| 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 function not only of collinearity, but also of the magnitude of the error variance and the sum of the means of the decision variables relative to the right hand side of the stochastic constraint In the application that motivated this research, the LP solutions were recommended fresh water inflows from Lake Texana into the estuaries of the Gulf of Mexico. The stochastic constraint estimates commercial fish harvest as a function of seasonal fresh water inflow. The historic data set used to estimate parameters of the constraint comprised rainfall data and fish harvest data prior to the construction of the Lake Texana dam, of necessity a small sample with collinear seasonal rainfall. It is not the authors' intent to solve this application, but rather to investigate through a simpler simulated systemwhether or not regression estimates in similar circumstances might introduce a systematic and predictable bias. The answer to this latter question is a qualified Yes!. |
