1. © J. Christopher Beck 20081 Lecture 26: Nurse Scheduling

2. © J. Christopher Beck 2008 2 Outline Introduction Problem types and characteristics Approaches for solving Conclusions Directions

3. © J. Christopher Beck 2008 3 Readings Burke et al., The State of the Art of Nurse Rostering, Journal of Scheduling, 7, 441-499, 2004.

4. © J. Christopher Beck 2008 4 Nurse Rostering The allocation of nurses to periods of work over several weeks Every hospital has its differences little standardization, hard to have a single “solution” Complex hard and soft constraints

5. © J. Christopher Beck 2008 5 Example 1 head nurse, 15 regular, 3 caretakers, 2 trainees full time: 38 hours/week, max. 6 night, max 2 weekends half time: max 10 assignments/month, 20 hours/week early, day, late and night shifts nurses have specified preferred off-days

6. © J. Christopher Beck 2008 6 Example trainee must be on shift with supervisor requirement for each skill category in each shift of each day over 4 weeks # regular nurses, # caretakers, …

7. © J. Christopher Beck 2008 7 Importance of Good Schedules 24/7 operations different staffing needs at different times of different days irregular shift work negative impact on workers (e.g., health) negative impact on work environment (productivity, quality) people die

8. © J. Christopher Beck 20088 Problems & Characteristics

9. © J. Christopher Beck 2008 9 Criteria [Warner, 1976] coverage: how well supply matches demand quality: fairness stability: consistency, predictability flexibility: handle changes cost: time/effort to make schedule personnel cost

10. © J. Christopher Beck 2008 10 Different Decisions [Bradley & Martin, 1990] staffing: long-term number of people employed for each skill type, including holidays, leave, etc. scheduling: assign personnel based on expected daily demand allocation: assign already scheduled person to a specific location

11. © J. Christopher Beck 2008 11 Cyclical Schedules Each person works a cycle of n weeks (or days) (and then starts again) Good for predictability, even workloads, avoidance of unhealthy patterns Problems not flexible, precise levels needed, not preferred by personnel

12. © J. Christopher Beck 2008 12 Administrative Modes Centralized: one dept does all personnel scheduling in the hospital easier to contain cost personnel feel “distanced”, local constraints not taken into account, politics, unfairness

13. © J. Christopher Beck 2008 13 Administrative Modes Unit: head nurses or unit managers each schedule their own unit (e.g., ward) Self-scheduling: staff do it themselves time consuming negotiation can lead to over- or under-staffing if staff’s preferences conflict with hospital’s needs easier to incorporate preferences

14. © J. Christopher Beck 2008 14 Complexity Drivers [Silvestro & Silvestro 2000] number of staff predictability of demand ratio of planned vs. emergency operations variability of demand variation in patient stay and staffing requirements skill mix variation in skill types and configurations

15. © J. Christopher Beck 2008 15 Uncertainty Required staffing levels are uncertain based on number and severity of patients demand forecasts are inaccurate after ~4 days Absenteeism Possible solution: float nurses

16. © J. Christopher Beck 2008 16 Optimality “For most real problems, the goal of finding the ‘optimal’ solution is not only completely infeasible, it is also largely meaningless. Hospital administrators want to quickly generate a high quality schedule that satisfies all hard constraints and as many of a wide range of soft constraints as possible.” (p. 452)

17. © J. Christopher Beck 200817 Solution Approaches

18. © J. Christopher Beck 2008 18 Mathematical Programming Not really appropriate for large and complex problems not easy to express problems in e.g., linear form, preferences? huge search space means no hope of finding optimal Mostly applied to smaller, simpler problems

19. © J. Christopher Beck 2008 19 Mathematical Programming Common to decompose the problem (like in sports scheduling) [Rosenbloom & Goertzen 1987]

20. © J. Christopher Beck 2008 20 Artificial Intelligence Approaches Richer representation e.g., fuzzy constraints Solution procedures tend to be complex and (a bit) ad hoc series of steps/phases mirroring manual steps hierarchical constraints partial CSP

21. © J. Christopher Beck 2008 21 Heuristics A series of steps to generate a schedule (or something close) sometimes not even feasible no way to evaluate optimality Often problem specific

22. © J. Christopher Beck 2008 22 Metaheuristics Metaheuristics are another term for sophisticated local search algorithms like tabu search (and many others) Allow a redefinition of “feasible” as constraints can be represented in cost function important as many problems are over- constrained

23. © J. Christopher Beck 2008 23 Tabu search Multiple neighbourhoods and oscillation between feasible/infeasible (constraints vs. preferences) [Dowsland 1998] MIP + tabu [Dowsland & Thompson 2000; Valouxis & Housos 2000] Tabu + human-inspired improvement techniques [Burke et al. 1999]

24. © J. Christopher Beck 200824 Conclusions

25. © J. Christopher Beck 2008 25 Conclusions 40 years of research and “very few of the developed approaches are suitable for directly solving real world problems” “modern hybridized artificial intelligence and operations research techniques which incorporate problem specific information form the basis of most successful real world implementations”

26. © J. Christopher Beck 2008 26 Research Challenges Multi-criteria reasoning Flexibility and dynamic rescheduling Robustness Ease of use Human/computer interaction Problem decomposition Hybridization Interdisciplinarity

27. © J. Christopher Beck 2008 27 What Do I Have to Know? You need to read the paper! Description of nurse rostering problem complexity, some constraints, preferences I won’t ask you to formulate a model High-level idea of the solution approaches Conclusions and directions Might make a good essay question