Title: Optimizing Prioritized and Nested Solutions

Abstract: A typical optimization model in operations research allocates limited resources among competing activities to derive an optimal portfolio of activities. In contrast, practitioners often form a rank-ordered list of activities, and select those with the highest priority, at least when choosing an activity is a yes-no decision. Ranking schemes that score activities individually are well known to be inferior. So, we describe a class of two-stage stochastic integer programs that accounts for structural and stochastic dependencies across activities and constructs an optimized priority list. We further discuss a class of optimization models, subject to a single "budget" constraint, that naturally leads to a family of optimal nested solutions at certain budget increments. We use several applications to both motivate the work and illustrate results, ranging from a stochastic facility location model to a hierarchical graph clustering problem. We also describe possible extensions.

Bio: David Morton is a Professor of Industrial Engineering and Management Sciences at Northwestern University. His research interests include stochastic and large-scale optimization with applications in security, public health, and energy systems. He received a B.S. in Mathematics and Physics from Stetson University and an M.S. and Ph.D. in Operations Research from Stanford University.  Prior to joining Northwestern, he was on the faculty at the University of Texas at Austin, worked as a Fulbright Research Scholar at Charles University in Prague, and was