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Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation

Author

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  • Karthik Natarajan

    (Department of Management Sciences, City University of Hong Kong, Hong Kong)

  • Chung Piaw Teo

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 117591)

  • Zhichao Zheng

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 117591)

Abstract

In this paper, we analyze mixed 0-1 linear programs under objective uncertainty. The mean vector and the second-moment matrix of the nonnegative objective coefficients are assumed to be known, but the exact form of the distribution is unknown. Our main result shows that computing a tight upper bound on the expected value of a mixed 0-1 linear program in maximization form with random objective is a completely positive program. This naturally leads to semidefinite programming relaxations that are solvable in polynomial time but provide weaker bounds. The result can be extended to deal with uncertainty in the moments and more complicated objective functions. Examples from order statistics and project networks highlight the applications of the model. Our belief is that the model will open an interesting direction for future research in discrete and linear optimization under uncertainty.

Suggested Citation

  • Karthik Natarajan & Chung Piaw Teo & Zhichao Zheng, 2011. "Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation," Operations Research, INFORMS, vol. 59(3), pages 713-728, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:713-728
    DOI: 10.1287/opre.1110.0918
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    References listed on IDEAS

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