Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time

We propose a novel approach to solve the long-standing challenge of airline overbooking management. We solve the problem using dynamic programming with an industrial setting characterised as near-to-perfect competition where airlines strategically overbook their flights to control their market shares instead of a more conventional setting with a revenue maximisation. The theorised optimisation problem is constructed using a terminal utility criterion and with the application of the Hamilton-Jacobi-Bellman equation. The analysis expands on four most commonly applicable overbooking strategies, and the results provide guidance on how airlines can choose a strategy to pursue an optimisation solution best suited to them.