A model of capacity control with overbooking for a two-leg airlines network

We consider a two-leg airline network and formulate the problem of capacity control as an infinite horizon MDP with an absorbing set. Customers arrive according to a non-homogenous Markov process. Cancellation and no-shows are allowed. And customers can request multiple seats (batch requests or group arrival) and can be over booked. We analyze the structure of an optimal policy, which is of the threshold type. Under realistic conditions, we demonstrate that an optimal booking policy is characterized by state-dependent booking limits for each fare class and each product or itinerary. We also provide a numerical example to show the structural property of the optimal booking limits.