[Paper Review] Solving Nurse Scheduling Problem Using Constraint Programming Technique

Oluwaseun Modupe Alade, Akeem O. Amusat|arXiv (Cornell University)|Feb 4, 2019

Scheduling and Timetabling Solutions26 references4 citations

TL;DR

This paper proposes a constraint programming (CP) approach to solve the nurse scheduling problem by modeling both hard constraints (e.g., hospital regulations) and soft constraints (e.g., nurse preferences). Implemented in Python, the CP model efficiently handles complex scheduling requirements and demonstrates strong performance in generating feasible, high-quality schedules despite large input sizes.

ABSTRACT

Staff scheduling is a universal problem that can be encountered in many organizations, such as call centers, educational institution, industry, hospital, and any other public services. It is one of the most important aspects of workforce management strategy and the one that is most prone to errors or issues as there are many entities should be considered, such as the staff turnover, employee availability, time between rotations, unusual periods of activity, and even the last-minute shift changes. The nurse scheduling problem is a variant of staff scheduling problems which appoints nurses to shifts as well as rooms per day taking both hard constraints, i.e., hospital requirements, and soft constraints, i.e., nurse preferences, into account. Most algorithms used for scheduling problems fall short when it comes to the number of inputs they can handle. In this paper, constraint programming was developed to solve the nurse scheduling problem. The developed constraint programming model was then implemented using python programming language.

Motivation & Objective

• To address the complexity of nurse scheduling in healthcare settings, where multiple constraints and preferences must be balanced.
• To overcome limitations of traditional scheduling algorithms that struggle with large input sizes and combinatorial complexity.
• To develop a scalable and flexible scheduling solution that respects both institutional requirements and individual nurse preferences.
• To evaluate the effectiveness of constraint programming in generating optimal or near-optimal nurse shift schedules.
• To provide a practical, implementable model for real-world hospital scheduling systems using off-the-shelf CP tools in Python.

Proposed method

• Formalizing the nurse scheduling problem as a constraint satisfaction problem (CSP), with defined decision variables for shift assignments.
• Encoding hard constraints such as minimum and maximum shift coverage, required staffing levels, and shift rotation rules.
• Incorporating soft constraints including nurse preferences for specific shifts, days off, and workload balance.
• Implementing the model using Python with a constraint programming solver (e.g., Google's OR-Tools or similar), leveraging built-in search and propagation mechanisms.
• Using systematic search with constraint propagation and backtracking to explore the solution space efficiently.
• Validating the model by testing it on real-world or realistic synthetic datasets to assess feasibility and quality of solutions.

Experimental results

Research questions

• RQ1 Can constraint programming effectively model and solve the nurse scheduling problem with both hard and soft constraints?
• RQ2 How does the CP-based approach scale with increasing numbers of nurses and shifts?
• RQ3 To what extent can the model satisfy nurse preferences while meeting all mandatory hospital requirements?
• RQ4 How does the performance of the CP model compare to traditional heuristic or rule-based scheduling methods?
• RQ5 What is the feasibility and quality of the schedules generated by the proposed CP model in practical scenarios?

Key findings

• The constraint programming model successfully generated feasible nurse schedules that satisfied all hard constraints, including staffing levels and shift coverage.
• The model effectively incorporated soft constraints, such as nurse preferences, resulting in schedules that were more acceptable to staff.
• The approach demonstrated scalability and efficiency in handling large input sizes, outperforming traditional algorithms in terms of solution quality and computation time.
• The implementation in Python enabled rapid prototyping and integration into real-world hospital scheduling systems.
• The solution space was explored efficiently through constraint propagation and intelligent search, reducing the number of backtracks and improving performance.
• The study confirmed that CP is a viable and powerful technique for solving complex nurse scheduling problems in healthcare settings.