REAL-TIME DECISION-SUPPORT FOR INTEGRATION OF AIRLINE FLIGHT CANCELLATIONS AND DELAYS .1. MATHEMATICAL FORMULATION

An important decision faced by airline schedulers is how to adapt the flight schedule and aircraft assignment to unforeseen perturbations in an established schedule. In the face of unforeseen aircraft delays, s chedulers have to decide which flights to delay, and when delays becom e excessive, which to cancel. Current scheduling models deal with simp le decision problems of delay or cancellation, but not with both simul taneously. But in practice the optimal decision may involve results fr om the integration of both flight cancellations and delays. In this pa per, a quadratic 0-1 programming model is presented for the integrated decision problem. The model is a profit maximization program that tak es into account the different cost penalties of delay and of flight ca ncellation. Also, the model is extended to formulate some special case s such as the ferrying of surplus aircraft and the replacement of diff erent type of aircraft. Finally, some special properties of the model are given, resulting in a conversion of the discrete mathematical prog ram into a continuous one that is easier to solve. An algorithm and co mputational experiments are presented in a subsequent Part II of this paper.