Nonclassical Discrete Optimization Problems

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In this research program, we will study several classes of discrete optimization models that arise in planning operations in complex manufacturing and service systems. These classes include network construction problems that deal with planning construction activities for building new transportation networks or restoring damaged networks; robust optimization models that deal with decision-making under uncertainty; online supply chain scheduling problems that help coordinate scheduling, batching, and delivery decisions in supply chains where little information about future demand is available; competitive project scheduling problems that model competition between firms in development of new products; models for choosing optimally locations of service facilities that may be subject to random failures, or locations and replenishment parameters of manufacturers and distribution centers that supply a given set of retailers facing random demand. The models are "non-classical" in the sense that they are new or appeared in the literature recently, and at present there are no sufficiently effective computational approaches to handle them. The main goal of this research program is to develop a set of theoretical results and computational methods that will allow to use these models in practice and to understand their possibilities and limitations. This will provide new powerful tools to practitioners who deal with planning complex operations, bring new understanding of the area, and open new important research directions.