Stochastic Runway Scheduling Problem with Partial Distribution Information of Random Parameters

Abstract

Air traffic flow management is one of the most important operations in terminal airports heavily relying on advanced intelligence transportation techniques. This work considers a two-stage runway scheduling problem given a set of flights with uncertain arrival times. The first-stage problem is to identify a sequence of aircraft weight classes (e.g., Heavy, Large and Small) that minimizes runway occupying time (i.e., makespan). Then the second-stage decision is dedicated to scheduling the flights as punctually as possible after their arrival times realized, which translates into determining a sequence of flights for each aircraft category such that the total deviation time imposed on the flights is minimized. Instead of an exactly known probability distribution, information on uncertain parameters is limited (i.e., ambiguous), such as means, mean absolute deviations and support set of random parameters derived from historical data. Under this information on the random parameters, an ambiguous mixed-integer stochastic optimization model is proposed. For such a problem, we approximately construct a worst-case discrete probability distribution with three possible realizations per random parameter, and adopt a hybrid sample average approximation algorithm in which genetic algorithms are used to replace commercial solvers. To illustrate the effectiveness and efficiency of the proposed model and algorithm, extensive numerical experiments are carried out.