A common practice in the world of air cargo transportation consists in charging the client for the weight of cargo that is actually transported and not for the one that was booked. As a result, it is not rare that the quantity of cargo booked by the client and the one that is actually delivered differ greatly. This distinctive source of uncertainty, typical of airfreight transportation, makes cargo routing an unusually difficult task for cargo airlines. To mitigate the effect of this variability in the quantity of cargo, airfreight carriers often resort to overbooking, i.e., they sell more capacity than is actually available. However, in case of excessive overbooking, the overflowing commodities must be reassigned to other flights on the day of departure, which may result in additional costs and cause delivery delays. In this talk, I will discuss a stochastic approach to the optimization of cargo shipping plans that aims at minimizing the expectation of overflow. In this approach, the uncertainty on the quantity of cargo is modelled in a way that makes it possible to derive an analytic expression for the expectation of overflow. I will show how this analytic expression can be approximated and used as the objective function of an integer program. Finally, I will present the preliminary results of simulation experiments in which this model is compared to an equivalent scenario-based stochastic linear program.