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

Operations Research, Vol. 59, No. 3, pp. 713-728, 2011

36 Pages Posted: 25 May 2016 Last revised: 13 Feb 2018

See all articles by Karthik Natarajan

Karthik Natarajan

Singapore University of Technology and Design (SUTD)

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences

Zhichao Zheng

Singapore Management University - Lee Kong Chian School of Business

Date Written: August 7, 2009

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 is 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.

Keywords: Mixed 0-1 Linear Program; Moments; Completely Positive Program

Suggested Citation

Natarajan, Karthik and Teo, Chung-Piaw and Zheng, Zhichao, Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation (August 7, 2009). Operations Research, Vol. 59, No. 3, pp. 713-728, 2011, Available at SSRN: https://ssrn.com/abstract=2783620

Karthik Natarajan

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences ( email )

15 Kent Ridge Drive
Mochtar Riady Building, BIZ 1 8-69
119245
Singapore

Zhichao Zheng (Contact Author)

Singapore Management University - Lee Kong Chian School of Business ( email )

50 Stamford Road
Singapore, 178899
Singapore
(65) 6808 5474 (Phone)
(65) 6828 0777 (Fax)

HOME PAGE: http://www.zhengzhichao.com

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