Integrated air-rail scheduling: A branch-and-price approach for adaptive passenger-centric planning

This paper addresses the air-rail schedule synchronisation problem by proposing a novel approach that designs integrated flight and train schedules from scratch. A passenger-centric approach is employed, considering a set of travel preference criteria: door-to-door travel time, price, and transportation mode. The problem is formulated as an adapted version of a Multi-Commodity Flow (MCF) problem on a time-expanded network, and solved through a branch-and-price procedure. To speed-up the solution process, we propose to couple the resolution of the column-generation sub-problem with a pattern search, performed in a preprocessing phase. The proposed methodology is tested on the French transportation network over a five-month period, considering 1500 commodities. The complete schedule is generated in twelve hours, including the preprocessing time. The final schedule satisfies over 95 % of passenger travel preferences, demonstrating the effectiveness of the approach in optimising multimodal connectivity.