Easily Solvable Cases of Robust Discrete Optimization Problems

  • Panos Kouvelis
  • Gang Yu
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 14)

Abstract

While the last chapter points out the difficulty associated with solving many classes of robust discrete optimization problems, the current chapter has an optimistic tone by describing polynomially solvable problems. The main source of difficulty of robust optimization problems comes from its min-max (or max-min) nature and its added dimensionality — the scenario sets. In many cases where both the decision variables and the scenario sets are continuous, the minimization and the maximization operations commute (order interchangeable), and thus the problem is much easier to solve. However, commutability requirement is a luxury in discrete optimization. Even the primal and its relaxation dual will in most cases inevitably lead to a gap between the corresponding objective values. We believe that the number of polynomially solvable discrete robust optimization problems is very limited.

Keywords

Order Quantity Robust Optimization Inventory Cost Robust Solution Demand Uncertainty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Panos Kouvelis
    • 1
  • Gang Yu
    • 2
  1. 1.Olin School of BusinessWashington University at St. LouisSt. LouisUSA
  2. 2.Center for Cybernetic StudiesThe University of TexasAustinUSA

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