Presenting a bi-objective random planning modelfor nursing services

One of the reasons for the high waiting time for patients in hospitals is the the lack of sufficient staff in the hospital, so the inefficiency of costs and job satisfaction of hospital nursing staff stems from the use of traditional and unscientific methods in allocating nurses to shifts. The present study is designed to determine the minimum number of nurse required according to the number of patients referred at different times, determine the shift schedule with the least required hours and schedule shifts for nurses in each shift with the lowest cost for the emergency department. The research method of the present study is of the mathematical modeling and research community, patients referring to the emergency department and nurses of a medical center. Data analysis is a combination of predictive methods, queuing theory models, and linear numerical programming. To predict the number of patients referring to the emergency, the time series method and ARIMA tools were used, and the M/M/C/K model was used to examine the queue system with limited capacity. One of the most important results of this study is to determine the maximum number of nurses available in each shift. Another result of this study is the comparison of the performance of each of the meta-heuristic Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Bee Algorithm (BA) with respect to the defined indicators.