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A mathematical programming model for optimizing the staff allocation in radiotherapy under uncertain demand

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  • Vieira, Bruno
  • Demirtas, Derya
  • van de Kamer, Jeroen B.
  • Hans, Erwin W.
  • van Harten, Wim

Abstract

As the number of people diagnosed with cancer increases, demand for radiotherapy (RT) services has been continuously growing. In RT, delays in the start of treatment have shown to increase the risk of tumor progression in various cancer types, and patients experience greater psychological distress when subject to longer waiting times. The RT process, which involves imaging and treatment planning before treatment, is subject to complexities that hamper resource planning and control. On the demand side, the amount of workload in each operation depends on the highly variable patient inflow. On the supply side, radiation therapy technologists (RTTs) have multiple skills, rotation needs and partial availability, which makes the allocation of RTTs a complex task that often leads to situations of understaffing, jeopardizing the fulfillment of the patients' waiting time standards. In this paper, we propose a stochastic mixed-integer linear programming model that optimizes the allocation of RTTs to multiple operations in RT over a set of scenarios of patient inflow. The scenarios are generated from historical patient data, and the final RTT allocation covers the workload associated with all scenarios. The goal is to maximize the (expected) number of patients completing pre-treatment within the waiting time target. Results for a case study in the RT department of the Netherlands Cancer Institute show that, on average, the number of patients able to start treatment within the maximum waiting time standards may increase from 91.3% to 97.9% for subacute patients, and from 96.3% to 100.0% for regular patients.

Suggested Citation

  • Vieira, Bruno & Demirtas, Derya & van de Kamer, Jeroen B. & Hans, Erwin W. & van Harten, Wim, 2018. "A mathematical programming model for optimizing the staff allocation in radiotherapy under uncertain demand," European Journal of Operational Research, Elsevier, vol. 270(2), pages 709-722.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:709-722
    DOI: 10.1016/j.ejor.2018.03.040
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    References listed on IDEAS

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    1. Ruiz, Rubén & Vázquez-Rodríguez, José Antonio, 2010. "The hybrid flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 205(1), pages 1-18, August.
    2. Sauré, Antoine & Patrick, Jonathan & Tyldesley, Scott & Puterman, Martin L., 2012. "Dynamic multi-appointment patient scheduling for radiation therapy," European Journal of Operational Research, Elsevier, vol. 223(2), pages 573-584.
    3. Antoine Legrain & Marie-Andrée Fortin & Nadia Lahrichi & Louis-Martin Rousseau, 2015. "Online stochastic optimization of radiotherapy patient scheduling," Health Care Management Science, Springer, vol. 18(2), pages 110-123, June.
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    Cited by:

    1. Dina Bentayeb & Nadia Lahrichi & Louis-Martin Rousseau, 2023. "On integrating patient appointment grids and technologist schedules in a radiology center," Health Care Management Science, Springer, vol. 26(1), pages 62-78, March.
    2. Bruno Vieira & Derya Demirtas & Jeroen B. Kamer & Erwin W. Hans & Louis-Martin Rousseau & Nadia Lahrichi & Wim H. Harten, 2020. "Radiotherapy treatment scheduling considering time window preferences," Health Care Management Science, Springer, vol. 23(4), pages 520-534, December.
    3. Andrés Miniguano-Trujillo & Fernanda Salazar & Ramiro Torres & Patricio Arias & Koraima Sotomayor, 2021. "An integer programming model to assign patients based on mental health impact for tele-psychotherapy intervention during the Covid–19 emergency," Health Care Management Science, Springer, vol. 24(2), pages 286-304, June.

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