Nurse scheduling problem by considering reserve nurses: a mathematical modeling and hybrid meta-heuristic algorithm

Saeed Saemi ()
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Saeed Saemi: Islamic Azad University

Operational Research, 2025, vol. 25, issue 4, No 15, 26 pages

Abstract: Abstract In this study, the Nurse Scheduling Problem (NSP), as one of the main staff scheduling problems in the healthcare system, is determined based on the hospital and clinical rules about employing nurses. In order to cover the work schedule of the regular nurses due to their possible unavailability and to meet the increasing demands of patients in receiving treatment, the problem is investigated by scheduling a number of existing nurses on each day as reserve ones to be on call to go to the workplace in case necessary. For this purpose, a Mixed-Integer Linear Programming (MILP) model is presented for the problem by scheduling the existing nurses on each shift-day into two types: as regular staff to serve the patients and as reserve one to be standby to be employed in case hospitals need their presence. Moreover, the problem is formulated to minimize nurses’ dissatisfaction score about being employed as a reserve on each shift-day and the cost related to nurses’ unbalanced work schedule. Due to the NP-hard complexity of the problem, a Hybrid Algorithm (HA) by combining genetic and simulated annealing algorithms is utilized to heuristically solve the problem. The results indicate the efficiency of the HA in finding solutions with 0.82% average gap and 4.02% average improvement rate in a reasonable CPU time compared to the solutions obtained by the exact method for the small and large scale problems, respectively. Moreover, the HA benefits from finding lower cost solutions compared to the simple genetic algorithm in approximately similar computing time for problems with different sizes.

Keywords: Nurse scheduling problem; Reserve nurse; Mathematical modeling; Hybrid meta-heuristic algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12351-025-00981-7

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