Qualitative sensitivity analysis for multi-commodity flow problems; cost allocation in K-Centrum optimization problems and toxic waste disposal problems

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I propose to continue my research in three main areas: i) Qualitative Sensitivity Analysis. This area is concerned with the development of a qualitative sensitivity analysis theory for multi-commodity flow problems. The development of such a theory will be particularly helpful for large scale problems where it is prohibitively expensive to make sensitivity analysis explorations by conventional methods. We successfully developed a theoretical qualitative analysis framework for single commodity network optimization problems, and we propose to extend the work to multi-commodity problems. Our extension could then be used to analyze large scale multi-commodity equilibrium procurement, production, distribution and dynamic production planning problems, and would allow manufacturers to respond optimally to market changes without significantly increasing cost, inventory, or response time. ii) K-Centrum Cost Allocation Problems. K-Centrum optimization problems, such as the bottleneck problem when K=1, are optimization problems wherein only the largest K-terms in the objective function are optimized. We will analyze cost allocation problems arising from the K-Centrum Chinese Postman problem and the K-Centrum assignment problem. iii) Toxic Waste Disposal Problems. In many industries, firms face important environmental problems related to toxic wastes disposal. Should they dispose of their toxic wastes independently, or form coalitions with others? Are there types of toxic wastes that could be sent in the same container or do they each need to be shipped separately? How long can toxic wastes be kept on site before they must be disposed? We will employ concepts of optimization and game theory to analyze various scenarios of this environmental problem. Tradeoffs will be considered with the attempt to derive closed form solutions and demonstrate that independent firms have incentives to cooperate with each other when considering the most efficient way to dispose of their toxic wastes.