A Dynamical Management Model for Accepting Reservations

Abstract

We consider a dynamical management problem for accepting reservations of airplane seats. When the penalty for the airline company canceling an accepted reservation is increasing as a period approaches to the flight day, how many reservations must the company accept or cancel in each period? We show that the optimal policy has two levels and in the n-th period such that if the accumulated number w _n of accepted reservations is smaller (larger) than , then the company can accept more reservations (must cancel accepted reservations) until and if , then the company should make no acception and no cancellation.