Optimal overbooking limits of a two‐dimensional cargo problem: A profit maximization approach

This article considers a two‐dimensional cargo overbooking problem, with the objective of finding the optimal weight and volume overbooking limits that maximize the profit from shipping cargos on a particular flight. The pricing structure is nonlinear because it uses the chargeable weight of the showing up cargo, as implemented in practice, as opposed to the approximate additive structure considered in the literature. An aggregate formulation that does not require much data is provided and solved under infinite and finite booking requests. The optimal overbooking curve is shown to be a ‘box’, defined by only two threshold numbers, one for volume and one for weight. Furthermore, the aggregate formulation can be solved efficiently and its simple ‘box’ solution can be implemented with ease by air cargo practitioners. The aggregate formulation is then compared to the detailed or actual overbooking formulation, in which the revenues are computed individually cargo by cargo. Using real‐life data, we show that our model approximates well the actual cargo problem, when the density of the cargo shipped is not highly variable, more specifically, when it ranges between 6.2 and 16.2lb/ft³, which is the case for high‐technology, low density products such as computers and consumer electronics. We find that this applies to 60 per cent of the flights. Also, we compare our model to the additive one, and numerically prove that savings up to 13.8 per cent can be achieved when implementing the aggregate model as opposed to the existing additive model.