Multi-Dimensional Problems In Single-Resource Revenue Management

This dissertation addresses three multi-dimensional problems in single-resource revenue management. Many problems in revenue management involve managing a single resource but their dynamic programming formulation still requires using a multi-dimensional vector as the state variable. For instance, singleflight-leg revenue management is an extensively studied problem where airlines use the same seat resource to accommodate different classes of customers. In these problems, due to the multi-dimensional state space, the exact formulation is either intractable, or the resulting optimal policy is inconvenient to implement operationally. We develop approximations for the exact formulations, which generate tractable and operationally attractive policies. The first problem we study is a strategic decision problem about whether or not to discontinue a product sold under warranty, whose failure probabilities are unknown initially and are learnt as sales take place and failure information is accumulated. Since there are multiple types of failures that the product can fail from, we formulate the problem as a multi-dimensional optimal stopping problem with Bayesian learning. Two approximations based on dynamic programming decomposition and deterministic approximation are developed, and insights about the value of learning are extracted from asymptotic analysis. Next we study a dual-channel pricing and capacity allocation problem for hotel revenue management. While one channel is the spot market in which we can adopt dynamic pricing, the other is a conference market with a fixed price offered for conference participants. Remaining rooms in the conference market will be released to the spot market if not booked by a deadline. Tactical decisions on number of rooms to reserve and fixed price to offer for the conference market need to be made at the beginning of the selling horizon. For the operational pricing problem in the spot market, because the two markets will join together in a future time, we need a two-dimensional dynamic program which tracks the remaining capacities in both markets to make optimal pricing decisions in the spot market. We develop a single-dimensional approximation to the exact two-dimensional formulation, which generates a robust and operationally attractive policy. For the tactical problem of finding the optimal capacity allocation between spot and conference markets and choosing the fixed price to charge in the conference market, we construct an asymptotically optimal policy through a deterministic formulation. Finally, we consider a revenue management problem where we sell a product to multiple markets with heterogeneous price sensitivities. We can allocate the capacity to different markets and charge different prices in different markets (separate pricing), in which case we gain pricing flexibility, or we can merge all markets together and serve them with a common price (joint pricing), in which case we obtain capacity flexibility. We study the tradeoff between pricing and capacity flexibilities and establish conditions under which one is more important than the other. For a hybrid model where separate pricing is adopted early in the selling horizon and joint pricing is used towards the end, we develop a single-dimensional approximation which gives rise to a policy with remarkably good performance especially for problem instances with tight capacity, large number of markets, or drastically different price sensitivities