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Nurse Scheduling Problem (NSP) is the assignment of a number of nurses to a number of shifts in order to satisfy hospital’s demand. The objectives of NSP are the minimization of the overall hospital cost, and the maximization of nurses’ preferences while taking into consideration the governmental rules and hospital standards. In this article, a proposed mathematical model for the NSP is presented, which is based on the idea of multi-commodity network flow model. The proposed model was verified using hypothetical instances as well as benchmark instances, then, it is applied to a real case study in an Egyptian hospital. The results demonstrate the advantage of using the proposed model in generating schedule required to solve the problem. Furthermore, it proves the superiority of the obtained schedule to those generated manually by the supervisor head nurse as it improves the level of nurses’ satisfaction by creating fair schedule system take care about nurses’ preferences as well as decreases the overall overtime cost by 36%.

A new formulation and solution for the nurse scheduling problem: A case study in Egypt