The multi-day aircraft maintenance routing problem

We solve the multi-day aircraft maintenance routing problem (AMRP) for a homogeneous fleet with a single-day flight schedule. Building on a methodology developed to solve the single-day AMRP, we include requirements that each aircraft receives maintenance every three days with limits on the maintenance facility capacity at each airport. We employ a compact flight connection graph called a hollow graph based on the minimum aircraft fleet size determined by deficit function theory. This negates the need for a plane count constraint. We solve the AMRP as a multicommodity integer linear program. Our main contributions are: (1) integrating the minimum fleet size into the AMRP, (2) using a more compact multicommodity flow formulation based on a reduced underlying flight connection graph, (3) introducing a reachability graph to reduce the number of integer binary variables by 51–80%, (4) shortening run time 21–80% by using our reduced connection graph instead of the all feasible joining connection graph, and (5) developing a heuristic with an optimality gap for twenty-one test problems of at most 0.73%.