Solution to a Class of Two-stage Stochastic Programs with Multivariate Normal Uncertainty

25 Pages Posted: 21 Mar 2011 Last revised: 16 Dec 2013

See all articles by Saurabh Bansal

Saurabh Bansal

Pennsylvania State University - Smeal College of Business

James Dyer

University of Texas at Austin

Date Written: September 21, 2012

Abstract

We provide results for an efficient analytical valuation of partial moments of the multivariate Gaussian distribution over convex polyhedrons to aid the solution, sensitivity analysis and structural analysis of a large number of two-stage resource acquisition and allocation problems. These results decompose a partial multivariate moment into a function of multivariate probabilities that can be easily determined using the existing efficient numerical routines. The results are most useful in practice when (i) the structure of the Stage 2 allocation problem is known a-priori, for example when a greedy allocation algorithm is known to be optimal as is commonly the case for many resource sharing problems, or (ii) when the performances of various a-priori policies need to be evaluated, or (iii) when the number of uncertainties is small. We illustrate the use and benefit of the results over traditional simulation based approaches using a multi-resource newsvendor problem of practical size.

Keywords: Operational Flexibility, Stochastic Programming

JEL Classification: C61, M11

Suggested Citation

Bansal, Saurabh and Dyer, James, Solution to a Class of Two-stage Stochastic Programs with Multivariate Normal Uncertainty (September 21, 2012). Available at SSRN: https://ssrn.com/abstract=1787682 or http://dx.doi.org/10.2139/ssrn.1787682

Saurabh Bansal (Contact Author)

Pennsylvania State University - Smeal College of Business ( email )

University Park, PA 16802
United States
8148633797 (Phone)

James Dyer

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

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