Nurse Scheduling Problem Optimization based on Water Flow-like, Vibration Damping and Bee Colony Algorithms

This research involves a nurse scheduling problem which is formulated as an integer programming model dealing with diverse constraints such as multi-skilled nurses’ requirements with different preferences and availabilities plus the hours and shifts related regulations. Due to its complex nature, two new meta-heuristic algorithms, namely, Water Flow-like Algorithm (WFA) and Vibration Damping Optimization (VDO) and another well-known meta-heuristic called Bee Colony Optimization (BCO) are developed. Two problem instances with up to 50 nurses and 35 days are defined considering a real case study via the data extracted from Isfahan-based Sina Hospital’s Infant Ward in Iran, the problems are solved to verify the effectiveness of the proposed algorithms and some comparison metrics are applied to evaluate their reliability. As the first problem yielded results displayed, 17 Pareto solutions have been gained for each objective function by the WFA algorithm, 2 Pareto solutions by VDO algorithm and 4 Pareto solutions through the BCO algorithm. And for the second problem, 50 Pareto solutions have been achieved by the WFA algorithm, 6 Pareto solutions by the VDO algorithm, and 9 Pareto solutions using the BCO algorithm. According to the results, the three approaches have the potential to solve the real nurse scheduling problems in large scale optimally (near-optimal) within minutes for both instances. Besides, the reported results show that compared to the other two algorithms, the WFA algorithm discovers the solutions with higher reliability.