Single-leg air-cargo revenue management

We consider a cargo booking problem on a single-leg flight with the goal of maximizing expected contribution. Each piece of cargo is endowed with a random volume and a random weight whose precise values are not known until just before the flight's departure. We formulate the problem as a Markov decision process (MDP). Exact solution of the formulation is impractical, because of its high-dimensional state space; therefore, we develop six heuristics. The first four heuristics are based on different value-function approximations derived from two computationally tractable MDPs, each with a one-dimensional state space. The remaining two heuristics are obtained from solving related methematical programming problems. We also compare the heuristics with the first-come, first-served (FCFS) policy. Simulation experiments suggest that the value function approximation derived from separate "volume" and "weight" problems offers the best approach. Comparisons of the expected contribution under the heuristic to an upper bound show that the heuristic is typically close to optimal.