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demand for nurses is modeled based on shift. The
number of staff required is determined to meet a
service measure such as for instance a ratio
nurse/patient (Ernst et al., 2004). In the operating
rooms, on the contrary, the demand for staff is based
on a list of tasks. Each task is a surgical intervention
characterized by a starting time and duration, to be
scheduled and performed.
The objectives considered when building the
nursing roster are usually the minimization of the
salary costs and the maximization of the nurses’
preferences. The nurses’ preferences are measured in
terms of requests to work at specific time periods
(shifts, day-offs, etc.) (Jaumard et al., 1998); (Bard
and Purnomo, 2005). However, the models were not
taking into account preferences in terms of co-
workers or affinities between the surgical team
members.
The objective of this paper is to form surgical
teams (surgeon, nurses) with a high affinity degree
while taking into account the availaibilities of nurses
and the legal constraints on working conditions
(days-off, breaks,…). We also want to minimize the
waiting time of nurses in the operating rooms so that
we minimize idle time and limit overtime payments.
We face a multiobjective problem with two
criteria : to minimize the waiting time of nurses and
to maximize the affinities of the surgical teams.
A lexicographic optimization was considered to
solve this problem in Di Martinelly and Meskens
(2013). It means that an order of importance was set
between the objectives: the first objective is
optimized; then the second one is optimized under
the constraint that the first one stays optimal. There
are 2 main limitations to this approach: the decision
maker has to determine which objective is the most
important to him and none of the solutions generated
is a compromise between the objectives; the solution
is optimal regarding one of the objectives. For
instance, the operating room manager (the decision
maker) will have to settle for a nurse schedule that is
either optimum for the waiting time or optimum for
the affinities of the surgical teams; he won’t be
provided with a compromise schedule that would
probably best suit him.
The approach considered in this paper is
different. There is no order of importance between
the objectives and both objectives are optimized. We
build the set of Pareto optimal solutions (or part of
it). The main advantage of this method is the
possibility to provide the operating room manager
with the set of compromise solutions (meaning the
non-dominated solutions in the Pareto sense). The
manager can thus choose among them the solution
he prefers and estimates the trade-offs between the
possible solutions.
The originality of the research is the integration
of personnel affinities in the rostering while keeping
the personnel costs under control. The problem is
modeled as a multiobjective mixed-integer program.
It is solved using an ε-constraint approach. The
approach is then tested on real data of a Belgian
hospital. The rest of the paper is organized as
follows: in section 2, we present the context of the
paper. In section 3, we propose a mixed-integer
program to build the surgical teams and nurse
rosters. The model is then tested on real data and the
results are discussed in section 4. We finish with
conclusion and future work.
2 THE GENERAL FRAMEWORK
The objective of the framework is to provide the
decision maker with a tool to obtain a surgical
schedule that both satisfy human and managerial
constraints. It uses a holistic view of the problem.
The first part consisted in a model developed by
Di Martinelly et al., (2011). It considered the
planning and scheduling of surgical interventions
over 5 days. Each surgical intervention is done by a
surgeon, which has availabilities over the week. It
requires a number of resources (rooms,
anesthesiologists, nurses) to be available. At every
time period, the suggested planning must satisfy the
constraints on the number of nurses available. The
results of this model indicate the starting time of
each surgical intervention in a specific room, on a
specific day.
The detailed surgical schedule over the week is
the workload pattern used to build the nurse rosters
and the surgical teams while taking into account the
working rules.
The remainder of this paper focuses on the
second part of the framework: a multiobjective
mixed-integer program that establishes surgical
teams maximizing the affinities between the nurses
and the surgeons while making the schedule efficient
for nurses. We then suggest a solving multiobjective
approach based on the -constraint method.
3 METHODOLOGY
3.1 Problem Description
Each surgical intervention requires a number of
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