  Booking control problems are sequential decision-making problems that occur
in the domain of revenue management. More precisely, freight booking control
focuses on the problem of deciding to accept or reject bookings: given a
limited capacity, accept a booking request or reject it to reserve capacity for
future bookings with potentially higher revenue. This problem can be formulated
as a finite-horizon stochastic dynamic program, where accepting a set of
requests results in a profit at the end of the booking period that depends on
the cost of fulfilling the accepted bookings. For many freight applications,
the cost of fulfilling requests is obtained by solving an operational
decision-making problem, which often requires the solutions to mixed-integer
linear programs. Routinely solving such operational problems when deploying
reinforcement learning algorithms may be too time consuming. The majority of
booking control policies are obtained by solving problem-specific mathematical
programming relaxations that are often non-trivial to generalize to new
problems and, in some cases, provide quite crude approximations.
  In this work, we propose a two-phase approach: we first train a supervised
learning model to predict the objective of the operational problem, and then we
deploy the model within reinforcement learning algorithms to compute control
policies. This approach is general: it can be used every time the objective
function of the end-of-horizon operational problem can be predicted, and it is
particularly suitable to those cases where such problems are computationally
hard. Furthermore, it allows one to leverage the recent advances in
reinforcement learning as routinely solving the operational problem is replaced
with a single prediction. Our methodology is evaluated on two booking control
problems in the literature, namely, distributional logistics and airline cargo
management.
