An Approximation Algorithm for Capacity Allocation Over a Single Flight Leg with Fare-Locking

Abstract

In this paper, we study a revenue management model over a single flight leg, where the customers are allowed to lock an available fare. Each customer arrives into the system with an interest in purchasing a ticket for a particular fare class. If this fare class is available, the customer either immediately purchases the ticket by paying the fare or locks the fare by paying a fee. If the customer locks the fare, then the airline reserves the capacity for the customer for a certain duration of time. At the end of this duration of time, the customer makes her ultimate purchase decision at the locked fare. The goal of the airline is to find a policy to decide which set of fare classes to make available at each time period to maximize the total expected revenue. Such fare locking options are commonly offered by airlines today, but the dynamic programming formulation of the revenue management problem with the option to lock an available fare has a high dimensional state variable that keeps track of the locked fares. We develop an approximate policy that is guaranteed to obtain at least half of the optimal total expected revenue. Our approach is based on leveraging a linear programming approximation to decompose the problem by the seats on the flight and solving a dynamic program that controls the capacity on each seat separately. We also show that our results continue to hold when the airline makes pricing decisions, instead of fare class availability decisions. Our numerical study shows that the practical performance our approximate policy is remarkably good when compared with a tractable upper bound on the optimal total expected revenue.

Algorithmic Optimization of the Calculation with the Consideration of the Interconnection of the Basic Economic Parameters of the Flight Route of the Model Air Carrier

“…Authors Ref. [19] deals with revenue management model through optimization of fare locking options commonly offered by airlines. The authors' approach is based on the approximation of linear programming in relation to the distribution of seats during the flight and the design of a dynamic program that separately manages the capacity of each seat.…”