A risk averse approach to the optimal capacity problem in the airline cargo industry

Abstract

The low margins in the airline industry have made them focus in the air cargo area to try to increase their profits. One of the decisions that the airlines face is determining the proportion of the capacity of a flight intended for long-term contracts (known as allotment) and for bookings that are more urgent and come closer to the departure of the flight (known as free). In general, allotment tariffs are lower than free market ones. This suggests that, if possible, one should favour the sale in the free market rather than the allotment contracts. However, demand in the free market has more uncertainty and usually does not arrive with the promised cargo even if the capacity was booked. In this paper we propose a two stage stochastic programming model to determine the total weight that should be assigned to allotment and free reservations, considering as random elements the demand, the tariff, and the show-up rate for the free mode. We also consider risk aversion in the objective function using the CVaR, departing from the classical expected value case. We show that more stable solutions, with low probability of experiencing extreme losses, can be obtained at the expense of reducing the gains. Moreover, we conclude that the use of stochastic programming model provides greater benefits in scenarios with high seasonalities and free demand variability, reaching a 2.28% increase in average income when compared to solving the problem replacing the random parameters by their average values.