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A relax-and-fix-based algorithm for the vehicle-reservation assignment problem in a car rental company

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  • Oliveira, Beatriz Brito
  • Carravilla, Maria Antónia
  • Oliveira, José Fernando
  • Toledo, Franklina M.B.

Abstract

Empty repositions are a major problem for car rental companies that deal with special types of vehicles whose number of units is small. In order to meet reservation requirements concerning time and location, companies are forced to transfer cars between rental stations, bearing significant costs and increasing the environmental impact of their activity due to the fuel consumption and CO2 emission. In this paper, this problem is tackled under a vehicle-reservation assignment framework as a network-flow model in which the profit is maximized. The reservations are allocated considering the initial and future availability of each car, interdependencies between rental groups, and different reservation priorities. To solve this model, a relax-and-fix heuristic procedure is proposed, including a constraint based on local branching that enables and controls modifications between iterations. Using real instances, the value of this approach is established and an improvement of 33% was achieved when compared to the company’s current practices.

Suggested Citation

  • Oliveira, Beatriz Brito & Carravilla, Maria Antónia & Oliveira, José Fernando & Toledo, Franklina M.B., 2014. "A relax-and-fix-based algorithm for the vehicle-reservation assignment problem in a car rental company," European Journal of Operational Research, Elsevier, vol. 237(2), pages 729-737.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:2:p:729-737
    DOI: 10.1016/j.ejor.2014.02.018
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    References listed on IDEAS

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    Cited by:

    1. Amanda O. C. Ayres & Betania S. C. Campello & Washington A. Oliveira & Carla T. L. S. Ghidini, 2021. "A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1047-1076, December.
    2. Rakiz, Asma & Absi, Nabil & Fenies, Pierre, 2023. "Comparing approaches for a multi-level planning problem in a mining industry," International Journal of Production Economics, Elsevier, vol. 265(C).
    3. Oliveira, Beatriz Brito & Carravilla, Maria Antónia & Oliveira, José Fernando, 2017. "Fleet and revenue management in car rental companies: A literature review and an integrated conceptual framework," Omega, Elsevier, vol. 71(C), pages 11-26.
    4. Absi, Nabil & van den Heuvel, Wilco, 2019. "Worst case analysis of Relax and Fix heuristics for lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 279(2), pages 449-458.
    5. Monnerat, Filipe & Dias, Joana & Alves, Maria João, 2019. "Fleet management: A vehicle and driver assignment model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 64-75.
    6. Oliveira, Beatriz Brito & Carravilla, Maria Antónia & Oliveira, José Fernando, 2018. "Integrating pricing and capacity decisions in car rental: A matheuristic approach," Operations Research Perspectives, Elsevier, vol. 5(C), pages 334-356.
    7. Nikzad, Erfaneh & Bashiri, Mahdi & Abbasi, Babak, 2021. "A matheuristic algorithm for stochastic home health care planning," European Journal of Operational Research, Elsevier, vol. 288(3), pages 753-774.

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