Distributionally Robust Mixed Integer Linear Programs: Persistency Models with Applications

European Journal of Operational Research, Vol. 233, No. 3, pp. 459–473, 2014

40 Pages Posted: 24 May 2016 Last revised: 13 Feb 2018

See all articles by Xiaobo Li

Xiaobo Li

National University of Singapore

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: January 26, 2013

Abstract

In this paper, we review recent advances in the distributional analysis of mixed integer linear programs with random objective coefficients. Suppose that the probability distribution of the objective coefficients is incompletely specified and characterized through partial moment information. Conic programming methods have been recently used to find distributionally robust bounds for the expected optimal value of mixed integer linear programs over the set of all distributions with the given moment information. These methods also provide additional information on the probability that a binary variable attains a value of 1 in the optimal solution for 0-1 integer linear programs. This probability is defined as the persistency of a binary variable. In this paper, we provide an overview of the complexity results for these models, conic programming formulations that are readily implementable with standard solvers and important applications of persistency models. The main message that we hope to convey through this review is that tools of conic programming provide important insights in the probabilistic analysis of discrete optimization problems. These tools lead to distributionally robust bounds with applications in activity networks, vertex packing, discrete choice models, random walks and sequencing problems, and news vendor problems.

Suggested Citation

Li, Xiaobo and Natarajan, Karthik and Teo, Chung-Piaw and Zheng, Zhichao, Distributionally Robust Mixed Integer Linear Programs: Persistency Models with Applications (January 26, 2013). European Journal of Operational Research, Vol. 233, No. 3, pp. 459–473, 2014, Available at SSRN: https://ssrn.com/abstract=2783628

Xiaobo Li

National University of Singapore ( email )

10 Kent Ridge Crescent
Singapore, 115260
Singapore

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

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
33
Abstract Views
466
PlumX Metrics