In this dissertation, we study three topics on revenue management. First, we consider a simplified air cargo problem. We show that a linear programming based approach proposed for airline seat inventory control can be used for air cargo as well. Because of the characteristics of demand and inventories, the formulation is a continuous linear program, and poses difficulties in forecasting and optimization. We focus on the optimization problem, show that the bid prices for the air cargo problem exist and present three approximation procedures. We prove asymptotic optimality of these approximation procedures. We provide an example to show that one does not need the optimal solution to the continuous problem for effective inventory control in air cargo.
Next, we consider an overbooking problem with multiple reservation and inventory classes, in which more than one inventory class may be used to satisfy the demand of a given reservation class. The problem is to determine the joint overbooking levels for the reservation classes. We model this problem as a two-period optimization problem. In the first period, reservations are accepted given only probabilistic knowledge of cancellations. In the second period, cancellations are realized and surviving customers are assigned to the various inventory classes to maximize the net benefit of assignments (e.g. minimize downgrading penalties). For this formulation, we show that the optimal overbooking level in one class is decreasing in the reservation levels of other classes. We then propose a stochastic gradient algorithm and prove its convergence. We illustrate our model and algorithm using examples from the airline industry.
Finally, we study a joint overbooking and seat inventory control problem for an airline network. We present a two-stage model that combines linear programming based bid pricing with cost-based overbooking. We analyze structural properties of the problem, and show that a control policy derived from our model is asymptotically optimal. We provide a solution procedure to determine the optimal policy parameters. We provide an extensive numerical study and compare our approach-and two other heuristics that rely on our model-to other ad hoc approaches to coordinate overbooking and seat inventory control.