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

我建议在三个主要领域继续我的研究：1)定性敏感性分析。这个领域涉及多商品流动问题的定性敏感性分析理论的发展。这种理论的发展将对大规模问题特别有帮助，在这些问题中，用传统方法进行灵敏度分析探索的成本过高。我们成功地开发了单一商品网络优化问题的理论定性分析框架，我们建议将工作扩展到多商品问题。然后，我们的扩展可以用于分析大规模的多商品均衡采购、生产、分销和动态生产计划问题，并允许制造商在不显著增加成本、库存或响应时间的情况下对市场变化做出最佳反应。K-Centrum成本分配问题。K- centrum优化问题，如K=1时的瓶颈问题，是只优化目标函数中最大K项的优化问题。我们将分析K-Centrum中国邮差问题和K-Centrum分配问题所产生的成本分配问题。iii)有毒废物处置问题。在许多工业中，公司面临着与有毒废物处理有关的重要环境问题。他们应该独立处理有毒废物，还是与其他公司联合处理？有毒废物的种类是可以装在同一个集装箱里还是需要分开装运？有毒废物在必须处置之前，可在现场存放多久？我们将运用最优化和博弈论的概念来分析这个环境问题的各种场景。将考虑权衡，试图得出封闭形式的解决办法，并证明独立公司在考虑处置其有毒废物的最有效方法时有相互合作的动机。

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.