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

我建议继续我的研究在两个主要领域：（一）动态定价和收入管理-尽管它被广泛认为是一个重要的问题，在选择正确的定价策略，在收入管理领域的大多数模型集中在垄断的设置，其中一个单一的零售商，有一个固定的股票，旨在最大限度地提高他的利润在相关的地平线。 最近，我们考虑了有限的，多周期的，固定的库存设置中的竞争，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曲折的访问模式。 随后，该模型被扩展到更一般的访问模式的消费者，非对称零售商和寡头竞争。将追求的一些重要的扩展，包括将战略消费者垄断和双寡头竞争模型，并施加能力限制和部分信息在我们的模型。(ii)定性敏感性分析-第二个领域是有关发展的定性敏感性分析理论的优化。 这一理论对于用传统方法进行灵敏度分析的昂贵费用的大规模问题特别有用。我们已经成功地开发了一个理论的定性分析框架确定性优化问题，我们建议研究两个主要扩展到这个理论。 最重要的扩展是随机优化问题。 这样的扩展可以用来分析，例如非确定性的生产规划，货币和能源管理问题。 第二个扩展的目的是发展一个定性的理论，以帮助评估网络系统的组件的可靠性。

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.