A Lifted Compact Formulation for the Daily Aircraft Maintenance Routing Problem

Given a set of flights for a specific fleet type, the aircraft routing problem (ARP) determines the flying sequence for each individual aircraft while incorporating specific considerations of minimum turn time, maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenances. This stage is significant to airline companies as it directly assigns operational routes and maintenance breaks for each aircraft in service. Most approaches related to the problem adopt set partitioning formulations that include exponentially many variables, which requires the design of specialized column generation or branch-and-price algorithms and codes. In this paper, we present a compact polynomial-sized representation for the ARP, which is then linearized and lifted using the reformulation-linearization technique. In addition, we propose two root-node strategies for further augmenting the model formulation. The resulting formulations remain polynomial in size, and we show that they can be solved very efficiently by commercial software without complicated algorithmic implementations. The numerical experiments demonstrate high-quality solutions and significant savings in computational time.