Network Modelling and Analysis with Applications to Operations Management

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***Qualitative Sensitivity Analysis. Decision makers strive to understand the impact of changes in the environment on their optimal plans. Over the years, I was involved with developing a qualitative sensitivity analysis methodology for various deterministic nonlinear network flow problems. Our qualitative analysis can be carried out without any computational work and is particularly useful for large nonlinear optimization problems, for which linear programming sensitivity analysis tools are not available.******Since many real world problems can be formulated as stochastic network flow problems, it is very important to develop qualitative sensitivity analysis tools for a stochastic environment. We propose to do so by extending the Monotonicity Theory of Granot and Veinott (MOR, 1985) to problems under uncertainty. The analysis would involve the establishment of conditions on the cost functions and the associated probability distributions under which the Monotonicity results hold. We will pursue numerous applications including studying the qualitative behavior of optimal solutions in production models where, e.g., demand and/or production costs are random with given distributions. ******Sustainability in Networks. Since CO2 emissions in supply chain networks account for about 20% of total global emissions, rationalizing CO2 emissions in supply chains is an important objective. We were the first to employ cooperative game theory methodology to this problem, and proposed the use of the Shapley value as a pollution responsibility allocation scheme. We proved that, in some sense, the Shapley value incentivizes firms to maximize their abatement efforts. ******Although the Shapley value has some nice properties, it is not “consistent”. Therefore, we plan to investigate the feasibility and benefits of using the Nucleolus, a consistent solution concept, as an alternative allocation scheme for pollution responsibilities. Partial results were obtained, and we propose to extend the analysis in several directions.******Cap-and-Trade Program. Governments curb emissions by using cap-and-trade programs. One of our objectives is to analyze the “trade” stage of this program by capitalizing on its similarity to the inventory transshipment problem. We will pursue several extensions of the model, such as providing firms with the option of buying carbon offsets in the market, as practiced by some firms in California. ******Benefits to Industry and the Environment. Since sensitivity analysis tools are indispensable for good decision-making, the development of qualitative analysis tools for a stochastic environment will assist managers in making better decisions and improve productivity and profitability. Our research concerning emission responsibilities and cap-and-trade programs addresses one of the most pressing environmental issues. The research results could contribute significantly to emissions reduction.