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Transportation problem on a graph

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Abstract

We consider a transportation problem defined on a node-weighted undirected graph. Weight is positive if the amount of commodity is stored at a node, and negative if the amount is needed at the node. We want to meet all demands by transporting commodities using vehicles prepared either at nodes or edges which only travel to and from neighbors. In a trip from a node to a neighbor we can send commodities and also bring back some other commodities. Problem is to decide whether we can meet all demands by carrying out a set of trips in a few rounds. We define three different schemes to solve the problem and examine their performances. We present a polynomial-time algorithm for deciding whether there is a single round of trips using one vehicle at each node that meet all demands for one-commodity case.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP20K11673. The author would like to thank David Kirkpatrick, Ryuhei Uehara, Takeshi Tokuyama, and Yota Otachi for helpful discussions, and also anonymous reviewers of the paper for pointing out many mistakes.

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  1. Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    Tetsuo Asano

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  1. Tetsuo Asano
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Correspondence to Tetsuo Asano.

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Asano, T. Transportation problem on a graph. Japan J. Indust. Appl. Math. 40, 289–302 (2023). https://doi.org/10.1007/s13160-022-00516-z

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  • DOI: https://doi.org/10.1007/s13160-022-00516-z

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