Optimal Dynamic Upgrading in Revenue Management

We consider a revenue management problem involving a two compartment aircraft flying a single leg, with no cancellations or over-booking. We apply the practice of transforming a choice revenue management model into an independent demand model. Within this assumed independent model, there are two sets of demands, business and economy, each with multiple fare class products. A business passenger can only be accepted into business. An economy passenger can be accepted into economy or upgraded into business. We define a two-dimensional dynamic program (DP) and show that the value function is sub-modular and concave in seat availability in the two compartments. Thus the bid prices are non-decreasing with respect to these state variables. We use this result to propose an exact algorithm to solve the DP. Our numerical investigation suggests that in contrast to standard backward induction, our method could be included in production revenue management systems. Further, when the economy compartment is capacity constrained, we observe a substantial monetary benefit from optimal dynamic upgrading compared to the static upgrading procedures currently used in practice.