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MILP models of a patient transportation problem

Author

Listed:
  • Martin Tóth

    (FERCAM GmbH)

  • Tamás Hajba

    (Széchenyi István University)

  • Adrián Horváth

    (Széchenyi István University)

Abstract

With ageing societies and increasing number of patients, there is a growing need for quality services that help transporting non-urgent patients to hospitals. In logistics, patient transportation problems are usually modeled as a dial-a-ride problem. In a Dial-a-Ride problem, a fleet of vehicles is providing the delivery services between the loading points and the delivery destinations. The demands are known in advance. In most cases the total travel distance of the vehicles is to be minimized. In this paper, we consider a specific dial-a-ride problem, where a single vehicle is used to transport patients to the same hospital. In determining the optimal route, the multiple and different travel needs of patients, such as their maximum travel time, are also taken into consideration. We introduce 4 different mixed integer linear programming models of the routing problem. Finally, the efficiency of the four models was compared using some real-life problems by solving them with a commercial solver.

Suggested Citation

  • Martin Tóth & Tamás Hajba & Adrián Horváth, 2024. "MILP models of a patient transportation problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(4), pages 903-922, December.
    • Handle: RePEc:spr:cejnor:v:32:y:2024:i:4:d:10.1007_s10100-023-00902-z
    DOI: 10.1007/s10100-023-00902-z
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    References listed on IDEAS

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    1. P. L. van den Berg & J. T. van Essen, 2019. "Scheduling Non-Urgent Patient Transportation While Maximizing Emergency Coverage," Transportation Science, INFORMS, vol. 53(2), pages 492-509, March.
    2. Ho, Sin C. & Szeto, W.Y. & Kuo, Yong-Hong & Leung, Janny M.Y. & Petering, Matthew & Tou, Terence W.H., 2018. "A survey of dial-a-ride problems: Literature review and recent developments," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 395-421.
    3. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    4. Andrew Lim & Zhenzhen Zhang & Hu Qin, 2017. "Pickup and Delivery Service with Manpower Planning in Hong Kong Public Hospitals," Transportation Science, INFORMS, vol. 51(2), pages 688-705, May.
    5. Agra, Agostinho & Christiansen, Marielle & Wolsey, Laurence, 2022. "Improved models for a single vehicle continuous-time inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 297(1), pages 164-179.
    6. Yuan Qu & Jonathan F. Bard, 2015. "A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity," Transportation Science, INFORMS, vol. 49(2), pages 254-270, May.
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