Copositive Duality for Discrete Markets and Games

Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have … Read more

Generation Expansion Planning with Revenue Adequacy Constraints

Generation capacity expansion models have traditionally taken the vantage point of a centralized planner seeking to find cost-optimal generation capacity to reliably meet load over decadal time scales. Often assuming perfectly competitive players, these models attempt to provide guidance for system planners without necessarily ensuring that individual generators are adequately remunerated for their generation, flexibility, … Read more

Logic-based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room Scheduling

The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample … Read more