A Goal Programming Model for Nurse Shift Scheduling Incorporating Flexible Constraints: A Case Study in an Operating Room Department

Background/Objectives: Operating room nurse scheduling is a complex healthcare optimization problem. Operating room settings are particularly challenging because permanent and subcontracted nurses operate under complex 16 h and 24 h shift structures, with continuous surgical coverage requirements and recovery-period requirements. To our knowledge, few existing models simultaneously integrate nurse preferences, recovery-period requirements, and heterogeneous shift structures within a unified goal programming framework. This study aims to develop and implement a goal programming model that incorporates nurses’ needs and preferences as flexible constraints to optimize shift scheduling in an operating room department. Methods: This single-center case study combined a qualitative component, an analysis of scheduling records, and mathematical optimization modeling. It was conducted at the operating room department of a public hospital in Türkiye employing 37 permanent and 7 subcontracted nurses in the shift rotation, together with a head nurse responsible for the roster. The hospital was selected purposively as a high-volume public center with a dual-tier staffing model and a fully manual scheduling process; semi-structured interviews were then conducted with all 37 permanent nurses and the head nurse (n = 38). The seven subcontracted nurses were not interviewed; the constraints applying to them were derived from national regulatory guidance and operational information provided by the head nurse. Scheduling requirements were formalized as five flexible constraints informed by nurses’ preferences and institutional requirements and incorporated into a goal programming model alongside obligatory coverage and staffing constraints. Penalty weights were calibrated through structured consultation with the head nurse. The model was solved to proven optimality using Python with the OR-Tools CP-SAT solver. Results: The optimized 28-day schedule eliminated direct night-to-day shift transitions, which, under the manual schedule, affected approximately three nurse assignments per week. Weekly night shifts were limited to a maximum of two per nurse in every planning block, a limit that individual nurses exceeded under the manual system. Monthly working days were standardized to a range of 18–20 days (mean = 19.84, SD = 0.49) from an irregular 14–26-day range (mean = 20.57, SD = 3.51), an 86% reduction in the standard deviation. All identified rest-period violations for subcontracted nurses on 16 h and 24 h duties were eliminated in the optimized schedule. Conclusions: A goal programming model integrating flexible constraints informed by nurses’ preferences and institutional requirements generated a schedule with greater equality in the distribution of monthly working days and improved compliance with the predefined scheduling objectives compared with the historical manual schedule. The model offers nurse managers a potentially adaptable decision-support tool that requires prospective validation in other settings. Future work should extend the model to incorporate dynamic patient demand, cost optimization, and multi-department scheduling scenarios.