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Two-Stage Robust Network Flow and Design Under Demand Uncertainty

Author

Listed:
  • Alper Atamtürk

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

  • Muhong Zhang

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

Abstract

We describe a two-stage robust optimization approach for solving network flow and design problems with uncertain demand. In two-stage network optimization, one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one to come up with less conservative solutions compared to single-stage optimization. However, this advantage often comes at a price: two-stage optimization is, in general, significantly harder than single-stage optimization.For network flow and design under demand uncertainty, we give a characterization of the first-stage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is (N-script)(P-script)-hard even for a network flow problem on a bipartite graph. We show, however, that if the second-stage network topology is totally ordered or an arborescence, then the separation problem is tractable.Unlike single-stage robust optimization under demand uncertainty, two-stage robust optimization allows one to control conservatism of the solutions by means of an allowed “budget for demand uncertainty.” Using a budget of uncertainty, we provide an upper bound on the probability of infeasibility of a robust solution for a random demand vector.We generalize the approach to multicommodity network flow and design, and give applications to lot-sizing and location-transportation problems. By projecting out second-stage flow variables, we define an upper bounding problem for the two-stage min-max-min optimization problem. Finally, we present computational results comparing the proposed two-stage robust optimization approach with single-stage robust optimization as well as scenario-based two-stage stochastic optimization.

Suggested Citation

  • Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
  • Handle: RePEc:inm:oropre:v:55:y:2007:i:4:p:662-673
    DOI: 10.1287/opre.1070.0428
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    References listed on IDEAS

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