• Denis M. Karamushko, Moscow Institute of Physics and Technology (Dolgoprudny, Russia)
• Alexey V. Chernov, Moscow Institute of Physics and Technology (Dolgoprudny, Russia)

Airline schedule planning is a complex multi-stage optimization process, including schedule design, fleet assignment, and aircraft routing. This paper proposes an integrated mathematical model for the joint optimization of fleet type assignment and flight departure times determination within a hub-and-spoke network structure. The model is formulated as a mixed-integer linear program built upon a space-time graph representation of the flight schedule. A key distinguishing feature of the model is the handling of connecting passenger itineraries: revenues from both point-to-point and transfer passengers are included in the objective function, along with fleet operating costs. Problem dimensionality is reduced by exploiting the rotation structure of hub-and-spoke networks: outbound and return legs between a hub and a spoke region are treated as a single rotation unit. The model was validated on real-world data from a major Russian airline, comprising 260 daily flights aggregated into 146 rotations and inter-hub flights, operated by a fleet of 61 aircraft across 5 fleet types. Two independent demand data sources were used for validation: the airline's own booking data and estimates generated via a gravity model. A two-step optimization scheme is proposed: in the first step, departure times are searched over a wider range with a coarser interval; in the second step, the solution is refined over a narrower range with a 5-minute resolution. The optimized schedule achieved a 4–9% increase in forecasted operational profit and a 19% improvement in the number of reachable transfer markets within a three-hour connection window. These results demonstrate that the simultaneous optimization of schedule timing and fleet assignment yields meaningful commercial gains and gives more convenient connection opportunities for passengers.

airline schedule optimization, fleet assignment model, linear programming, mathematical modelling

2026-09-03