  


Distribution of the Optimal Value of a Stochastic Mixed ZeroOne Linear Optimization Problem under Objective Uncertainty
Karthik Natarajan (knatarajcityu.edu.hk ) Abstract: This paper is motivated by the question to approximate the distribution of the completion time of a project network with random activity durations. In general, we consider the mixed zeroone linear optimization problem under objective uncertainty, and develop an approach to approximate the distribution of its optimal value when the random objective coefficients follow a multivariate normal distribution. Linking our model to the classical Stein’s Identity, we show that the best normal approximation of the random optimal value, under the L^2norm, can be computed by solving the persistency problem, first introduced by Bertsimas et al. (2006). We further extend our method to the minimum quadratic regret problem, and show that for any general mixed zeroone linear optimization problem, the minimum quadratic regret solution can be computed by solving a related persistency problem. Extensive computational studies are presented to demonstrate the advantages of the new method. Keywords: stochastic mixed zeroone linear optimization; persistency; distribution approximation; regret; completely positive programming; project management; portfolio selection Category 1: Stochastic Programming Category 2: Integer Programming ((Mixed) Integer Linear Programming ) Category 3: Applications  OR and Management Sciences Citation: Download: Entry Submitted: 06/20/2011 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  