Sustainability and Qualitative Sensitivity Analysis in Network Models

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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.