Optimal Decision Rules Under Uncertainty in Linear and Quadratic Models

Abstract

Linear models with quadratic objective functions to minimize or maximize have been most widely used in applied decision models under uncertainty. Reasons are several e.g., computational ease, certainty equivalence and linearity of optimal decision rules. Also there exist many situations when the objective function is not quadratic, yet maximizing its expected value leads to a quadratic optimization model. For applications in various management decision problems, three types of models are most useful as follows:

• A. Decision models under uncertainty, which do not involve inequalities in an essential sense; hence the optimal decision rules are usually analytic.

• B. Stochastic linear programs, which involve inequalities in an essential sense, before or after the relevant uncertainty is introduced.

• C. Stochastic control models, which essentially involve dynamic phenomena over time and the information sequence plays a critical role through the stochastic process