Sustainability and Qualitative Sensitivity Analysis in Network Models

提出的研究计划的动机是需要合理化供应链中的温室气体排放，并希望获得参数凸网络流问题的敏感性分析结果。供应链网络的可持续性和减少污染。鉴于实现巴黎联合国气候变化大会设定的目标所面临的挑战，应该指出的是，全球最大的2500家公司供应链的温室气体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做出重要贡献。在Gopalakrishnan等人的《供应链中的激励与排放责任分配》（2019a）中，我们将温室气体排放责任问题制定为合作博弈，称为GREEN博弈，并使用合作博弈方法建议供应链中企业之间的温室气体排放责任分配。特别是，我们已经描述了GREEN游戏的Shapley值，并且我们已经证明了它具有几个理想的属性。然而，尽管Shapley值具有吸引人的特点，但人们发现它在某种定义明确的意义上并不“一致”，这促使人们采用核仁作为污染责任的分配方法。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，我们已经表明，核仁在某种意义上是供应链中“一致”的唯一的单点博弈论解决方案概念。我们计划研究其他相关问题，包括将我们开发的用于计算供应链是树时核仁的二次算法扩展到更一般的供应链结构，并且我们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。作为线性规划中灵敏度分析的补充，我们最近开发了一种定性分析理论，用于定义在有向图上的最小凸成本参数多商品网络流问题。我打算从事几个相关的项目。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。事实上，F. Granot和Veinott （MOR, 1985）以及Ciurria-Infosino等人（Networks, 2019）开发的定性分析理论假设了一个确定性的环境，而我的目标是将该理论扩展到随机环境。分析的关键是建立成本函数和相关的概率分布的条件，在这些条件下，例如，对确定性网络流问题成立的单调性结果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.