Utilizing Maximin Value Functions

摘要

A maximin value function applies when the criteria are totally nonsubstitutable: a decrease in a critical criterion cannot be compensated for by an increase in another criterion. This paper illustrates situations where a maximin value function is an appropriate model, develops a method to measure a decision maker's (DM) maximin value function, and demonstrates how a maximin value function can be used in applications. The measurement technique is easy to understand, and most DMs can complete the process in less than 30 minutes. The measurement technique asks the DM to choose the best balance between the criteria thereby allowing the DM to consider all relevant objectives in making his choice. The data is then used to construct a piecewise linear approximation of the maximin value function that represents the DM's preferences. When the resultant maximin value function is used as the objective function in a mathematical programming model, the optimal solution provides the best balance between the criteria according to the DM's preferences. Preemptive goal programming is shown to be a special case.