Air-cargo capacity allocation for multiple freight forwarders

We consider a single air-cargo carrier, which wants to allocate cargo capacity to multiple forwarders before a booking horizon starts. A contribution that the carrier earns from each forwarder is based on the actual allotment usage at the end of the horizon. The airline's problem is to choose the allotments that maximize the expected total contribution. We derive a probability distribution of the actual usage by using a discrete Markov chain and solve the problem by using a dynamic programming method. Two heuristics for a large-scale allocation problem are also proposed, and their performances are tested via numerical experiments.