Future Scenario Generation, Minimum Regret Decisions and Linear Programming

Abstract

After determining the set of future scenarios that an organization may encounter, practitioners must also provide the organization with the decision rule it should adopt for exploiting, or hedging against, anticipated scenarios. This paper argues that the most advantageous rule available is the minimum regret decision rule. Regret is defined as the difference between the decision taken and the optimal one given the contingency. The larger the difference, the greater the sense of regret that decision-makers will feel for having failed to make the (unpredictable) right choice. The minimum regret decision is the one that minimizes the maximum of this difference. It is a decision rule that was first proposed in the very early days of operations research (in the 1950s) in the works of Wald and Savage, to temper the extremely pessimistic view of the min-max decision rule. Later, in the early 1980s, some authors proved that the rule satisfies a set of axioms, providing an alternative to the expected utility model for modeling real and behavioral decision-making. As a consequence, one can develop operational decision models that are based on regret computations. The application of minimum regret as a normative tool for operational problems obliges practitioners to design all scenarios and feasible decisions carefully, as regret does not satisfy the transitivity principle of the expected utility. As such, mathematical programming tools are needed to solve minimum regret models. We discuss these mathematical tools by analyzing a flood management problem, based on a real-life application to the Iowa River.