Approximate dynamic programming-based thresholds for cargo capacity management considering postponements

We consider an airline that operates sequential flights in an origin–destination pair. Cargo products are opaque in terms of which specific transportation vessel or routing is used to carry a shipment. Hence, based on the time sensitivity, shipments can be postponed to later flight departures to accommodate the high-value requests. The objective is to assist the airline with joint capacity control and overbooking decisions, considering all the complexities associated with the cargo product. We model the master problem as an infinite-horizon dynamic program (DP) with frequent arrivals and infrequent departures, and relax the cargo divisibility assumption while computing offload costs. We decompose the master problem into several DP sub-problems, with each one focusing on individual flights considered in the study. As the proposed DP sub-problem solution becomes intractable, we resort to approximate dynamic programming to find an implementable solution. Specifically, the space of policies based on control limits or thresholds is looked upon as they are easily implementable. Hence, we use approximate policy iteration to find the implementable solution, where we prove the convergence and existence of such a solution. Numerical results illustrate that the proposed solution of the sub-problem performs 6%–9% better than the first-come, first-served policy and approximates 88%–94% of the upper bound. Additionally, about 4%–10% of revenue improvements are possible if the postponement strategy is considered. Extensions to time-dependent thresholds, aircraft selection, and policy beyond allowable limits are also discussed.