Sustainability and Qualitative Sensitivity Analysis in Network Models

提出的研究计划的动机是需要使供应链中的温室气体排放合理化，以及希望得到参数凸网络流问题的灵敏度分析结果。供应链网络中的可持续性和减少污染。鉴于实现在巴黎举行的联合国气候变化会议确定的目标所面临的挑战，应该指出的是，来自2,500家最大的全球公司供应链的温室气体(GHG)排放量占全球温室气体排放量的近20%。因此，使供应链中的温室气体排放合理化可以为减缓气候变化作出重要贡献。在Gopalakrishnan等人的《供应链中的激励和排放责任分配》(2019a)中，我们将温室气体排放责任问题描述为一个合作博弈，称为绿色博弈，并使用合作博弈论方法建议在供应链中的企业之间分配温室气体排放责任。特别地，我们刻画了绿色对策的Shapley值，并且我们已经证明了它具有几个所需的性质。然而，尽管Shapley值具有吸引力，但人们发现它在某种明确的意义上并不“一致”，这促使引入核仁作为污染责任的一种分配方法。事实上，在Gopalakrishnan等人的“能源供应链中排放责任的一致分配”(2019b)中，我们已经证明，在某种意义上，核仁是供应链中唯一的“一致”的单点博弈论解概念。我们计划研究其他相关问题，包括将我们开发的计算供应链是树时的核仁的二次算法扩展到更一般的供应链结构，我们还将进一步研究与激励、实施和公理化相关的其他问题。参数网络优化问题的定性分析。作为对线性规划灵敏度分析的补充，我们最近发展了一种定性分析理论，用于定义在有向图上的一类最小凸费用参数多商品网络流问题。我计划进行几个相关的项目。例如，我将尝试将定性分析理论扩展到随机参数网络优化问题。的确，F.Granot和Veinott(Mor，1985)和Ciurria-Infosino等人发展的定性分析理论。(Network，2019)假设了一个确定性的环境，我的目标是将该理论扩展到随机环境。分析的关键是建立关于成本函数和相关概率分布的条件，这些条件对不确定性建模，例如，单调性结果适用于确定性网络流问题，也适用于随机参数网络流问题。

The proposed research program is motivated by the need to rationalize Greenhouse Gas Emissions in supply chains, and the desire to derive sensitivity analysis results for parametric convex network flow problems. Sustainability and Pollution Reduction in Supply Chain Networks. In view of the challenges of meeting the goals set at the UN Climate Change Conference in Paris, it should be noted that the greenhouse gas (GHG) emissions from the supply chains of the 2,500 largest global corporations account for almost 20% of global GHG emissions. Therefore, rationalizing GHG emissions in supply chains could make an important contribution to mitigating climate change. In Gopalakrishnan et al., "Incentives and Emission Responsibility Allocation in Supply Chains", (2019a), we formulated the GHG emission responsibility problem as a cooperative game, referred to as the GREEN game, and used cooperative game theory methodology to suggest allocations of GHG emission responsibility among the firms in a supply chain. In particular, we have characterized the Shapley value for GREEN games, and we have shown that is has several desired properties. However, notwithstanding the attractive features of the Shapley value, it is found to be not "consistent" in some well-defined sense, which has motivated the introduction of the nucleolus as an allocation method of pollution responsibilities. Indeed, in Gopalakrishnan et al., "Consistent Allocation of Emission Responsibility in Energy Supply Chains", (2019b), we have shown that the nucleolus is, in some sense, the unique single-point game theoretic solution concept which is "consistent" in a supply chain. We plan to investigate other related issues, including the extension of the quadratic algorithm we developed to compute the nucleolus when the supply chain is a tree to more general supply chain structures, and we will further study other issues related to incentives, implementation and axiomatization. Qualitative Analysis in Parametric Network Optimization Problems. As a complement to sensitivity analysis in linear programming, we have recently developed a qualitative analysis theory  for the class of minimum convex-cost parametric multicommodity network-flow problems defined over directed graphs. I plan to pursue several related projects. For example, I will attempt to extend the qualitative analysis theory to stochastic parametric network optimization problems. Indeed, the qualitative analysis theory developed by F. Granot and Veinott (MOR, 1985) and Ciurria-Infosino et al. (Networks, 2019) assume a deterministic environment, and my objective is to extend the theory to a stochastic environment. The crux of the analysis would involve the establishment of conditions on the cost functions and the associated probability distributions which model the uncertainty, under which, e.g., monotonicity results, which hold for deterministic network flow problems, are also valid for stochastic parametric network flow problems.