A Bayesian model for multicriteria sorting problems

Abstract

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive Bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM’s response, we update the prior distribution using Bayes’ Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement.

Keywords:

• Multiple criteria
• sorting
• Bayesian dynamic programming

Acknowledgments

The authors would like to thank Murat Köksalan for his comments and suggestions and the anonymous associate editor and referees for their valuable feedback.

Additional information

Notes on contributors

Canan Ulu

Canan Ulu is an associate professor at Georgetown University’s McDonough School of Business. She received her PhD from Duke University, and she holds a BS and an MS degree in Industrial Engineering from the Middle East Technical University in Ankara, Turkey. Dr. Ulu studies Bayesian learning in sequential decision problems, multi-criteria decision-making problems and uses behavioral decision theory to improve decision analysis methods. Her work has been published in journals such as Operations Research, Management Science and Psychological Science among others. Dr. Ulu serves as the department editor for the decision analysis and analytics department at IISE Transactions; she is also an associate editor for the decision analysis area at Operations Research and for Manufacturing & Service Operations Management.

Thomas S. Shively

Tom Shively is the Joe B. Cook Professor of Business and a Professor of Statistics in the McCombs School of Business at the University of Texas at Austin. He received a BA in Mathematics from Middlebury College, an MBA from the University of Chicago, and a PhD in Statistics from the University of Chicago. Professor Shively’s methodological research is primarily in the areas of nonparametric regression, hierarchical Bayes models and model selection techniques. He has also done applied work in the fields of marketing, energy, and environmental science.