Modeling Customer Behavior for Revenue Management
In this thesis, we model and analyze the impact of two behavioral aspects of customer decision making upon the revenue maximization problem of a monopolist firm. First, we study the revenue maximization problem of a monopolist firm selling a homogeneous good to a market of risk-averse, strategic customers. Using a discrete (but arbitrary) valuation distribution, we show how the dynamic pricing problem with strategic customers can be formulated as a mechanism design problem, thereby making it more amenable to analysis. We characterize the optimal solution, and solve the problem for several special cases. We perform asymptotic analysis for the low risk-aversion case and show that it is asymptotically optimal to offer at most two products. Second, we consider a revenue-maximizing monopolist firm that serves a market of customers that are heterogeneous with respect to their valuations and desire for a quality attribute. Instead of optimizing the net utility that results from an appropriate combination of product price and quality, as in the traditional model of customer behavior, we consider a setting where customers purchase the cheapest product subject to its quality exceeding a customer specific quality threshold. We call such preferences threshold preferences. We solve the firm’s product design problem in this setting, and contrast with the traditional model of customer choice behavior. We consider several scenarios where such preferences might arise, and identify the optimal solution in each case. In addition to these product design problems, we study the problem of identifying the optimal putting strategy for a golfer. We develop a model of golfer putting skill, and combine it with a putt trajectory and holeout model to identify a golfer’s optimal putting strategy. The problem of identifying the optimal putting strategy is shown to be equivalent to a two-dimensional stochastic shortest path problem, with continuous state and control space, and solved using approximate dynamic programming. We calibrate the golfer model to professional and amateur player data, and use the calibrated model to answer several interesting questions, e.g., how does green reading ability affect golfer performance, how do professional and amateur golfers differ in their strategy, how do uphill and downhill putts compare in difficulty, etc.
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