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

Marisa Cenci (), Mirko Giacomo () and Francesco Mason
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Marisa Cenci: University of Rome III
Mirko Giacomo: University of Rome III

Journal of the Operational Research Society, 2017, vol. 68, issue 11, 1363-1376

Abstract: 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.

Keywords: logistics; networks and graphs; grid graph; vehicle routing; transport (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1057/s41274-016-0152-9

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