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A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure

Author

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  • Gregory D. Glockner

    (ILOG, Inc., 1080 Linda Vista Avenue, Mountain View, California 94043)

  • George L. Nemhauser

    (Logistics Engineering Center, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We consider a dynamic network flow problem where the arc capacities are random variables. This gives a multistage stochastic linear program. We describe the randomness using a multi-scenario approach. Because of the multilayered structure, there are several ways to decompose the linear program. We classify different decomposition schemes, and we develop a scheme called compath decomposition , which is derived from path decomposition for network flows. We give a polynomial-time algorithm to find a cheapest compath that can solve the subproblems resulting from compath decomposition. Finally, compath decomposition is extended to multicommodity flow problems.

Suggested Citation

  • Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:233-242
    DOI: 10.1287/opre.48.2.233.12384
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    References listed on IDEAS

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