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A continuous approximation model for the fleet composition problem

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  • Jabali, Ola
  • Gendreau, Michel
  • Laporte, Gilbert

Abstract

This paper presents a continuous approximation model to determine the long-term vehicle fleet composition needed to perform distribution activities. The problem is a realistic variant of the vehicle routing problem, in which the fleet size and mix are also decision variables. The types of vehicles differ in terms of their capacities, fixed costs and variable costs. The objective is to minimize the total cost, subject to capacity and route duration constraints. We assume customers are distributed over a circular service region partitioned into zones, each of which is serviced by a single vehicle. The routing costs are assessed through a continuous approximation model. We present a mixed integer non-linear formulation for the problem, followed by computationally efficient upper and lower bounding procedures. The performance of the model and of its bounds is assessed on several test instances.

Suggested Citation

  • Jabali, Ola & Gendreau, Michel & Laporte, Gilbert, 2012. "A continuous approximation model for the fleet composition problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1591-1606.
    • Handle: RePEc:eee:transb:v:46:y:2012:i:10:p:1591-1606
    DOI: 10.1016/j.trb.2012.06.004
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    10. Mehdi Nourinejad & Matthew J. Roorda, 2017. "A continuous approximation model for the fleet composition problem on the rectangular grid," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 373-401, March.
    11. John Gunnar Carlsson & Siyuan Song, 2018. "Coordinated Logistics with a Truck and a Drone," Management Science, INFORMS, vol. 64(9), pages 4052-4069, September.
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    14. Baller, Annelieke C. & Dabia, Said & Dullaert, Wout E.H. & Vigo, Daniele, 2019. "The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1013-1033.
    15. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "Thirty years of heterogeneous vehicle routing," European Journal of Operational Research, Elsevier, vol. 249(1), pages 1-21.
    16. Figliozzi, Miguel & Saenz, Jesus & Faulin, Javier, 2020. "Minimization of urban freight distribution lifecycle CO2e emissions: Results from an optimization model and a real-world case study," Transport Policy, Elsevier, vol. 86(C), pages 60-68.
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    20. Mohamed Amjath & Laoucine Kerbache & James MacGregor Smith, 2024. "A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System," Logistics, MDPI, vol. 8(1), pages 1-38, March.
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    23. Franceschetti, Anna & Honhon, Dorothée & Laporte, Gilbert & Woensel, Tom Van & Fransoo, Jan C., 2017. "Strategic fleet planning for city logistics," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 19-40.

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