A General Framework for Physician Rostering Using Mixed-Integer Programming and a Web-Based Graphical User Interface

TL;DR

This work addresses the practical problem of physician rostering across hospitals with diverse roster structures by proposing a general, GUI-enabled MIP framework. The approach supports planning horizons of $T$ days, a rich set of constraints (rest times, absences, duty/shift blocks, pools for fairness, and weekend rules) and physician preferences, all configurable through a web interface. Real-world validation across internal medicine, cardiology, and orthopedics/trauma demonstrates roster quality comparable to department-specific models, with total solve times under a few minutes using the CBC solver. The web-based deployment facilitates non-expert use, improves transparency, and enables easy adaptation to evolving roster structures and regulations. The work thus offers a practical pathway to scalable, department-agnostic physician rostering with clear directions for future integration and enhancements such as cyclic rosters and HIS integration.

Abstract

Physician rostering in hospitals is complex due to varying shift structures, qualifications, and department- or hospital-specific regulations. Most existing optimization models are highly tailored to a single hospital or department and rarely see practical use. We present a general framework and a corresponding mixed-integer programming (MIP) model for physician rostering that accommodates a wide variety of roster structures and constraints. The model is integrated into a web application with an advanced graphical user interface (GUI), allowing physicians to specify preferences and hospital staff to configure the MIP model to their roster requirements without any mathematical or technical background. This approach enables easy adaptation to different hospitals or departments and straightforward updates in response to structural changes, such as new duties or modified qualifications. The applicability and effectiveness of the framework are demonstrated using real-world data from three departments in different hospitals specializing in internal medicine, cardiology, and orthopedics/trauma surgery. In one department, the system is already in everyday use, while in the other two, our model achieves comparable or improved roster quality relative to existing department-specific models, highlighting its potential as a versatile and practical tool for physician rostering.

Figures (2)

• Figure 1: Creation of a duty block consisting of different duties over a week in the web application.
• Figure 2: Input interfaces for specifying physicians’ preferences in the web application. (a) Duty-specific preferences; (b) Weekly preferences.