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

多商品流动问题的定性敏感性分析；

• 批准号: 3998-2013
• 负责人: Granot, Frieda
• 金额: $ 1.89万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568331
• 关键词: Qualitative; sensitivity; analysis; multi; commodity

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.

我建议在三个主要方面继续我的研究： I)定性敏感性分析。这一领域涉及多商品流动问题的定性灵敏度分析理论的发展。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成本高得令人望而却步。我们成功地建立了单商品网络优化问题的理论定性分析框架，并提出将工作扩展到多商品网络优化问题。然后，我们的扩展可以用于分析大规模多商品均衡采购、生产、分销和动态生产计划问题，并将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优响应。 二)K-Centrum成本分配问题。K-Centrum优化问题，如K=1时的瓶颈问题，是只对目标函数中最大的K项进行优化的优化问题。我们将分析由K-Centrum中国邮递员问题和K-Centrum分配问题引起的成本分配问题。 (Iii)有毒废物处理问题。在许多行业中，企业面临着与有毒废物处理相关的重要环境问题。他们应该独立处理自己的有毒废物，还是应该与其他公司结盟？有没有几种有毒废物可以装在同一个集装箱里运送，或者它们是否都需要分开运输？有毒废物在必须处置之前可以在现场存放多久？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情景。将考虑权衡，试图得出封闭形式的解决方案，并证明独立公司在考虑最有效的处置其有毒废物的方法时，有相互合作的动机。