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© J. Christopher Beck 2008 1
Lecture 26: Nurse Scheduling
© J. Christopher Beck 2008 2
Outline Introduction Problem types and characteristics Approaches for solving Conclusions Directions
© J. Christopher Beck 2008 3
Readings
Burke et al.,The State of the Art of Nurse Rostering, Journal of Scheduling, 7, 441-499, 2004.
© 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
© 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
© 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, …
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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
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Problems & Characteristics
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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
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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
© 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
© 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
© 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
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ComplexityDrivers [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
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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
© 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)
© J. Christopher Beck 2008 17
Solution Approaches
© 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
© J. Christopher Beck 2008 19
Mathematical Programming
Common to decompose the problem (like in sports scheduling) [Rosenbloom & Goertzen 1987]
© 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
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Heuristics
A series of steps to generate a schedule (or something close) sometimes not even feasible no way to evaluate optimality
Often problem specific
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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
© 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]
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Conclusions
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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”
© 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
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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