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

© J. Christopher Beck 2008 1

Lecture 26: Nurse Scheduling


Outline Introduction Problem types and characteristics Approaches for solving Conclusions Directions


Readings

Burke et al.,The State of the Art of Nurse Rostering, Journal of Scheduling, 7, 441-499, 2004.


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


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


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, …


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


Problems & Characteristics


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


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


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


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


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


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


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


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)


Solution Approaches


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


Mathematical Programming

Common to decompose the problem (like in sports scheduling) [Rosenbloom & Goertzen 1987]


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


Heuristics

A series of steps to generate a schedule (or something close) sometimes not even feasible no way to evaluate optimality

Often problem specific


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


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]


Conclusions


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”


Research Challenges

Multi-criteria reasoning Flexibility and dynamic rescheduling Robustness Ease of use Human/computer interaction Problem decomposition Hybridization Interdisciplinarity


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

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

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