Weighted Time-Band Approximation Model for Flight Operations Recovery considering Simplex Group Cycle Approaches in China

Abstract

The time-band approximation model for flight operations recovery following disruption (Bard, Yu, Arguello, IIE Transactions, 33, 931-947, 2001) is constructed by partitioning the recovery period into time bands and by approximating the delay costs associated with the possible flight connections. However, for disruptions occurring in a hub-and-spoke network, a large number of possible flight connections are constructed throughout the entire flight schedule, so as to obtain the approximate optimal. In this paper, we show the application of the simplex group cycle approach to hub-and-spoke airlines in China, along with the related weighted threshold necessary for controlling the computation time and the flight disruption scope and depth. Subsequently, we present the weighted time-band approximation model for flight operations recovery, which incorporates the simplex group cycle approach. Simple numerical experiments using actual data from Air China show that the weighted time-band approximation model is feasible, and the results of stochastic experiments using actual data from Sichuan Airlines show that the flight disruption and computation time are controlled by the airline operations control center, which aims to achieve a balance between the flight disruption scope and depth, computation time, and recovery value.2 Mathematical Problems in Engineering network (representing an airline network) in which the nodes represent the flights and the arcs are the total time losses on individual flights. Hence, a branch and bound procedure was developed to minimize the total passenger delay when an aircraft is grounded. Further, Teodorović and Stojković [3] have introduced a lexicographic dynamic programming approach and a heuristic algorithm to minimize the total passenger delays and the number of cancelled flights. Two minimumcost network flow models to address aircraft shortages have also been introduced by Jarrah et al. [4]. The first is a delay model that allows for flights to be delayed or cancelled, aircraft to be alternated among scheduled flights, or the usage of surplus aircraft to be requested. The second model minimizes the total flight leg cancellation costs by similarly selecting multiple cancellations, employing aircraft substitution, and utilizing spare aircraft. However, accurate flight delay costs can not yet be quickly and easily determined, and the scope and depth of the flight disruption are not considered in the above models. In contrast, delay costs can be approximated with accuracy using the time-band approximation model introduced by Yu et al., which was developed in order to retain the superiority of the resource assignment model and the multicommodity flow model. Further, Yu [5] has introduced a time-based two-commodity network optimization model for aircraft routing. One commodity in the network model represents aircraft, while the other represents flight cancellations. In addition, Yan and Yang [6] have published a single model to initially combine flight cancellations and delays and to ferry fl...