Bid Prices When Demand Is a Mix of Individual and Batch Bookings

Industries such as aviation, hospitality, and package tours often face both individual and batch bookings, requiring one unit and multiple units of capacity, respectively. Using bid prices is a common practice in accepting or rejecting an incoming booking (or equivalently, deciding which price bucket to offer to the incoming bookings at a given time). Most of the literature and existing applications for making accept/reject decisions model the arrival stream as individual bookings. In this paper, we propose an effective approach to determine bid prices when there is a mixed demand pattern with individual and batch bookings. We propose decomposing the demand into “small” and “large” bookings, using dynamic programming for large bookings, and a fast, high-quality approximation for small bookings. We present an application of our approach in the air cargo industry, where cargo is often separated into two categories, namely, mail and packages (small cargo) and freight (large cargo). To obtain bid prices for small cargo, we approximate cargo booking requests with passenger arrival models and develop an efficient and effective algorithm to solve the probabilistic nonlinear formulation of the seat allocation problem from the passenger literature. To obtain bid prices for large cargo, we solve a dynamic program decomposed by flight leg, which is tractable due to the scattered arrivals and large sizes of the bookings. Our approach leads to a significant potential increase in revenues compared to the first-come, first-served (FCFS) approach and the solution from the deterministic formulation (DIP), two methods commonly used in practice.