Does optimization systematically lead to solutions that appear better than they actually turn out to be when implemented? The answer can be yes if there are errors in estimating objective function coefficients. Even if such errors are unbiased, the calculated value of the objective function for the optimal solution will, in an expected value sense, overstate that solution's true performance. This presupposes that errors in the constraint set are relatively unimportant. The existence of such a bias is shown by proof; Monte Carlo simulations of two realistic water resources optimization problems show its significance for water planners. The most important implication is that the estimated net benefits of model solutions may be exaggerated compared to existing water systems, whose performance is generally known with more accuracy.
221-222]:most would agree that applications of modeling designed to i•l• or aid decision-makers should only rarely, if at all, be designed to provide actual decisions regarding often complex management or policy problems the model output serves only to focus the debate about what to do; it is not itself a substitute for the planning, managing, or policy making process.Model solutions are just one of many inputs to the decision process. Solutions are modified to reflect institutional considerations and are often subjected to extensive simulation. Or optimization may be used just to screen out obviously inferior solutions. Optimization can also yield insights into the workings of the system, the critical issues, and the general form of good solutions.In this paper, we focus on the use of optimization to predict the performance of alternative designs, operating rules, and government policies. We address the following question, Do estimation errors in objective function coefficients cause optimization to have a fundamental bias toward optimism? Specifically, will such errors lead us to expect to gain more than we really will when we implement the optimal solution? Below, we show that under certain circumstances, the answer is yes.
152HOBBS AND HEPENSTAL: IS OPTIMIZATION OPTIMISTICALLY BIASED? 153 HoBBs AND HEPENSTAL: IS OPTIMIZATION OPTIMISTICALLY BIASED. 9 edited by M. A. H. Dempster, pp. 245-262, Academic, San Diego, Calif., 1980.