Optimizing Airline Overbooking Using a Hybrid Gradient Approach and Statistical Modeling

We develop an overbooking approach for airline revenue management. We estimate a revenue function by employing a statistical modeling approach, specifically a multivariate adaptive regression splines approximation of a stochastic network model. We develop an overbooking cost function using a binomial distribution to model the number of customers that show up for the flight. We implement a hybrid gradient algorithm that combines Newton’s and a steepest ascent method to optimize profit. Finally, we compare our method to one that overbooks based on the probability that the number of customers that show up for a flight exceeds the flight capacity. Revenue management is defined as, “Selling the right seat at the right time to the right passenger for the right price” (Vinod 1995). After deregulation in 1979, revenue management research has evolved to efficiently utilize resources and generate higher revenue. One of the revenuecapturing concepts identified was overbooking, where airlines sell more seats than the capacity of the flight. Overbooking is essential because not all customers who buy tickets show up on the day of departure. Some of them are cancellations (customers who cancel a purchased ticket), while others are no-shows (customers who do not show up for their ticketed flight). The overbooking level (or authorization level) specifies the number of seats that may be overbooked on a flight. In this paper, we present an approach to determine optimal overbooking levels, so as to generate higher profit (revenue − cost). The revenue is estimated using a design and analysis of computer experiments (DACE, Sacks et al. 1989) approach, and only overbooking costs are estimated. (We ignored other airline costs, such as fuel burn, labor, etc. that are generally considered independent of the booking process.) To optimize profit, a hybrid algorithm that combines Newton’s method and a steepest ascent method is developed (Bertsekas 1999). Perishable goods need to be utilized well before the end of their life cycle. The overbooking concept can be applied to various transportation sectors, such as auto rentals, ferries, rail, tour operators, cargo, and cruises. Other areas, like hotels and resorts, extended stay hotel, health care, and companies that produce perishable goods can also use overbooking. In the airline industry, once a flight takes off the seats are said to be “perished.” Hence, we should efficiently utilize those seats. Given the schedule, flight capacities, and demand distributions, how many seats should be overbooked on each flight, so that the seats are efficiently utilized and higher profits are achieved? The remainder of this section provides background on airline overbooking, and describes the contribution of this paper. Section 1 explains the methodology adapted in this paper to determine the optimal overbooking levels, and Section 2 presents computational results. Finally, concluding remarks are given in Section 3. Overbooking Concept Let nc be the number of cancellations and no-shows, and let y be the overbooking level.