Groupe d’études et de recherche en analyse des décisions

# A stochastic approach to reoptimizing air cargo shipping plans

## Paul Zago, Patrick Munroe, Issmail El Hallaoui et François Soumis

Overbooking is a common practice in the air cargo industry because booked and actual demands often differ greatly. As a consequence, in case of excessive overbooking, the overflowing commodities must be reassigned to other flights on the day of departure. We propose a stochastic approach to reoptimizing cargo shipping plans so that the expectation of cargo overflow is minimized. A probability distribution consisting of the mixture of a normal and a constant $$0$$ distribution is introduced to model the show-up rate so that no-show is taken into account. From this mixture distribution, we derive an analytic expression for the expectation of overflow. An approximation of this expression is then used as the objective function of the formulation of an integer programming model to reoptimize an air cargo shipping plan. In a series of simulation experiments, we compare the resulting analytical model with an equivalent scenario-based stochastic linear program. It is found that the analytical model delivers results that are similar to the ones of the scenario-based stochastic program, but with a significant reduction in computation time.

, 23 pages