Lecture 26:
Nurse Scheduling
© J. Christopher Beck 2008
1
Outline





Introduction
Problem types and characteristics
Approaches for solving
Conclusions
Directions
© J. Christopher Beck 2008
2
Readings

Burke et al.,
The State of the Art of Nurse
Rostering, Journal of Scheduling,
7, 441-499, 2004.
© J. Christopher Beck 2008
3
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
4
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
5
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, …
© J. Christopher Beck 2008
6
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
© J. Christopher Beck 2008
7
Problems & Characteristics
© J. Christopher Beck 2008
8
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
© J. Christopher Beck 2008
9
Different Decisions

staffing: long-term number of people
employed




[Bradley & Martin, 1990]
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
10
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
11
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
12
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
© J. Christopher Beck 2008
13
Complexity
Drivers [Silvestro & Silvestro 2000]


number of staff
predictability of demand


variability of demand


ratio of planned vs. emergency operations
variation in patient stay and staffing
requirements
skill mix

variation in skill types and configurations
© J. Christopher Beck 2008
14
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
15
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
16
Solution Approaches
© J. Christopher Beck 2008
17
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
18
Mathematical Programming

Common to decompose the problem
(like in sports scheduling) [Rosenbloom &
Goertzen 1987]
© J. Christopher Beck 2008
19
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
© J. Christopher Beck 2008
20
Heuristics

A series of steps to generate a schedule
(or something close)



sometimes not even feasible
no way to evaluate optimality
Often problem specific
© J. Christopher Beck 2008
21
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 overconstrained
© J. Christopher Beck 2008
22
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]
© J. Christopher Beck 2008
23
Conclusions
© J. Christopher Beck 2008
24
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
25
Research Challenges
Multi-criteria reasoning
 Flexibility and dynamic rescheduling
 Robustness
 Ease of use
 Human/computer interaction
 Problem decomposition
 Hybridization
 Interdisciplinarity
© J. Christopher
Beck 2008

26
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 2008
27