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Primal dual algorithms for the vehicle refueling problem

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  • George Steiner
  • Dan Wang
  • Yufei Yuan

Abstract

Mehrez, Stern, and Ronen have defined a vehicle refueling problem in which a fleet of vehicles travels on a round‐trip, self‐contained mission from a common origin, with the objective of maximizing the operational range of the fleet. They have defined a “pure refueling chain” strategy for transferring fuel between vehicles in the fleet, and have solved the problem in the special cases when all vehicles have the same fuel capacity or consumption rate. In this article we present algorithms for the general case, where vehicles have different capacities and consumption rates. Our approach is based on a new primal dual formulation of the problem. The exact algorithm was effective to find the optimal solution for a fleet size n ⩽13. For larger fleets, we present an approximation version of it, which very quickly found a solution within 1% of the maximum possible range for arbitrarily large (up to n = 200) fleets. We also show that a small number of the best vehicles can always reach almost the same range as a large fleet. © 1992 John Wiley & Sons, Inc.

Suggested Citation

  • George Steiner & Dan Wang & Yufei Yuan, 1992. "Primal dual algorithms for the vehicle refueling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 905-918, December.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:7:p:905-918
    DOI: 10.1002/1520-6750(199212)39:73.0.CO;2-T
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    References listed on IDEAS

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    1. Abraham Mehrez & Helman I. Stern & David Ronen, 1983. "Vehicle fleet refueling strategies to maximize operational range," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 319-342, June.
    2. F. P. Kelly, 1982. "A Remark on Search and Sequencing Problems," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 154-157, February.
    3. Avraham A. Melkman & Helman I. Stern & Avraham Mehrez, 1986. "Optimal refueling sequence for a mixed fleet with limited refuelings," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 759-762, November.
    4. Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1984. "A Cutting Plane Algorithm for the Linear Ordering Problem," Operations Research, INFORMS, vol. 32(6), pages 1195-1220, December.
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