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.

2.2 Designs and Implementation

All possible shift patterns were generated according to the hospital’s regulation. There were 3.471shift patterns. This is different with Li and Aickelin [2], which used 411 shift patterns from previous hospital’s schedule for 52 weeks. This generated pattern shift was performed because the lack of data for this particular case. It was only found 473 previous shift patterns from the hospital. In Li and Aickelin [2] paper, the hospital only has two shift periods and in this study case there are three shifts period that are morning, afternoon, and night. To acquire data of preferences of the nurse for particular work shift, questioner was distributed to 26 nurses at Pavilliun 11. Nurses were asked to choose their preference, in range of 1 to 4. Value 1 indicates they strongly like and value 4 if they strongly dislike. Validity and reliability tests [4] were performed on the result. There were 26 respondents and 28 questions. Software SPSS 10.0 was used to perform the tests. To verify if the questions were valid, corrected item-total correlation r result was compared to value of r table. Value of r table for d.f.: 26 – 2 = 24 with α: 0,05 was 0,2598. This value was greater than value of r table therefore the data was valid. For reliability test, the alpha value of nurse’s preference was 0,9102. This value was greater than value of r table 0,2598 therefore the data was reliable. For making the schedule, this information is required: a. Data of the nurses. Name, preference, and team AB. b. Data of nurse requirement. Number and grade c. Data of particular one-day weekly vacation request by nurse Specific schedule request by nurse will be weighted according to the importance: Information and Communication Technology Seminar, Vol. 1 No. 1, August 2005 ISSN 1858-1633 2005 ICTS 74 − 0: Emergency. − 1: Very Important. − 2: Important. − 3: Less important d. Data of previous week schedule. This data was required because there was a hospital’s rule that every nurse must work in night shift on two successive days every two weeks. Delphi and SQL server were used to make the scheduling program and database of the nurse. Figure 2 shows the proposed schedule for period of 1-7 August 2004 for team A After running one cycle of modified Bayesian optimization algorithm, program will display message dialog that show lowest fitness function value in that cycle and let user to decide continue the program or not. If user does not satisfy with current fitness function, program will ignore the lowest one-day weekly vacation request by nurse to create new schedule. This will be repeated until the last priority and program will display the value of fitness function, nurse’s preference, and penalty of current requirement. .Figure 2 Proposed Schedule of Team A for period 1-7 August 2004

2.3. Comparison Proposed Schedule with Real Schedule