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A Stochastic Multiperiod Multimode Transportation Model

Author

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  • Joseph L. Midler

    (The Rand Corporation, Santa Monica, California)

Abstract

This paper develops a dynamic programming model for selecting an optimal combination of transportation modes over a midtiperiod planning horizon. The formulation explicitly incorporates uncertainty regarding future requirements or demands for a number of commodity classes. In addition to determining the optimal modes to employ, the model assigns individual commodity classes to various modes, determines which supply points serve which destinations, and reroutes carriers from destinations to alternative sources where they will be most effective. The model is formulated as an optimal discrete time stochastic control problem where cost is quadratic and dynamic equations linear in the state and control variables. This model may be solved in closed form by an efficient dynamic programming algorithm that permits the treatment of relatively large scale systems. Also developed is an alternative, generally suboptimal method of solution, based upon solving a sequence of convex programming problems over time. This technique may be employed for a more general class of problems. In both methods the use of “shadow prices” that arise is discussed.

Suggested Citation

  • Joseph L. Midler, 1969. "A Stochastic Multiperiod Multimode Transportation Model," Transportation Science, INFORMS, vol. 3(1), pages 8-29, February.
    • Handle: RePEc:inm:ortrsc:v:3:y:1969:i:1:p:8-29
    DOI: 10.1287/trsc.3.1.8
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