Designs and Implementation SCHEDULING MODEL AND IMPLEMENTATION
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.