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Routing in Point-to-Point Delivery Systems: Formulations and Solution Heuristics

Author

Listed:
  • Janny M. Y. Leung

    (Yale University, New Haven, Connecticut)

  • Thomas L. Magnanti

    (MIT, Cambridge, Massachusetts)

  • Vijay Singhal

    (Resource Management Systems, Cambridge, Massachusetts)

Abstract

We develop an optimization-based approach for a point-to-point route planning problem that arises in many large scale delivery systems (for example, less-than-truckload freight, rail, mail and package delivery, communications). In these settings, a firm which must ship goods between many origin and destination pairs on a network needs to specify a route for each origin–destination pair so as to minimize transportation costs and/or transit times. Typically, the cost structure is very complicated. The approach discussed in this paper exploits the structure of the problem to decompose it into two smaller subproblems, each amenable to solution by a combination of optimization and heuristic techniques. One subproblem is an “assignment” problem with capacity constraints. The other subproblem is a mixed-integer multicommodity flow problem. We propose solution methods based on Lagrangian relaxation for each subproblem. Computational results with these methods and with a heuristic procedure for the multicommodity flow problem on a problem met in practice are encouraging and suggest that mathematical programming methods can be successfully applied to large-scale problems in delivery systems planning and other problems in logistical system design.

Suggested Citation

  • Janny M. Y. Leung & Thomas L. Magnanti & Vijay Singhal, 1990. "Routing in Point-to-Point Delivery Systems: Formulations and Solution Heuristics," Transportation Science, INFORMS, vol. 24(4), pages 245-260, November.
    • Handle: RePEc:inm:ortrsc:v:24:y:1990:i:4:p:245-260
    DOI: 10.1287/trsc.24.4.245
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    Cited by:

    1. Bernardes Real, Luiza & O'Kelly, Morton & de Miranda, Gilberto & Saraiva de Camargo, Ricardo, 2018. "The gateway hub location problem," Journal of Air Transport Management, Elsevier, vol. 73(C), pages 95-112.
    2. G. Guastaroba & M. G. Speranza & D. Vigo, 2016. "Intermediate Facilities in Freight Transportation Planning: A Survey," Transportation Science, INFORMS, vol. 50(3), pages 763-789, August.
    3. Tamvada, Srinivas Subramanya & Mansouri, Bahareh & Hassini, Elkafi & Pribytkov, Theodore, 2021. "An integer programming model and directed Steiner-forest based heuristic for routing less-than-truckload freight," International Journal of Production Economics, Elsevier, vol. 232(C).
    4. M-G Yoon & J Current, 2008. "The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 80-89, January.
    5. Jianjun Zhang & Ou Tang & Jin Zhao & Jiazhen Huo & Yonggang Xia, 2013. "CPEL Redesigns Its Land Express Network," Interfaces, INFORMS, vol. 43(3), pages 221-231, May-June.
    6. Lin, Cheng-Chang, 2001. "The freight routing problem of time-definite freight delivery common carriers," Transportation Research Part B: Methodological, Elsevier, vol. 35(6), pages 525-547, July.
    7. Klaus Büdenbender & Tore Grünert & Hans-Jürgen Sebastian, 2000. "A Hybrid Tabu Search/Branch-and-Bound Algorithm for the Direct Flight Network Design Problem," Transportation Science, INFORMS, vol. 34(4), pages 364-380, November.
    8. Mehdy Roayaei & Mohammadreza Razzazi, 2017. "Augmenting weighted graphs to establish directed point-to-point connectivity," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 1030-1056, April.
    9. J. F. Campbell & A. T. Ernst & M. Krishnamoorthy, 2005. "Hub Arc Location Problems: Part I---Introduction and Results," Management Science, INFORMS, vol. 51(10), pages 1540-1555, October.
    10. Meuffels, W.J.M., 2015. "The design of road and air networks for express service providers," Other publications TiSEM d3266cb8-bc55-41be-adc7-4, Tilburg University, School of Economics and Management.
    11. Louwerse, I. & Mijnarends, J. & Meuffels, I. & Huisman, D. & Fleuren, H.A., 2012. "Scheduling Movements in the Network of an Express Service Provider," Econometric Institute Research Papers EI 2012-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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