Stability of linear programming solutions using regression coefficients

Abstract

In at least one important application of stochastic linear programming (Lavaca-Tres Palacios Estuary:A Study of the Influence of Freshwater Inflows, 1980)constraint parameters are simultaneously estimated using multiple regression with historic data for the values of the decision variables and the right hand side of the constraint function. In this circumstance, the question immediately arises How stable is the linear programming (LP) solution with regard to regression issues such as sample size, magnitude of the error variance, centroids of the decision variables, apd collinearity? This paper reports a simulation designed to assess the stability of the LP solution and to compare the effectiveness of ridge as an alternative to ordinary least squares (OLS) regression. For the given scenario, the LP solution is consistently biased. The amount of bias is exacerbated by small samples, large error variances, and collinearity among observations of the decision variables. The best regression criterion is a f...