| Discrete brand choice is a microeconomics problem which is concerned with demand predictions, pricing, and how personal choice behaviors affect the supply-demand equation. It is an important problem addressed by many including McFadden and Heckman who won the Nobel Prize in 2000 because of their work on this topic. The discrete brand choice problem involves "selection among alternative sets in markets to maximize a customer's own self-interest defined by a utility function under the consumer consumption level constraint". The role of models, including those of the operations research variety, in advancing the state of the art of this problem domain has been postulated. However, very few discrete brand choice models encountered in the literature study the choice dynamics from the market share perspective. There is clearly a need for more precise integration of more information and robust estimation techniques.; In this thesis, we study brand choice problem via the following three perspectives: a company's market share management, introduction of customers with different perspectives, and an analysis of an application domain which is illustrative of these issues. Our contributions following these perspectives include: (1) development of a stochastic differential-jump game (SDJG) model for brand competition in a specific situation wherein market share is modeled by a jump-diffusion process, (2) a robust hierarchical logit/probit model for market heterogeneity, and (3) applications of logit/probit model to the dynamic pricing problem occurring in production-inventory systems with jump events.; First, we develop an SDJG model for brand competition. An SDJG model has the ability to model continuous variables and jump/discrete events simultaneously. Jump events are modeled by mark-time Poisson processes, with advertising effort as the control input. Hamilton-Jacobi-Bellman (HJB) equation is the modeling framework proposed for this problem but we resort to a Markov chain approximation method as the favored computational strategy due to the difficulty of obtaining a closed-form solution for a general HJB. The SDJG model is explicitly defined and applied in market competition. To our knowledge, this is the first application of this type in the literature.; Next, we consider a Bayesian robust hierarchical logit/probit model in the analysis of market heterogeneity. A hierarchical model combines features of products with characteristics of customers. Markov Chain Monte Carlo (MCMC) simulation is used for the estimation component. A robust hierarchical logit/probit model is then developed and validated using credit card data from a regional bank system. Our model represents an improvement over a general hierarchical logit/probit model based on better prediction precision and higher log margin density (LMD).; Finally, we employ a logit/probit model by imbedding it in a dynamic pricing problem. The resultant dynamic pricing model integrates information of production, inventory, and customers' choice. We not only consider more complex demand processes modeled by the Cox-Ingersoll-Ross (CIR) process, but also production systems with jump events. The dynamic pricing problem considered here is more complex and comprehensive situation than those found in current literature.; Our research explores the use of quantitative method of operations research to control the dynamics of market share and provides a precise estimation method to integrate more detail information in discrete brand choice models. |
