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

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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.