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In this thesis, we address air cargo capacity and revenue management. The traditional air cargo supply chain is composed by the shippers, the freight forwarders and the airlines. The freight forwarders have to secure capacity with airlines in order to accommodate the shippers' demand. They have to bid for capacity six to twelve month before the actual departure date of the aircraft, and confirm the capacity they need a few days before departure. On the other end, the airlines sell the capacity left after honoring committed contracts and allotments (capacity committed to freight forwarders months in advance) during a booking period of fifteen to thirty days before the aircraft's departure. Currently, there is no penalty for the freight forwarders to commit to more capacity than they actually need, and the airlines are faced with release of capacity on the day of departure, capacity that could have been sold during the booking period and that translates into lost revenue.
We address the freight forwarders problem of confirming needed capacity based on balancing the costs of ordering too much capacity versus ordering too little. We define the problem as a perishable inventory problem with backlocking options and lead times. We show the value function is convex in the state variables when the lead time is one or two periods. We present the structure of the optimal policy and show it is a stationary policy, i.e., it depends on the state variables only, and not on the period of time the order is placed. We find the limiting equations. In addition we present some simple solutions to the extended case when we have subcontracting options and the orders have a due date.
We also address the airlines' revenue management problem, in particular the problems of (1) accepting/rejecting incoming bookings based on bid prices (threshold values used in the process of accepting/rejecting demand), and of (2) estimating the show-up rate (ratio of bookings handed in at departure out of the bookings on hand) with impact on overbooking. We identify the need of splitting the cargo into two categories: small cargo, which is mail and small packages, and large cargo, which is the bulk of commercial cargo, based on their different arrival behaviors. The small cargo is approximated with the passengers arrival, and we propose a new algorithm to solve the traditional probabilistic nonlinear problem from the passengers side. The large cargo is solved using a dynamic program, which is decomposed at the leg level using a fare-prorating scheme. The solution from our new approach is shown via simulation to be superior to the two approaches used in practice: the first come first served, and the deterministic linear program.
The show-up rate is estimated using wavelets and we show that a discrete show-up rate is more suitable than the traditional Normal estimator used in practice. The new estimator results in considerable more potential revenue.
