Models and formulations for multivariate dominance-constrained stochastic programs

Abstract

The use of a stochastic dominance constraint to specify risk preferences in a stochastic program has been recently proposed in the literature. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. This article proposes a constraint using a different version of multivariate stochastic dominance. This version is natural due to its connection to expected utility maximization theory and relatively tractable. In particular, it is shown that such a constraint can be formulated with linear constraints for the second-order dominance relation and with mixed-integer constraints for the first-order relation. This is in contrast with a constraint on second-order positive linear dominance, for which no efficient algorithms are known. The proposed formulations are tested in the context of two applications: budget allocation in a setting with multiple objectives and finding radiation treatment plans in the presence of organ motion.

Keywords:

• Stochastic dominance
• stochastic programming

Additional information

Notes on contributors

Benjamin Armbruster

Benjamin Armbruster received his Ph.D. in Management Science and Engineering from Stanford University. He is currently an Assistant Professor in the Department of Industrial Engineering and Management Sciences. His research focuses on modeling problems related to infectious diseases.

James Luedtke

James Luedtke is an Assistant Professor in the Department of Industrial and Systems Engineering at the University of Wisconsin–Madison. His earned his Ph.D. at Georgia Tech and did a postdoc at the IBM T.J. Watson Research Center. He research lies seems in the areas of stochastic and mixed-integer programming, with interest in applications such as service systems and energy. He is a recipient of an NSF CAREER award, was a finalist in the INFORMS JFIG Best Paper competition, and was awarded the 2013 INFORMS Optimization Society Prize for Young Researchers.