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The Round-Trip p -Center and Covering Problem on a Tree

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  • Antoon Kolen

    (Erasmus University, Rotterdam, The Netherlands)

Abstract

A task performed by a vehicle consists of picking up goods at a given client and delivering it to another client. The round-trip distance is the distance traveled by the vehicle between the departure from and the return to its depot. The round-trip p-center problem is to locate p depots with respect to a finite number of pairs of clients so as to minimize the maximum round-trip cost, which is defined as a nonlinear increasing function of the round-trip distance from the nearest depot. The round-trip covering problem is to find the minimum number of depots such that each round-trip cost is no more than a given constant. For both problems a dual problem is defined and in case the underlying network is a tree a strong duality result is proved. We give algorithms to solve both tree round-trip location problems in polynomial time.

Suggested Citation

  • Antoon Kolen, 1985. "The Round-Trip p -Center and Covering Problem on a Tree," Transportation Science, INFORMS, vol. 19(3), pages 222-234, August.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:3:p:222-234
    DOI: 10.1287/trsc.19.3.222
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    Cited by:

    1. Capelle, Thomas & Cortés, Cristián E. & Gendreau, Michel & Rey, Pablo A. & Rousseau, Louis-Martin, 2019. "A column generation approach for location-routing problems with pickup and delivery," European Journal of Operational Research, Elsevier, vol. 272(1), pages 121-131.

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