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A multi-commodity flow network design problem

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  • Foulds, L. R.

Abstract

There exist systems which can be usefully described by a network containingarcs through which a commodity of one type flows. This paper is concerned with finding a solution procedure for a particular multi-commodity flow network design problem. The problem is to identify a set of arcs in the network such that if travel is prohibited in them all flow travels by feasible paths and its total cost is minimal. The total flow in each arc may not exced its capacity, which is a known constant. Each arc and each node of the network has a non-negative constant unit traversal cost. Between each pair of distinct nodes there is a given non-negative rate of flow from the first vertex to the second which may be split up among a number of paths according to some constant traversal cost flow assignment process. The optimality criterion is the total traversal cost of all flow, which is to be minimized. Previous work on network design problems of this type is surveyed. The principal contribution of this paper is the presentation of a solution procedure for the above problem based on branch and bound enumeration. An illustrative numerical example is included. Computational experience gained in using the procedure with a FORTRAN IV program on an IBM 370 is favourable.

Suggested Citation

  • Foulds, L. R., 1981. "A multi-commodity flow network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 273-283, August.
    • Handle: RePEc:eee:transb:v:15:y:1981:i:4:p:273-283
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    Cited by:

    1. Les Foulds & Daniel Duarte & Hugo Nascimento & Humberto Longo & Bryon Hall, 2014. "Turning restriction design in traffic networks with a budget constraint," Journal of Global Optimization, Springer, vol. 60(2), pages 351-371, October.
    2. Karimi Dehnavi, Hadi & Rezvan, Mohammad Taghi & Shirmohammadli, Abdolmatin & Vallée, Dirk, 2013. "A solution for urban road selection and construction problem using simulation and goal programming—Case study of the city of Isfahan," Transport Policy, Elsevier, vol. 29(C), pages 46-53.
    3. Gallo, Mariano & D'Acierno, Luca & Montella, Bruno, 2010. "A meta-heuristic approach for solving the Urban Network Design Problem," European Journal of Operational Research, Elsevier, vol. 201(1), pages 144-157, February.
    4. Li, Xiaopeng & Medal, Hugh & Qu, Xiaobo, 2019. "Connected infrastructure location design under additive service utilities," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 99-124.
    5. Giulio Cantarella & Antonino Vitetta, 2006. "The multi-criteria road network design problem in an urban area," Transportation, Springer, vol. 33(6), pages 567-588, November.
    6. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

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