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Constrained Optimization for Decision Making in Health Care Using Python: A Tutorial

Author

Listed:
  • K. H. Benjamin Leung

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada
    Scottish Ambulance Service, Edinburgh, Scotland, UK)

  • Nasrin Yousefi

    (Smith School of Business, Queen’s University, Kingston, ON, Canada)

  • Timothy C. Y. Chan

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada)

  • Ahmed M. Bayoumi

    (MAP Centre for Urban Health Solutions, St. Michael’s Hospital, Unity Health Toronto, Toronto, ON, Canada
    Department of Medicine, University of Toronto, Toronto, ON, Canada
    Division of General Internal Medicine, University of Toronto, Toronto, ON, Canada
    Institute of Health Policy, Management and Evaluation, University of Toronto, ON, Canada)

Abstract

Constrained optimization can be used to make decisions aimed at maximizing some quantity in the face of fixed limits, such as resource allocation problems in health where tradeoffs between alternatives are inherent, and has been applied in a variety of health-related applications. This tutorial guides the reader through the process of mathematically formulating a constrained optimization problem, providing intuitive explanations for each component within the problem. We discuss how constrained optimization problems can be implemented using software and provide instructions on how to set up a solution environment using Python and the Gurobi solver engine. We present 2 examples from the existing literature that illustrate different constrained optimization problems in health and provide the reader with Python code used to solve these problems as well as a discussion of results and sensitivity analyses. This tutorial can be used to help readers formulate constrained optimization problems in their own application domains. Highlights This tutorial provides a user-friendly guide to mathematically formulating constrained optimization problems and implementing them using Python. Two examples are presented to illustrate how constrained optimization is used in health applications, with accompanying Python code provided.

Suggested Citation

  • K. H. Benjamin Leung & Nasrin Yousefi & Timothy C. Y. Chan & Ahmed M. Bayoumi, 2023. "Constrained Optimization for Decision Making in Health Care Using Python: A Tutorial," Medical Decision Making, , vol. 43(7-8), pages 760-773, October.
    • Handle: RePEc:sae:medema:v:43:y:2023:i:7-8:p:760-773
    DOI: 10.1177/0272989X231188027
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