Â | 1 | 1 | Â |
27.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
28.3 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
29.1 | Â | 1 | 1 | 1 | 1 | 1 | 1 |
Type 2 (LPN) | |||||||
2.5 | Â | Â | Â | 1 | 1 | 1 | 1 |
3.4 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
4.1 | Â | Â | Â | Â | Â | Â | 1 |
5.6 | 1 | Â | 1 | 1 | Â | Â | Â |
6.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
7.6 | Â | Â | Â | Â | 1 | 1 | 1 |
8.4 | Â | Â | 1 | Â | Â | Â | Â |
9.2 | 1 | Â | Â | Â | Â | 1 | 1 |
10.5 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
11.2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Type 3 (NA) | |||||||
1.7 | Â | Â | 1 | 1 | 1 | 1 | Â |
3.2 | Â | 1 | 1 | 1 | 1 | 1 | Â |
4.2 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
Type 4 (HCT) | |||||||
1.7 | 1 | 1 | Â | Â | Â | Â | Â |
2.7 | Â | Â | Â | Â | Â | Â | 1 |
3.5 | 1 | 1 | 1 | Â | Â | 1 | Â |
Week 2 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.6 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
3.3 | Â | Â | Â | Â | Â | 1 | 1 |
4.3 | Â | 1 | 1 | 1 | Â | 1 | Â |
5.6 | 1 | 1 | Â | 1 | 1 | Â | Â |
6.1 | 1 | Â | 1 | 1 | 1 | 1 | 1 |
7.6 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
8.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
9.6 | Â | Â | 1 | 1 | 1 | 1 | Â |
10.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
11.3 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
12.3 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
13.6 | 1 | 1 | 1 | Â | 1 | Â | 1 |
14.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
15.6 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
16.1 | 1 | Â | 1 | 1 | 1 | Â | 1 |
17.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
18.3 | 1 | Â | 1 | Â | 1 | 1 | Â |
19.1 | 1 | Â | 1 | 1 | 1 | Â | Â |
20.6 | Â | 1 | 1 | 1 | Â | Â | 1 |
21.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
22.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
23.1 | 1 | 1 | Â | 1 | Â | 1 | 1 |
24.3 | Â | 1 | 1 | 1 | 1 | Â | 1 |
25.1 | Â | 1 | Â | 1 | 1 | 1 | 1 |
26.1 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
27.6 | 1 | Â | Â | Â | 1 | 1 | 1 |
29.1 | Â | 1 | Â | 1 | Â | 1 | 1 |
Type 2 (LPN) | |||||||
1.4 | Â | Â | 1 | Â | 1 | 1 | 1 |
2.5 | 1 | Â | Â | 1 | 1 | Â | Â |
3.6 | Â | Â | Â | Â | Â | Â | 1 |
4.5 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
5.3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
7.7 | Â | Â | 1 | 1 | 1 | 1 | 1 |
8.2 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
9.2 | 1 | Â | 1 | 1 | 1 | Â | Â |
10.5 | Â | Â | Â | Â | Â | Â | 1 |
Type 3 (NA) | |||||||
1.5 | Â | 1 | 1 | Â | Â | Â | 1 |
2.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
3.7 | 1 | 1 | Â | Â | Â | Â | Â |
4.5 | Â | Â | Â | Â | Â | 1 | Â |
Type 4 (HCT) | |||||||
1.2 | Â | 1 | 1 | Â | 1 | 1 | 1 |
2.2 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
3.4 | 1 | 1 | Â | 1 | Â | Â | Â |
Week 3 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
2.6 | Â | 1 | 1 | Â | 1 | 1 | 1 |
3.3 | Â | 1 | Â | Â | Â | 1 | 1 |
4.6 | 1 | Â | 1 | Â | 1 | 1 | Â |
5.3 | 1 | Â | 1 | 1 | Â | 1 | Â |
6.1 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
7.1 | Â | 1 | 1 | 1 | Â | 1 | 1 |
8.6 | 1 | Â | Â | 1 | Â | 1 | 1 |
9.1 | 1 | Â | 1 | 1 | 1 | 1 | 1 |
10.6 | Â | 1 | Â | 1 | 1 | 1 | Â |
11.6 | Â | 1 | Â | 1 | 1 | Â | 1 |
12.6 | 1 | Â | 1 | Â | 1 | 1 | Â |
13.6 | 1 | 1 | 1 | 1 | Â | Â | Â |
14.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
15.1 | 1 | 1 | Â | 1 | 1 | Â | Â |
16.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
17.1 | 1 | Â | 1 | 1 | 1 | 1 | 1 |
18.1 | 1 | 1 | 1 | Â | Â | Â | 1 |
19.6 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
20.1 | Â | 1 | 1 | 1 | 1 | 1 | 1 |
21.6 | 1 | Â | 1 | 1 | Â | Â | 1 |
22.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
23.6 | 1 | 1 | Â | 1 | 1 | Â | Â |
24.3 | 1 | Â | 1 | 1 | 1 | Â | 1 |
25.3 | 1 | 1 | Â | Â | 1 | Â | 1 |
26.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
27.3 | Â | 1 | 1 | 1 | 1 | 1 | Â |
29.3 | 1 | Â | 1 | Â | 1 | Â | 1 |
Type 2 (LPN) | |||||||
1.2 | Â | 1 | 1 | Â | Â | 1 | 1 |
3.2 | Â | Â | Â | 1 | Â | Â | Â |
4.2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
8.4 | 1 | Â | 1 | 1 | 1 | 1 | 1 |
9.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
11.4 | Â | 1 | Â | Â | Â | Â | Â |
Type 3 (NA) | |||||||
1.2 | Â | Â | 1 | Â | Â | Â | Â |
2.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
3.2 | 1 | Â | Â | Â | 1 | 1 | 1 |
4.7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Type 4 (HCT) | |||||||
1.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
2.2 | 1 | 1 | Â | 1 | 1 | Â | Â |
3.3 | Â | 1 | 1 | 1 | Â | 1 | 1 |
Week 4 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.1 | 1 | Â | Â | Â | Â | 1 | 1 |
2.6 | Â | Â | Â | Â | 1 | Â | Â |
4.3 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
5.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
6.6 | 1 | Â | 1 | Â | Â | 1 | 1 |
7.1 | 1 | Â | 1 | 1 | 1 | Â | 1 |
8.6 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
9.6 | 1 | 1 | Â | 1 | 1 | Â | Â |
10.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
11.1 | Â | 1 | 1 | 1 | 1 | 1 | 1 |
12.3 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
13.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
14.6 | 1 | 1 | Â | 1 | Â | 1 | Â |
15.1 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
16.6 | 1 | Â | 1 | 1 | Â | Â | 1 |
17.1 | 1 | 1 | Â | 1 | Â | 1 | Â |
18.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
19.6 | Â | 1 | 1 | 1 | Â | 1 | Â |
20.6 | 1 | Â | 1 | Â | 1 | 1 | Â |
21.6 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
22.1 | 1 | Â | 1 | Â | 1 | Â | 1 |
23.3 | Â | 1 | 1 | 1 | 1 | 1 | 1 |
24.1 | Â | 1 | 1 | 1 | 1 | Â | 1 |
25.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
26.1 | Â | 1 | 1 | 1 | Â | 1 | Â |
27.3 | 1 | Â | 1 | 1 | Â | 1 | 1 |
28.6 | Â | 1 | Â | Â | 1 | 1 | 1 |
29.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
Type 2 (LPN) | |||||||
2.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
3.2 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
5.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
6.4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
8.5 | 1 | Â | Â | Â | Â | Â | Â |
10.7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
11.2 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
TYPE 3 (NA) | |||||||
1.2 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
3.5 | Â | 1 | 1 | Â | Â | 1 | Â |
Type 4 (HCT) | |||||||
2.2 | Â | Â | 1 | Â | 1 | Â | 1 |
3.5 | Â | Â | Â | 1 | 1 | Â | 1 |
Appendix 3: Results of Nurse Scheduling with Two Preferences Shift (One for Weekdays and One for Weekends)
 | Preferences | Assignments | Satisfication | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Weeks | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
Type 1 (RN) | ||||||||||||
1 | (6,6) | (6,1) | (3,6) | (1,3) | (6,6) | (6,1) | (3,6) | (1,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
2 | (1,6) | (1,3) | (6,1) | (6,6) | (1,1) | (1,3) | (6,1) | (6,6) | (Y,N) | (Y,Y) | (Y,Y) | (Y,Y) |
3 | (6,6) | (3,1) | (3,6) | (1,6) | (3,6) | (3,1) | (3,6) | (1,6) | (N,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
4 | (1,3) | (3,3) | (6,6) | (3,1) | (1,3) | (3,3) | (6,6) | (3,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
5 | (1,6) | (6,6) | (1,6) | (1,3) | (1,6) | (6,6) | (1,6) | (1,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
6 | (6,1) | (1,3) | (1,1) | (6,3) | (6,1) | (1,3) | (1,1) | (6,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
7 | (6,6) | (6,3) | (1,1) | (1,3) | (6,6) | (6,3) | (1,1) | (1,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
8 | (3,6) | (1,3) | (6,6) | (6,1) | (3,6) | (1,3) | (6,6) | (6,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
9 | (1,6) | (6,1) | (1,6) | (6,6) | (1,6) | (6,1) | (1,6) | (6,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
10 | (6,1) | (1,3) | (6,3) | (3,3) | (6,1) | (1,3) | (6,3) | (3,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
11 | (3,3) | (3,1) | (6,6) | (1,1) | (3,3) | (3,1) | (6,6) | (1,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
12 | (3,3) | (3,1) | (6,3) | (3,6) | (3,3) | (3,1) | (6,3) | (3,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
13 | (6,3) | (6,1) | (6,3) | (3,3) | (6,3) | (6,1) | (6,3) | (3,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
14 | (3,1) | (3,3) | (1,1) | (6,1) | (3,1) | (3,3) | (1,1) | (6,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
15 | (6,6) | (6,6) | (1,6) | (1,6) | (6,6) | (6,6) | (1,6) | (1,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
16 | (3,1) | (1,1) | (1,3) | (6,1) | (3,1) | (1,1) | (1,3) | (6,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
17 | (3,1) | (1,3) | (1,6) | (1,6) | (3,1) | (1,3) | (1,6) | (1,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
18 | (3,3) | (3,1) | (1,1) | (1,6) | (3,3) | (3,1) | (1,1) | (1,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
19 | (1,3) | (1,1) | (6,3) | (6,1) | (1,3) | (1,1) | (6,3) | (6,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
20 | (1,1) | (6,3) | (1,1) | (6,3) | (1,1) | (6,3) | (1,1) | (6,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
21 | (6,1) | (3,1) | (6,6) | (6,6) | (6,1) | (3,1) | (6,6) | (6,6) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
22 | (3,3) | (3,6) | (3,1) | (1,3) | (3,3) | (3,6) | (3,1) | (1,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
23 | (6,1) | (1,3) | (6,6) | (3,3) | (6,1) | (1,3) | (6,6) | (3,3) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
24 | (6,1) | (3,3) | (1,6) | (1,1) | (6,1) | (3,1) | (3,6) | (1,1) | (Y,Y) | (Y,N) | (N,Y) | (Y,Y) |
25 | (3,1) | (1,6) | (6,3) | (3,1) | (3,1) | (1,6) | (3,3) | (3,1) | (Y,Y) | (Y,Y) | (N,Y) | (Y,Y) |
26 | (3,6) | (1,3) | (1,1) | (1,6) | (3,6) | (1,3) | (3,1) | (1,6) | (Y,Y) | (Y,Y) | (N,Y) | (Y,Y) |
27 | (1,3) | (6,1) | (3,3) | (3,1) | (1,3) | (6,1) | (3,3) | (3,1) | (Y,Y) | (Y,Y) | (Y,Y) | (Y,Y) |
28 | (3,6) | (3,6) | (3,1) | (6,6) | (3,6) | (1,1) | (1,1) | (6,6) | (Y,Y) | (N,N) | (N,Y) | (Y,Y) |
29 | (1,3) | (1,1) | (6,1) | (3,3) | (1,3) | (1,1) | (3,1) | (3,3) | (Y,Y) | (Y,Y) | (N,Y) | (Y,Y) |
Type 2 (LPN) | ||||||||||||
1 | (1,6) | (4,6) | (2,4) | (3,4) | (2,6) | (7,6) | (2,4) | (2,2) | (N,Y) | (N,Y) | (Y,Y) | (N,N) |
2 | (5,3) | (5,6) | (4,4) | (5,5) | (5,4) | (2,6) | (7,1) | (5,5) | (Y,N) | (N,Y) | (N,N) | (Y,Y) |
3 | (4,6) | (6,5) | (1,5) | (6,7) | (4,1) | (4,5) | (5,5) | (5,5) | (Y,N) | (N,Y) | (N,Y) | (N,N) |
4 | (1,7) | (5,3) | (2,1) | (7,7) | (2,7) | (5,2) | (2,5) | (2,7) | (N,Y) | (Y,N) | (Y,N) | (N,Y) |
5 | (6,3) | (3,4) | (3,5) | (5,6) | (5,3) | (3,4) | (3,1) | (5,1) | (N,Y) | (Y,Y) | (Y,N) | (Y,N) |
6 | (5,6) | (6,3) | (1,5) | (4,4) | (5,1) | (6,3) | (5,5) | (4,4) | (Y,N) | (Y,Y) | (N,Y) | (Y,Y) |
7 | (6,5) | (7,7) | (4,4) | (5,6) | (4,5) | (7,7) | (1,1) | (1,1) | (N,Y) | (Y,Y) | (N,N) | (N,N) |
8 | (4,6) | (1,4) | (4,2) | (3,6) | (7,4) | (2,2) | (4,2) | (4,2) | (N,N) | (N,N) | (Y,Y) | (N,N) |
9 | (6,2) | (1,7) | (5,2) | (4,6) | (2,2) | (2,2) | (5,2) | (5,5) | (N,Y) | (N,N) | (Y,Y) | (N,N) |
10 | (5,4) | (5,4) | (6,2) | (7,6) | (5,4) | (5,6) | (2,2) | (7,2) | (Y,Y) | (Y,N) | (N,Y) | (Y,N) |
11 | (2,7) | (6,2) | (4,7) | (6,3) | (2,1) | (4,2) | (2,7) | (2,2) | (Y,N) | (N,Y) | (N,Y) | (N,N) |
Type 3 (NA) | ||||||||||||
1 | (7,3) | (5,3) | (1,6) | (7,4) | (7,5) | (5,3) | (2,2) | (7,2) | (Y,N) | (Y,Y) | (N,N) | (Y,N) |
2 | (1,1) | (5,5) | (5,3) | (6,5) | (4,1) | (5,5) | (5,2) | (2,5) | (N,Y) | (Y,Y) | (Y,N) | (N,Y) |
3 | (2,4) | (7,5) | (4,2) | (6,3) | (2,2) | (7,5) | (4,2) | (2,5) | (Y,N) | (Y,Y) | (Y,Y) | (N,N) |
4 | (2,3) | (5,2) | (7,1) | (7,1) | (2,5) | (5,2) | (7,4) | (2,2) | (Y,N) | (Y,Y) | (Y,N) | (N,N) |
Type 4 (HCT) | ||||||||||||
1 | (3,5) | (3,4) | (5,1) | (7,4) | (2,5) | (2,2) | (5,5) | (7,5) | (N,Y) | (N,N) | (Y,N) | (Y,N) |
2 | (7,2) | (2,6) | (6,5) | (1,1) | (5,2) | (2,6) | (2,5) | (2,5) | (N,Y) | (Y,Y) | (N,Y) | (N,N) |
3 | (5,2) | (4,7) | (3,4) | (6,3) | (5,2) | (4,1) | (3,5) | (4,4) | (Y,Y) | (Y,N) | (Y,N) | (N,N) |
Appendix 4: Results of Assignments with Respect to Each Day with Two Preferences for Weekdays and Weekends (Employees Who Do Not Appear in this Table Mean They Do Not Need to Work in that Corresponding Week)
Week 1 | Â | ||||||
---|---|---|---|---|---|---|---|
(ID.Shift) | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.6 | 1 | Â | 1 | 1 | Â | ||
2.1 | 1 | Â | 1 | 1 | 1 | 1 | Â |
3.6 | Â | Â | Â | Â | Â | Â | 1 |
4.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
4.3 | Â | Â | Â | Â | Â | Â | 1 |
5.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
5.6 | Â | Â | Â | Â | Â | Â | 1 |
6.1 | Â | Â | Â | Â | Â | 1 | 1 |
6.6 | Â | 1 | 1 | 1 | Â | Â | Â |
7.6 | 1 | 1 | Â | 1 | 1 | 1 | Â |
8.3 | Â | Â | 1 | 1 | 1 | Â | Â |
8.6 | Â | Â | Â | Â | Â | 1 | Â |
9.1 | 1 | 1 | 1 | 1 | Â | Â | Â |
10.1 | Â | Â | Â | Â | Â | Â | 1 |
10.6 | Â | Â | 1 | 1 | 1 | Â | Â |
11.3 | 1 | Â | 1 | 1 | 1 | 1 | Â |
12.3 | 1 | 1 | Â | Â | Â | 1 | 1 |
13.3 | Â | Â | Â | Â | Â | Â | 1 |
13.6 | 1 | 1 | 1 | Â | 1 | Â | Â |
14.1 | Â | Â | Â | Â | Â | 1 | 1 |
14.3 | 1 | 1 | 1 | Â | Â | Â | Â |
15.6 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
16.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
17.1 | Â | Â | Â | Â | Â | 1 | 1 |
17.3 | 1 | Â | 1 | 1 | Â | Â | Â |
18.3 | Â | Â | 1 | 1 | 1 | 1 | Â |
19.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
19.3 | Â | Â | Â | Â | Â | 1 | Â |
20.1 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
21.1 | Â | Â | Â | Â | Â | 1 | 1 |
21.6 | 1 | Â | 1 | Â | Â | Â | Â |
22.3 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
23.1 | Â | Â | Â | Â | Â | 1 | 1 |
23.6 | 1 | 1 | 1 | 1 | Â | Â | Â |
24.1 | Â | Â | Â | Â | Â | Â | 1 |
24.6 | Â | 1 | 1 | 1 | 1 | Â | Â |
25.3 | 1 | 1 | 1 | 1 | Â | Â | Â |
26.3 | Â | 1 | 1 | Â | 1 | Â | Â |
26.6 | Â | Â | Â | Â | Â | 1 | 1 |
27.1 | Â | 1 | 1 | 1 | 1 | Â | Â |
27.3 | Â | Â | Â | Â | Â | 1 | 1 |
28.3 | 1 | 1 | Â | 1 | 1 | Â | Â |
28.6 | Â | Â | Â | Â | Â | 1 | 1 |
29.1 | 1 | 1 | Â | 1 | 1 | Â | Â |
29.3 | Â | Â | Â | Â | Â | Â | 1 |
Type 2 (LPN) | |||||||
1.2 | 1 | 1 | Â | Â | Â | Â | Â |
1.6 | Â | Â | Â | Â | Â | Â | 1 |
2.4 | Â | Â | Â | Â | Â | Â | 1 |
2.5 | Â | Â | Â | Â | 1 | Â | Â |
3.4 | 1 | 1 | 1 | Â | 1 | Â | Â |
4.7 | Â | Â | Â | Â | Â | 1 | 1 |
5.3 | Â | Â | Â | Â | Â | 1 | 1 |
5.5 | 1 | Â | 1 | 1 | Â | Â | Â |
6.1 | Â | Â | Â | Â | Â | Â | 1 |
6.5 | 1 | 1 | Â | 1 | 1 | Â | Â |
7.4 | Â | Â | Â | 1 | Â | Â | Â |
7.5 | Â | Â | Â | Â | Â | 1 | 1 |
8.4 | Â | Â | Â | Â | Â | 1 | Â |
8.7 | 1 | 1 | Â | Â | Â | Â | Â |
9.2 | Â | Â | Â | Â | 1 | 1 | 1 |
10.5 | Â | 1 | 1 | Â | 1 | Â | Â |
11.2 | 1 | 1 | Â | 1 | 1 | Â | Â |
Type 3 (NA) | |||||||
1.5 | Â | Â | Â | Â | Â | Â | 1 |
1.7 | Â | Â | 1 | 1 | 1 | Â | Â |
3.2 | Â | Â | 1 | Â | Â | 1 | Â |
4.2 | 1 | 1 | 1 | 1 | 1 | Â | Â |
4.5 | Â | Â | Â | Â | Â | 1 | Â |
Type 4 (HCT) | |||||||
1.2 | Â | Â | 1 | 1 | Â | Â | Â |
1.5 | Â | Â | Â | Â | Â | 1 | 1 |
2.2 | Â | Â | Â | Â | Â | Â | 1 |
2.5 | Â | Â | 1 | 1 | Â | Â | Â |
3.2 | Â | Â | Â | Â | Â | 1 | 1 |
3.5 | 1 | 1 | Â | Â | Â | Â | Â |
Week 2 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.1 | Â | Â | Â | Â | Â | Â | 1 |
1.6 | 1 | 1 | 1 | 1 | 1 | Â | Â |
2.3 | Â | Â | Â | Â | Â | Â | 1 |
3.1 | Â | Â | Â | Â | Â | 1 | 1 |
4.3 | Â | Â | 1 | 1 | 1 | 1 | Â |
5.6 | Â | 1 | Â | 1 | 1 | Â | 1 |
6.1 | 1 | Â | 1 | 1 | 1 | Â | Â |
6.3 | Â | Â | Â | Â | Â | 1 | Â |
7.3 | Â | Â | Â | Â | Â | Â | 1 |
7.6 | Â | 1 | 1 | 1 | 1 | Â | Â |
8.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
8.3 | Â | Â | Â | Â | Â | Â | 1 |
9.1 | Â | Â | Â | Â | Â | 1 | 1 |
9.6 | 1 | 1 | 1 | 1 | Â | Â | Â |
10.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
10.3 | Â | Â | Â | Â | Â | 1 | Â |
11.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
12.1 | Â | Â | Â | Â | Â | 1 | 1 |
12.3 | 1 | 1 | 1 | 1 | Â | Â | Â |
13.6 | 1 | 1 | 1 | 1 | 1 | Â | Â |
14.3 | 1 | 1 | 1 | Â | 1 | 1 | Â |
15.6 | 1 | Â | Â | Â | 1 | 1 | 1 |
16.1 | 1 | 1 | Â | Â | 1 | 1 | 1 |
17.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
18.1 | Â | Â | Â | Â | Â | Â | 1 |
18.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
19.1 | 1 | 1 | Â | Â | 1 | 1 | Â |
20.3 | Â | Â | Â | Â | Â | 1 | Â |
20.6 | 1 | Â | 1 | 1 | Â | Â | Â |
21.1 | Â | Â | Â | Â | Â | Â | 1 |
21.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
22.3 | 1 | Â | Â | 1 | 1 | Â | Â |
22.6 | Â | Â | Â | Â | Â | 1 | Â |
23.1 | 1 | Â | Â | 1 | Â | Â | Â |
23.3 | Â | Â | Â | Â | Â | 1 | 1 |
24.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
25.1 | 1 | 1 | 1 | 1 | Â | Â | Â |
25.6 | Â | Â | Â | Â | Â | 1 | 1 |
26.1 | Â | 1 | 1 | 1 | 1 | Â | Â |
26.3 | Â | Â | Â | Â | Â | Â | 1 |
27.1 | Â | Â | Â | Â | Â | 1 | 1 |
27.6 | Â | 1 | 1 | Â | Â | Â | Â |
29.1 | Â | 1 | 1 | 1 | 1 | 1 | Â |
Type 2 (LPN) | |||||||
1.6 | Â | Â | Â | Â | Â | 1 | 1 |
2.2 | Â | 1 | 1 | 1 | 1 | Â | Â |
2.6 | Â | Â | Â | Â | Â | 1 | Â |
3.4 | Â | Â | Â | Â | 1 | Â | Â |
3.5 | Â | Â | Â | Â | Â | 1 | 1 |
4.5 | 1 | 1 | 1 | 1 | 1 | Â | Â |
5.3 | Â | 1 | Â | Â | Â | Â | Â |
5.4 | Â | Â | Â | Â | Â | 1 | 1 |
6.3 | Â | Â | Â | Â | Â | Â | 1 |
6.6 | 1 | Â | Â | Â | 1 | Â | Â |
7.7 | Â | Â | Â | 1 | 1 | 1 | 1 |
8.2 | 1 | 1 | Â | 1 | 1 | Â | Â |
9.2 | 1 | Â | 1 | Â | 1 | Â | 1 |
10.5 | 1 | 1 | Â | Â | 1 | Â | Â |
10.6 | Â | Â | Â | Â | Â | 1 | Â |
11.2 | Â | Â | Â | Â | Â | 1 | 1 |
11.4 | Â | Â | Â | 1 | Â | Â | Â |
Type 3 (NA) | |||||||
1.3 | Â | Â | Â | Â | Â | 1 | Â |
1.5 | Â | Â | 1 | 1 | Â | Â | Â |
2.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
3.5 | Â | Â | Â | Â | Â | 1 | 1 |
3.7 | 1 | 1 | 1 | Â | Â | Â | Â |
4.2 | Â | Â | Â | Â | Â | 1 | Â |
Type 4 (HCT) | |||||||
1.2 | Â | Â | Â | 1 | Â | 1 | 1 |
2.2 | 1 | 1 | 1 | Â | Â | Â | Â |
2.6 | Â | Â | Â | Â | Â | Â | 1 |
3.4 | 1 | 1 | 1 | Â | Â | Â | Â |
Week 3 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
2.1 | Â | Â | Â | Â | Â | Â | 1 |
2.6 | Â | Â | Â | Â | 1 | Â | Â |
3.3 | Â | Â | Â | 1 | 1 | Â | Â |
4.6 | 1 | Â | 1 | 1 | 1 | 1 | Â |
5.1 | Â | 1 | 1 | 1 | 1 | Â | Â |
6.1 | 1 | 1 | Â | 1 | 1 | 1 | 1 |
7.1 | Â | 1 | Â | 1 | 1 | 1 | 1 |
8.6 | 1 | 1 | Â | 1 | 1 | Â | 1 |
9.1 | 1 | Â | 1 | 1 | 1 | Â | Â |
9.6 | Â | Â | Â | Â | Â | Â | 1 |
10.3 | Â | Â | Â | Â | Â | 1 | 1 |
10.6 | Â | 1 | Â | 1 | Â | Â | Â |
11.6 | 1 | Â | Â | 1 | 1 | 1 | 1 |
12.3 | Â | Â | Â | Â | Â | 1 | 1 |
12.6 | Â | 1 | 1 | 1 | Â | Â | Â |
13.3 | Â | Â | Â | Â | Â | 1 | 1 |
13.6 | 1 | 1 | 1 | Â | Â | Â | Â |
14.1 | 1 | 1 | Â | Â | 1 | 1 | 1 |
15.1 | Â | 1 | 1 | 1 | 1 | Â | Â |
15.6 | Â | Â | Â | Â | Â | 1 | Â |
16.1 | 1 | 1 | 1 | 1 | Â | Â | Â |
16.3 | Â | Â | Â | Â | Â | 1 | 1 |
17.1 | 1 | 1 | 1 | 1 | Â | Â | Â |
17.6 | Â | Â | Â | Â | Â | Â | 1 |
18.1 | 1 | Â | 1 | 1 | Â | 1 | 1 |
19.3 | Â | Â | Â | Â | Â | 1 | 1 |
19.6 | 1 | Â | 1 | 1 | Â | Â | Â |
20.1 | 1 | 1 | 1 | Â | 1 | 1 | 1 |
21.6 | Â | 1 | 1 | 1 | 1 | 1 | Â |
22.1 | Â | Â | Â | Â | Â | Â | 1 |
22.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
23.6 | 1 | 1 | 1 | Â | 1 | Â | Â |
24.3 | 1 | Â | Â | 1 | 1 | Â | Â |
24.6 | Â | Â | Â | Â | Â | 1 | 1 |
25.3 | Â | 1 | 1 | Â | 1 | 1 | 1 |
26.1 | Â | Â | Â | Â | Â | 1 | 1 |
26.3 | 1 | 1 | 1 | Â | Â | Â | Â |
27.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
29.1 | Â | Â | Â | Â | Â | 1 | Â |
29.3 | 1 | 1 | 1 | 1 | Â | Â | Â |
Type 2 (LPN) | |||||||
1.2 | Â | Â | Â | 1 | Â | Â | Â |
2.7 | Â | Â | Â | Â | 1 | Â | Â |
3.5 | Â | Â | Â | Â | Â | 1 | 1 |
4.2 | 1 | 1 | 1 | 1 | Â | Â | Â |
4.5 | Â | Â | Â | Â | Â | Â | 1 |
5.3 | Â | 1 | Â | 1 | 1 | Â | Â |
6.5 | Â | 1 | 1 | 1 | 1 | 1 | 1 |
8.2 | Â | Â | Â | Â | Â | 1 | 1 |
8.4 | 1 | Â | 1 | 1 | Â | Â | Â |
9.5 | 1 | 1 | 1 | 1 | 1 | Â | Â |
10.2 | 1 | 1 | Â | Â | 1 | 1 | Â |
11.2 | 1 | 1 | Â | Â | Â | Â | Â |
11.7 | Â | Â | Â | Â | Â | 1 | 1 |
Type 3 (NA) | |||||||
1.2 | Â | Â | 1 | 1 | 1 | 1 | Â |
2.2 | Â | Â | Â | Â | Â | Â | 1 |
2.5 | 1 | Â | 1 | Â | Â | Â | Â |
3.2 | Â | Â | Â | Â | Â | Â | 1 |
3.4 | Â | 1 | Â | Â | 1 | Â | Â |
4.4 | Â | Â | Â | Â | Â | 1 | 1 |
4.7 | 1 | 1 | 1 | 1 | Â | Â | Â |
Type 4 (HCT) | |||||||
1.5 | 1 | 1 | Â | 1 | 1 | Â | Â |
2.2 | Â | Â | 1 | Â | 1 | Â | Â |
2.5 | Â | Â | Â | Â | Â | 1 | Â |
3.3 | 1 | Â | 1 | Â | 1 | Â | Â |
Week 4 | Â | ||||||
 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
Type 1 (RN) | |||||||
1.1 | 1 | Â | Â | 1 | Â | Â | Â |
1.3 | Â | Â | Â | Â | Â | 1 | 1 |
2.6 | Â | 1 | Â | Â | 1 | 1 | 1 |
3.6 | Â | Â | Â | Â | Â | Â | 1 |
4.1 | Â | Â | Â | Â | Â | Â | 1 |
4.3 | Â | 1 | 1 | 1 | 1 | Â | Â |
5.1 | 1 | 1 | Â | 1 | 1 | Â | Â |
5.3 | Â | Â | Â | Â | Â | 1 | 1 |
6.3 | Â | Â | Â | Â | Â | Â | 1 |
6.6 | 1 | Â | 1 | Â | 1 | Â | Â |
7.1 | 1 | 1 | Â | Â | 1 | Â | Â |
7.3 | Â | Â | Â | Â | Â | 1 | 1 |
8.1 | Â | Â | Â | Â | Â | 1 | 1 |
8.6 | 1 | 1 | Â | 1 | Â | Â | Â |
9.6 | Â | 1 | Â | 1 | 1 | 1 | 1 |
10.3 | 1 | 1 | 1 | 1 | 1 | Â | 1 |
11.1 | Â | Â | 1 | 1 | 1 | 1 | 1 |
12.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
13.3 | 1 | 1 | 1 | Â | 1 | 1 | Â |
14.1 | Â | Â | Â | Â | Â | 1 | Â |
14.6 | 1 | 1 | 1 | 1 | Â | Â | Â |
15.1 | 1 | 1 | 1 | Â | 1 | Â | Â |
15.6 | Â | Â | Â | Â | Â | 1 | Â |
16.1 | Â | Â | Â | Â | Â | 1 | 1 |
16.6 | Â | Â | 1 | 1 | Â | Â | Â |
17.1 | Â | 1 | 1 | 1 | 1 | Â | Â |
17.6 | Â | Â | Â | Â | Â | Â | 1 |
18.1 | 1 | 1 | 1 | Â | 1 | Â | Â |
18.6 | Â | Â | Â | Â | Â | 1 | Â |
19.1 | Â | Â | Â | Â | Â | 1 | 1 |
19.6 | 1 | 1 | 1 | Â | Â | Â | Â |
20.3 | Â | Â | Â | Â | Â | Â | 1 |
20.6 | 1 | Â | 1 | Â | 1 | Â | Â |
21.6 | 1 | 1 | 1 | 1 | 1 | Â | Â |
22.1 | 1 | 1 | 1 | 1 | Â | Â | Â |
23.3 | 1 | 1 | 1 | 1 | 1 | 1 | Â |
24.1 | Â | 1 | 1 | 1 | Â | 1 | 1 |
25.1 | Â | Â | Â | Â | Â | 1 | 1 |
25.3 | 1 | 1 | Â | 1 | Â | Â | Â |
26.1 | 1 | 1 | 1 | 1 | 1 | Â | Â |
27.3 | 1 | 1 | 1 | 1 | 1 | Â | Â |
28.6 | Â | Â | Â | 1 | 1 | 1 | 1 |
29.3 | 1 | Â | 1 | 1 | 1 | 1 | Â |
Type 2 (LPN) | |||||||
1.2 | 1 | Â | Â | 1 | Â | 1 | Â |
2.5 | 1 | 1 | 1 | 1 | Â | 1 | 1 |
3.5 | 1 | 1 | 1 | 1 | 1 | Â | Â |
4.7 | Â | Â | Â | Â | Â | 1 | 1 |
5.5 | 1 | 1 | 1 | 1 | 1 | Â | Â |
6.4 | Â | Â | Â | 1 | Â | Â | Â |
8.2 | Â | Â | Â | Â | Â | 1 | Â |
8.4 | Â | 1 | Â | Â | Â | Â | Â |
9.5 | Â | Â | Â | Â | 1 | Â | 1 |
10.2 | Â | Â | Â | Â | Â | 1 | 1 |
10.7 | Â | Â | Â | Â | 1 | Â | Â |
11.2 | 1 | Â | Â | Â | 1 | Â | 1 |
Type 3 (NA) | |||||||
1.2 | Â | Â | Â | Â | Â | Â | 1 |
1.7 | Â | 1 | 1 | Â | Â | Â | Â |
2.2 | 1 | 1 | 1 | Â | Â | Â | Â |
2.5 | Â | Â | Â | Â | Â | 1 | Â |
3.2 | Â | 1 | 1 | 1 | 1 | Â | Â |
4.2 | Â | Â | Â | Â | 1 | Â | Â |
Type 4 (HCT) | |||||||
1.5 | Â | Â | Â | Â | Â | Â | 1 |
1.7 | 1 | Â | Â | 1 | Â | Â | Â |
2.2 | Â | 1 | 1 | 1 | Â | Â | Â |
2.5 | Â | Â | Â | Â | Â | 1 | Â |
3.4 | 1 | Â | 1 | Â | 1 | 1 | 1 |
 |  |  |  |  |  |  | 1 |
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fan, N. et al. (2013). Nurse Scheduling Problem: An Integer Programming Model with a Practical Application. In: Pardalos, P., Georgiev, P., Papajorgji, P., Neugaard, B. (eds) Systems Analysis Tools for Better Health Care Delivery. Springer Optimization and Its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5094-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5094-8_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5093-1
Online ISBN: 978-1-4614-5094-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)