Destination selection and flight scheduling for regional airlines at slot-constrained airports

We present the problem of a regional airline based at a slot‐constrained airport, which must select a set of destinations to serve, how many flights per day to operate to each destination, at what time the flights take place and which aircraft operates each flight. Restricting ourselves to the special case of regional airlines, which fly round trips from a central hub, we are able to tackle the four above decisions jointly. By contrast, in the existing literature, these decisions are usually optimised separately for generic airline networks. To solve the proposed problem, we introduce two compact integer formulations: a three‐index and a two‐index formulation. This latter, however, only solves a relaxation of the original problem because it cannot guarantee that all constraints are respected. Therefore, we embed the two‐index formulation into an iterative algorithm which dynamically adds violated constraints. Computational experiments highlight the validity of this approach and provide insights into the characteristics of the solutions.