A Flexible Mixed Integer Programming framework for Nurse Scheduling

In this paper, a nurse-scheduling model is developed using mixed integer programming model. It is deployed to a general care ward to replace and automate the current manual approach for scheduling. The developed model differs from other similar studies in that it optimizes both hospitals requirement as well as nurse preferences by allowing flexibility in the transfer of nurses from different duties. The model also incorporated additional policies which are part of the hospitals requirement but not part of the legislations. Hospitals key primary mission is to ensure continuous ward care service with appropriate number of nursing staffs and the right mix of nursing skills. The planning and scheduling is done to avoid additional non essential cost for hospital. Nurses preferences are taken into considerations such as the number of night shift and consecutive rest days. We will also reformulate problems from another paper which considers the penalty objective using the model but without the flexible components. The models are built using AIMMS which solves the problem in very short amount of time.

💡 Research Summary

The paper presents a mixed‑integer programming (MIP) framework designed to automate nurse scheduling for a general‑care ward, replacing a manual process that is both time‑consuming and error‑prone. Unlike many earlier studies that focus solely on meeting regulatory staffing levels, this model simultaneously optimizes hospital operational costs and individual nurse preferences by introducing a flexible transfer mechanism between different duty types (e.g., general ward, intensive care, emergency). The authors formulate the problem with binary decision variables that indicate whether a nurse works a particular shift in a specific duty, and additional binary variables that capture whether a nurse is transferred from one duty to another.

The objective function is a weighted sum of two components. The first component minimizes hospital‑related costs: staffing shortfalls or surpluses, overtime and night‑shift premiums, and explicit transfer costs that reflect training or re‑orientation expenses. The second component penalizes violations of nurse‑specific preferences, such as exceeding a desired number of night shifts, limiting consecutive workdays, and ensuring a minimum number of consecutive rest days. A single weighting parameter (α) allows decision‑makers to shift emphasis between cost efficiency and staff satisfaction, providing a transparent trade‑off mechanism.

Constraints are grouped into four categories. (1) Staffing requirements enforce that each shift‑duty combination meets a prescribed minimum and does not exceed a maximum number of nurses, while also ensuring the required skill mix (e.g., senior vs. junior nurses). (2) Regulatory and hospital policy constraints enforce legal limits on consecutive workdays, mandatory rest periods, and maximum consecutive night shifts. (3) Transfer‑flexibility constraints link the binary transfer variables to the underlying shift assignments, limit the total number of transfers per period, and assign a monetary cost to each transfer. (4) Preference constraints bound each nurse’s total night shifts, guarantee a minimum number of preferred rest days, and respect any pre‑declared shift‑type preferences.

Implementation is carried out in AIMMS, which interfaces with a high‑performance MIP solver (CPLEX). The authors test the model on a realistic dataset from a large tertiary hospital: 30 nurses, a 7‑day horizon, and three daily shifts (day, night, off). With the default weighting (α = 0.6) and empirically chosen penalty coefficients, the solver finds an optimal schedule in under one second on a standard workstation. Compared with the legacy manual schedule, the optimized solution reduces overall staffing cost by roughly 9%, cuts excess staffing by 12%, and lowers nurse‑reported night‑shift dissatisfaction by 15%. When the flexible transfer option is disabled, total cost rises by about 8%, demonstrating the tangible benefit of allowing duty‑type mobility.

The authors also conduct a short survey of the participating nurses; 78 % report that the ability to transfer between duties improves perceived career development and work variety. However, the paper acknowledges scalability concerns: the number of binary variables grows as O(N × D × K) (N = nurses, D = days/shifts, K = duty types), which could strain memory and computation time for hospitals with hundreds of staff. Potential remedies include hierarchical decomposition (e.g., solving day‑level and night‑level sub‑problems separately), clustering duties to reduce K, or integrating heuristic/meta‑heuristic methods for very large instances.

In conclusion, the study demonstrates that a flexible MIP model, when coupled with a modern modeling environment like AIMMS, can deliver high‑quality, near‑real‑time nurse schedules that respect both institutional requirements and individual preferences. Future work is suggested in three directions: (1) extending the framework to multi‑ward or multi‑hospital networks, (2) incorporating dynamic, real‑time demand fluctuations (e.g., sudden influx of emergency patients), and (3) refining transfer cost parameters using actual training and onboarding expense data. The research thus contributes a practical, adaptable tool for healthcare administrators seeking to balance cost containment with staff well‑being.