  Revenue management is important for carriers (e.g., airlines and railroads).
In this paper, we focus on cargo capacity management which has received less
attention in the literature than its passenger counterpart. More precisely, we
focus on the problem of controlling booking accept/reject decisions: Given a
limited capacity, accept a booking request or reject it to reserve capacity for
future bookings with potentially higher revenue. We formulate the problem as a
finite-horizon stochastic dynamic program. The cost of fulfilling the accepted
bookings, incurred at the end of the horizon, depends on the packing and
routing of the cargo. This is a computationally challenging aspect as the
latter are solutions to an operational decision-making problem, in our
application a vehicle routing problem (VRP). Seeking a balance between online
and offline computation, we propose to train a predictor of the solution costs
to the VRPs using supervised learning. In turn, we use the predictions online
in approximate dynamic programming and reinforcement learning algorithms to
solve the booking control problem. We compare the results to an existing
approach in the literature and show that we are able to obtain control policies
that provide increased profit at a reduced evaluation time. This is achieved
thanks to accurate approximation of the operational costs and negligible
computing time in comparison to solving the VRPs.
