Information and Communication Technology Seminar, Vol. 1 No. 1, August 2005
ISSN 1858-1633 2005 ICTS 72
MODIFIED BAYESIAN OPTIMIZATION ALGORITHM FOR NURSE SCHEDULING
I N. Sutapa, I. H. Sahputra, V. M. Kuswanto
Industrial Engineering Department, Petra Christian University 142-144 Siwalankerto Surabaya, Indonesia
Email: mantapapetra.ac.id, iwanhpetra.ac.id
ABSTRACT
This paper discusses the application of modified Bayesian optimization algorithm for weekly schedules
of nurses that cover the demand for nurses for every grade considering their preferences. All probable shift
patterns were generated in the algorithm. The first population of rule strings shift patterns was chosen
randomly using roulette wheel method from all probable shift patterns. A particular shift pattern was
determined for every nurse using four building rules. The process would be repeated continuously until the
desired fitness function is found. The result was proposed schedule can cover the requirement of nurse
for every grade with minimum preference value. It can be seen from the mean of fitness function proposed
schedule was 1.903,73, which was less than real one, which was 3.268,67. The proposed schedule also was
better than real one in quality and fairness aspects. Keywords : modified Bayesian optimization
algorithm, nurse scheduling
1. INTRODUCTION
Nurse scheduling is a challenging job because it’s complexity. For every work shift period, there is
particular number requirement of nurses with specific grade. A good scheduling also considers the
preference of the nurse for work shift period and also vacation period. In the previous work done by
Oktopina [1] cyclical scheduling method that every nurse would have a particular cyclic work shift pattern
was used. But the weakness of this cyclic shift pattern is not flexible. In other work done by Li and Aickelin
[2], Bayesian optimization algorithm was used. But in their case, there was no rule that every nurse must take
two successive night shifts at least every two weeks as in this particular hospital case. In this case after the
nurse works at night shift she has one vacation day. Also in Li and Aickelin [2] there were only two work-
shift times that are day and night. In this case, there are three work-shift times : morning, afternoon, and
night. It is also to be considered in this case that higher-grade nurse can replace the lower one, but not
reversible. Because of the nature of the problem in this case, some modification had been made in the
Bayesian Algorithm. A pavilliun in the hospital, which has capacity
39 patients, was used for study case. There are 29 nurses including one room chief and 2 vice chief.
Grades of nurse in this hospital are senior, medior, and junior. For scheduling reason, the nurses are divided
into 2 teams that are team A and team B. Number of nurses and grade for every team is same. There is
scheduling rotation for nurses from team A to team B or reversible every 3 month. Schedule will be issued
weekly on Saturday, which covers Sunday until following Saturday. There are 3 work-shift times :
morning 07.00-14.00, afternoon 14.00-21.00 and night 21.00-07.00. Every nurse can request particular
schedule for one-day weekly vacation but the decision depends on the room chief. Table 1 shows the
requirement of number and grade of nurses.
Table 1. Requirement of number and grade of nurses
Grade Shift
Senior Medior junior Total
Morning 6 2 2 10 Afternoon 3
2 4 9
Night 1 2
3
This paper discuss the solution for nurse scheduling problem at the particular hospital,
considering the number of nurses required, grade of nurses, and minimum preference value of the nurses.
2. SCHEDULING MODEL AND IMPLEMENTATION
A modified Bayesian optimization method was used to make the scheduling of the nurses. First a
Bayesian network model was formed and then modified Bayesian optimization was applied to
produce a scheduling for some period of time. The result from this algorithm was compared to the real
scheduling using statistical analysis.
2.1. The Bayesian Network Model and Modified Bayesian Optimization
For this hospital scheduling purpose, a Bayesian network was formed for all nurses in Pavilliun 11. The
network was consisted of 45.123 nodes, with 13 nurses and 3.471 shift pattern. Special for period of 24
- 30 October 2004 and 31 October - 6 November 2004, the number of nurses was 14 for every team.
The Bayesian network can be seen in figure 1.
Modified Bayesian Optimization Algorithm for Nurse Scheduling – I N Sutapa, I H Sahputra, V M Kuswanto
ISSN 1858-1633 2005 ICTS 73
Figure 1 Bayesian Network for Nurse Scheduling
This is the original algorithm as in Li and Aickelin [2] and Pelikan [3]:
1. Set t = 0, and seed initial population P0 randomly
2. Using roulette-wheel method to choose solution candidates rule strings St from Pt
3. Count the conditional probability of every node
4. For every nurse, roulette-wheel is used to choose one rule shift pattern based on
conditional probability of all nodes to develop a new rule string. A new rule strings Ot will
be produced in this step
5. Create new population Pt+1 by replacing some rule strings from Pt with Ot, and set t
= t+1 6. If stop condition is reached, back to step 2.
First, the authors tried to use this algorithm to produce a scheduling and then were compared to real
one. But the result was the proposed scheduling using the algorithm could not cover the requirement. After
considering the first model result, the authors made some modification in the algorithm, especially in the
step 4.
Instead of using roulette-wheel method to choose the rule shift pattern, the authors used sequential step
using four building rules methods to choose the rule for particular nurse. The first building method was
cover rule method. For each shift pattern in a nurse’s feasible set, calculate the total number of uncovered
shifts and would be covered if the nurse worked that shift pattern. This method does not include how many
nurses still needed for particular shift. If after applied this method, two or more shift pattern was found, k-
cheapest building rules was used to choose the shift pattern for particular nurse.
Without considering the feasibility of the shift pattern, the k-cheapest rule chooses randomly a shift
pattern from k-list of the shift pattern, which has minimum preference. If there was still more than two
shift patterns is chosen, the conditional probability was used to choose the shift pattern for particular
nurse.
Finally if there was still more than two shift patterns was chosen, contribution rule was used. This
rule is designed to considering the preference of the nurses. This rule also considers the uncovered
limitations that give preference to shift pattern that cover the uncovered shift. This rule goes through to
the all-feasible shift patterns for particular nurse and gives score to each pattern. Shift pattern, which has
highest score, will be chosen. If there were two or more shift pattern has the same highest score, the first
shift pattern found would be chosen.
2.2 Designs and Implementation
