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The dynamic transportation problem: A survey

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  • James H. Bookbinder
  • Suresh P. Sethi

Abstract

The dynamic transportation problem is a transportation problem over time. That is, a problem of selecting at each instant of time t, the optimal flow of commodities from various sources to various sinks in a given network so as to minimize the total cost of transportation subject to some supply and demand constraints. While the earliest formulation of the problem dates back to 1958 as a problem of finding the maximal flow through a dynamic network in a given time, the problem has received wider attention only in the last ten years. During these years, the problem has been tackled by network techniques, linear programming, dynamic programming, combinational methods, nonlinear programming and finally, the optimal control theory. This paper is an up‐to‐date survey of the various analyses of the problem along with a critical discussion, comparison, and extensions of various formulations and techniques used. The survey concludes with a number of important suggestions for future work.

Suggested Citation

  • James H. Bookbinder & Suresh P. Sethi, 1980. "The dynamic transportation problem: A survey," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 65-87, March.
    • Handle: RePEc:wly:navlog:v:27:y:1980:i:1:p:65-87
    DOI: 10.1002/nav.3800270107
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    Cited by:

    1. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
    2. Jian Yang & Patrick Jaillet & Hani Mahmassani, 2004. "Real-Time Multivehicle Truckload Pickup and Delivery Problems," Transportation Science, INFORMS, vol. 38(2), pages 135-148, May.

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