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Decision-making problems that arise in complex systems (e.g., power grids, emergency logistics, communications networks and supply chains) invariably involve uncertainty and risk. These problems are further complicated by the combinatorial nature of the decisions involved. First, we consider multi-stage linear optimization problems under reliability or quality of service considerations, which we model as chance-constrained linear programs. At the first stage, decisions must be made when some parameters are uncertain. As the uncertainty unfolds, recourse decisions are made at later stages to mitigate the risk. Using an example from inventory control, we demonstrate that significant cost savings are observed at desirable service levels when the decisions are adaptive to the realizations of uncertain data. We propose branch-and-cut and decomposition algorithms to solve the resulting large-scale mixed-integer programs. Next, we address the additional challenges with two-stage stochastic programs when there are discrete variables at both stages. We give finitely convergent decomposition algorithms based on the convexification of the second-stage integer programs. Our computational experiments show that our methods scale well with increasing number of scenarios.
Simge Küçükyavuz is an associate professor in the Integrated Systems Engineering Department at the Ohio State University. Prior to joining the faculty at Ohio State, Dr. Küçükyavuz was an assistant professor at the University of Arizona, and a research associate at Hewlett-Packard Laboratories. She received her PhD in Industrial Engineering and Operations Research from the University of California, Berkeley. Her research interests are in mixed-integer programming, large-scale optimization, optimization under uncertainty, and their applications. Her research is supported by multiple grants from the National Science Foundation, including the 2011 CAREER Award. Her work has been published in Mathematical Programming, Operations Research, Management Science and other leading journals.
She serves on the editorial boards of Computational Optimization and Applications, and Wiley Encyclopedia of Operations Research and Management Science.