On dynamic pricing models and on qualitative analysis of non-deterministic models

我建议在两个主要领域继续我的研究：(I)动态定价和收入管理--尽管人们普遍认为竞争是选择正确定价策略的主要问题，但收入管理领域的大多数模型都集中在垄断环境中，其中单个零售商拥有固定的库存，目标是在相关的范围内最大化自己的利润。最近，我们通过考虑两个利润最大化的零售商，通过考虑两个利润最大化的零售商，每个零售商都可以满足整个市场，他们在价格上竞争。我们首先考虑了一个简单的竞争环境，其中零售商是对称的，消费者被限制在一个锯齿形的访问模式。随后，该模型被扩展到考虑更一般的消费者访问模式、非对称零售商和寡头垄断竞争。将寻求的一些重要扩展包括将战略消费者纳入垄断和双寡头竞争模型，并在我们的模型中施加能力约束和部分信息。(Ii)定性敏感性分析-第二个领域涉及优化的定性敏感性分析理论的发展。该理论对于用传统方法进行敏感性分析探索成本高得令人望而却步的大规模问题特别有用。我们已经成功地开发了确定性优化问题的理论定性分析框架，我们建议研究该理论的两个主要扩展。其中最重要的扩展是随机优化问题。然后，这样的扩展可以用于分析非确定性生产计划、货币和能源管理问题。第二个扩展的目的是发展定性理论，以帮助评估元件网络系统的可靠性。

I propose to continue my research in two main areas:(i) Dynamic pricing and revenue management - Notwithstanding the fact that it is broadly recognized that competition is a major issue in choosing the right pricing strategy, most models in the revenue management area focus on the monopoly setting wherein a single retailer, having a fixed stock, aims to maximize his profit over the relevant horizon.  Recently, we have incorporated competition in a finite, multi-period, fixed inventory settng, by considering two profit-maximizing retailers, each of whom can satisfy the entire market, who compete over prices.  We have first considered a simple competitive setting, wherein the retailers are symmetric and consumers are restricted to a zigzag visiting pattern.  Subsequently, the model was extended to account for more general visit patterns of consumers, non-symmetric retailers, and oligopolistic competition. Some important extensions that will be pursued include incorporating strategic consumers to monopoly and duopoly competition models and imposing capacity constraints and partial information in our models.(ii) Qualitative sensitivity analysis - The second area is concerned with the development of a qualitative sensitivity analysis theory of optimizatin.  This theory is particularly helpful for large scale problems where it is prohibitively expensive to make sensitivity analysis explorations by conventional methods. We have successfully developed a theoretical qualitative analysis framework for deterministic optimization problems, and we propose to study two main extensions to this theory.  The most important extension is to stochastic optimization problems.  Such an extension could then be used to analyze, e.g. non-deterministic production planning, currency and energy management problems.  The aim of the second extension is to develop a qualitative theory to help evaluate the reliability of a network system of components.