On generating utility functions in Stochastic Multicriteria Acceptability Analysis

Stochastic Multicriteria Acceptability Analysis (SMAA) has become a popular Multi-Criteria Decision Aiding tool when some parameters of the decision problem are uncertain or have not been set. SMAA methods use Monte-Carlo simulation of the uncertain values to obtain indicators that inform decision making. While there is considerable literature on sampling of attribute weights, the problem of generating utility values is addressed less frequently. In this paper, we show that direct assignment of random utility values can lead to a biased sample of utility functions. We then introduce new methods to avoid this bias and discuss desirable properties for generating such utility functions. Then, we present a computational study to compare the different methods with regards to the desired properties, concluding that the new approaches perform much better. We also show how these techniques can be extended to consider only utility functions of a specific shape such as concave, convex or s-shaped. Besides SMAA multi-criteria analyses, the techniques studied in this paper can also be used in other contexts, e.g., decision trees and game theory, whenever utility functions need to be simulated to inform decision makers or to study the behavior of different methods.