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A note on a mixed routing and scheduling problem on a grid graph

Author

Listed:
  • Marisa Cenci

    (University of Rome III)

  • Mirko Giacomo

    (University of Rome III)

  • Francesco Mason

    (University of Venice)

Abstract

We consider a particular case of the Fleet Quickest Routing Problem (FQRP) on a grid graph of m × n nodes that are placed in m levels and n columns. Starting nodes are placed at the first (bottom) level, and nodes of arrival are placed at the mth level. A feasible solution of FQRP consists in n Manhattan paths, one for each vehicle, such that capacity constraints are respected. We establish m*, i.e. the number of levels that ensures the existence of a solution to FQRP in any possible permutation of n destinations. In particular, m* is the minimum number of levels sufficient to solve any instance of FQRP involving n vehicles, when they move in the ways that the literature has until now assumed. Existing algorithms give solutions that require, for some values of n, more levels than m*. For this reason, we provide algorithm CaR, which gives a solution in a graph m* × n, as a minor contribution.

Suggested Citation

  • Marisa Cenci & Mirko Giacomo & Francesco Mason, 2017. "A note on a mixed routing and scheduling problem on a grid graph," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1363-1376, November.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:11:d:10.1057_s41274-016-0152-9
    DOI: 10.1057/s41274-016-0152-9
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    References listed on IDEAS

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    1. Ángel Marín, 2006. "Airport management: taxi planning," Annals of Operations Research, Springer, vol. 143(1), pages 191-202, March.
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    Cited by:

    1. Mirko Giacomo & Francesco Mason & Marisa Cenci, 2020. "A note on solving the Fleet Quickest Routing Problem on a grid graph," 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. 28(3), pages 1069-1090, September.

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