Network Modelling and Analysis with Applications to Operations Management

定性敏感性分析。决策者努力了解环境变化对其最优计划的影响。多年来，我参与开发了一种定性灵敏度分析方法，用于各种确定性非线性网络流问题。我们的定性分析可以在没有任何计算工作的情况下进行，对于大型非线性优化问题特别有用，对于线性规划灵敏度分析工具是不可用的。由于许多现实世界的问题可以表述为随机网络流问题，因此开发针对随机环境的定性灵敏度分析工具是非常重要的。我们建议将Granot和Veinott （MOR, 1985）的单调性理论推广到不确定条件下的问题。分析将涉及建立成本函数和相关概率分布的条件，在这些条件下单调性结果成立。我们将追求许多应用，包括研究生产模型中最优解的定性行为，例如，需求和/或生产成本是随机的，具有给定的分布。网络的可持续性。由于供应链网络中的二氧化碳排放量约占全球总排放量的20%，因此使供应链中的二氧化碳排放合理化是一个重要目标。我们首次将合作博弈论方法应用于这一问题，并提出使用Shapley值作为污染责任分配方案。我们证明，在某种意义上，沙普利值激励企业最大化其减排努力。尽管Shapley值有一些不错的属性，但它并不“一致”。因此，我们计划研究使用一致解决方案Nucleolus作为污染责任分配方案的可行性和效益。得到了部分结果，并建议在几个方向上扩展分析。总量管制与排放交易计划。政府通过限额与交易计划来控制排放。我们的目标之一是分析该计划的“贸易”阶段，利用其与库存转运问题的相似性。我们将对这一模式进行扩展，比如向企业提供在市场上购买碳补偿的选择，就像加州的一些企业所做的那样。对工业和环境的好处。由于敏感性分析工具对于良好的决策是必不可少的，因此开发针对随机环境的定性分析工具将有助于管理者做出更好的决策，提高生产力和盈利能力。我们关于排放责任和限额交易计划的研究解决了最紧迫的环境问题之一。研究结果对减排具有重要意义。

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.