Tail assignment problem with hour-to-cycle ratio constraints

Effective management of hour-to-cycle performance is crucial for any aircraft operating under an operating lease contract. This protects an airline from incurring supplemental rental payments that arise from leasing contract terms. One way of managing accumulated flight hours and flight cycles on aircraft is integrating related performance measures in the tail assignment decisions. This study introduces the tail assignment problem (TAP) considering aircraft’s hour-to-cycle ratio performance. We introduce a novel TAP formulation explicitly incorporating aircraft hour-to-cycle ratio constraints, which are typically overlooked in traditional models. Our numerical analysis demonstrates that overlooking the hour-to-cycle performance of aircraft in tail assignment decisions can result in drastic deviations from target ratios. Therefore, we propose a mathematical model that includes penalty costs for violating the aircraft’s target hour-to-cycle ratios. We propose one McCormick linearization and one second-order conic reformulation for the nonlinear constraints in the model. We perform computational analyses by generating problem instances derived from an actual flight schedule. Computational results show that within a given time limit the model with McCormick linearization solves more instances to optimum than the model with conic reformulation. Also, it achieves an average optimality gap of 1.62% while the average gap is 6.39% for the solutions obtained with the conic formulation.