From 0–1 Goal Programming to Binary Integer Programming: An Improved Formulation for Optimizing Nurse Rostering in a Malaysian Military Maternity Ward

ABSTRACT This study examines the nurse rostering problem in the maternity ward of a military hospital to improve operational efficiency while maintaining nurse well‐being. In the initial phase, a preemptive 0–1 goal programming model (GP) is introduced to generate feasible nurse duty rosters. This model guarantees fair rotation within specified working‐day limits, avoids overlapping assignments for all nurses across all shift types and prevents nurses from working 7 consecutive days. Additionally, three soft constraints are considered, where the model prevents irregular rest patterns, such as isolated work or off days, and ensures equitable workload distribution. Although the 0–1 GP model generates satisfactory schedules, the soft constraint of avoiding isolated working days is not fulfilled. Therefore, the model is further refined by using binary integer programming (BIP), which incorporates nurse categories (senior, community, and health assistants' nurses) as key components in the maternity ward. The soft constraints addressed in an initial model are now treated as hard constraints. Apart from that, this improved model also considers additional hard constraints, including night shift sequencing and recovery, daily‐on‐call duty, and adequate rest days constraints to improve nurse well‐being. Actual duty rosters collected from the head nurse of a maternity ward are used to evaluate the performance of both models. Computational results show that the improved BIP model produces optimal schedules that satisfy operational requirements outlined by Lumut Armed Forces Hospital. For a 14‐day scheduling cycle, the model, however, requires a minimum of 15 nurses, with each category comprising at least the average number of nurses to ensure model feasibility. Overall, the findings demonstrate that extending the initial formulation, from a 0–1 GP model to an improved BIP model results in a comprehensive model and improves solution quality for complex healthcare rostering problems.