Dynamic Pricing Strategy For Revenue Management With Model Uncertainty

Revenue management is a collection of strategies and tactics firms use to scientifically manage demand for their products and services by controlling inventory or price to maximize their revenue. Traditional research on dynamic pricing strategy for revenue management uses stochastic model to represent the uncertain demand and assumes that the stochastic demand model is known so as to optimize the pricing decision based on this model. In practice, however, the decision-maker usually does not posses complete information about the demand model and the optimized pricing may be wrong when using incorrect model. This dissertation will relax this full information assumption and studies the dynamic pricing problem of a monopolist retailing firm with finite inventory in the presence of model uncertainty. By considering model uncertainty in optimization, we can make the pricing policy more applicable in practice.First, we study the limited inventory pricing problem for perishable products in the presence of structured model uncertainty. Bayesian method is applied to learn some uncertain parameters of the demand model during the selling process, and dynamic pricing problems with continuous-time demand learning and periodic demand learning are studied, respectively. For the dynamic pricing problem with continuous-time demand learning, customer arrival process is modeled as a Bernoulli process and the arrival probability in each period is updated by applying Bayesian theorem. The dynamic pricing problem is formulated as a stochastic dynamic programming. Structural properties for optimal pricicing policy and optimal value function are analyzed. For the dynamic pricing problem with periodic demand learning, the multiplicative demand function is applied to model the demand in each period and Bayesian method is used to learn the uncertain parameters in the distribution of random variable. The pricing problem is formulated as a history dependant stochastic dynamic programming. Stuctural properties for optimal value function are analyzed.Next, we study the limited inventory pricing problem for perishable products with unstructured model uncertainty. Relative entropy is used to characterize the model uncertainty, the pricing problem is model as a two-person zero-sum game between decision-maker and"nature"and two robust pricing models based on relative entropy constraint and relative entropy penalty are built, respectively. For the single-period pricing problem, we analyze properties of the optimla price. For the multi-period robust pricing problem, we show that the optimal pricing policy can be computed recursively by dynamic programming. The relationship between robust pricing problem and risk-averse pricing problem with exponential utility is also analyzed.Then, we extend the above single product robust dynamic pricing model to the multi-product case and study the pricing problem for multiple related perishable products with the consideration of model uncertainty. Relative entropy is used to model model uncertainty, and dynamic pricing models with single ambiguity level and multi-ambiguity levels are studied. For the former, we prove that it can be solved by dynamic programming recursively. The optimal pricing policy, however, is hard to compute because of the"curse of dimension". We propose a hybrid intelligent algorithm that integrates neural network, generic algorithm and stochastic simulation to compute the optimal pricing policy; for the latter, dynamic programming cannot be applied to compute the pricing policy. Therefore, we propose a heuristic algorithm that integrates generic algorithm and stochastic simulation to compute the open-loop policy. Numerical experiments justify the effectiveness of the algorithms.At last, we extend the idea of robust dynamic pricing model for perishable product to non-perishable product case, and study the revenue management problem for non-perishable products with limited inventory in the presence of unstructured model uncertainty. The nominal problem is modeled by stochastic optimal control theory and the structural properties of the optimal value function and the optimal pricing policy are studied. Then, the concept of relative entropy process is generalized to describe model uncertainty. The robust dynamic pricing problem is formulated as a two-person zero-sum stochastic differential game and the Hamilton-Jacobi-Isaacs equation the optimal value function satisfied is derived. A verification theorem is proved to show that the solutions the HJI equation is the value function of the dynamic pricing problem. The results are illustrated by an example with exponential nominal demand rate.