Performance Models with Data Evolution

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Integer and combinatorial optimization models have many applications in engineering design as well as operations of manufacturing and distribution systems. For example, issues dealing with setup timereduction, batch size determination, scheduling, routing, etc. often call for integer and combinatorial optimization models. Traditional approaches to these problems assume that data are known with certainty. In many practical problems, data are not only uncertain, but also evolve over time. This research is devotedto models and algorithms that allow data evolution within integer programming models. This project's approach to data evolution draws upon the theory of stochastic programming, which has mainly focused on linear and convex optimization models. Because there are effective algorithms for stochastic linear and convex optimization problems, this research is dedicated to developing convex approximations for stochastic integer programs. The decision making problems to be considered involve a decision process and a data evolution process that are interwoven over time. In these models, resource commitments and operations are modeled using a mixed integer program, while data evolution is captured via a scenario tree. By combining mixed integer programming with stochastic optimization, this project will provide the next generation of Operations Research models for decision making under uncertainty.