Two mathematical programming models were applied to this case study. Model I is the holiday schedule model based on self-scheduling in order to allow the shift-table to apply nursing staff resources most efficiently. Model II is scheduled the entire shift-table to obtain the most appropriate shift-table.
A blank shift-table was offered for the nursing staff to the holiday self-schedule method.
All nursing staffs marked their own desired off days on the blank shift-table, in case of conflicts we had to negotiate and set priority with the head nurse guidance, in order to solve these conflicts.
This model uses LINGO to identify the optimal solution of a complete off-shift table.
Off Days Schedule
List the number of off days and holidays available for each nursing staff, then have all of the nursing staff mark their own desired off days.
When too many staff select the same day, the head nurse has to negotiate and set priority, ranking the importance of the reasons of different individuals for wanting the day off. When negotiation is unsuccessful, the dispute is settled by a lucky draw.
Schedule a complete day off table. (Use LINGO in this step).
Calculate the shortage of off days on holidays and weekdays for each staff member.
After scheduling a complete off-shift table, the entire shift-table can be simply completed by arranging the shifts for each nursing staff on their work days.
Using MINLP model, a GA is further adopted to solve the optimal schedule and is written using MATLAB language.
The entire Schedule
Case study in the AMC hospital
OFF DAY SCHEDULE
During the schedule rotation,nursing staff scheduled off days as they desired.
After that the head nurse had to make some coordination and adjustment.
Most of off days (90.3%) are identical to the original schedule preferred by the staff.
Results In Table.1
Final Entire Schedule
In the second stage, GA is adopted to optimize the nurse schedule. This study established parameters such as population size, probability of mutation and so on for executing GA.
A total of eight (2 x 2 x 2) combinations of different controlling factors were used. Thirty tests were conducted for each combination. The termination condition is set at the 50th generation, and the chance of obtaining the best solution is set at the 30th generation. Therefore, this study set the termination condition at the 50th generation.
Results in Table.2
A survey was conducted in the 4th floor and distributed to the staff, regarding self-scheduling method.
Results and figures in Table.3
Chang-Chun Tsaia, Cheng-Jung Leeb
Optimization of Nurse Scheduling Problem with a Two-Stage Mathematical Programming Model, aDepartment of Business Administration, Trans World University.
Arab Medical Center
This study was supported by the AMC, special thanks to the head nurse Osama for his cooperation and continuous support.