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G-2025-82

Dynamic constraint aggregation for the multiple-depot bus scheduling problem

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Bus scheduling problem is a core optimization problem for public transit agencies. Given a set of timetabled trips to cover during a day and a homogeneous bus fleet assigned to multiple depots, the multiple-depot vehicle scheduling problem (MDVSP) consists in finding least-cost feasible schedules that cover each trip exactly once. To solve large-scale MDVSPs, we develop a column generation (CG) heuristic that is applied to a block-based set-partitioning model, where a block starts and ends at a depot without intermediate returns. To reduce degeneracy and improve performance, we combine CG with an improved dynamic constraint aggregation procedure (IDCA). We further devise a hybrid dual-disaggregation (HDD) step to accelerate convergence. Computational results on real-world instances with up to 6,296 trips show significant speed ups resulting from i) using a block-based model rather than a schedule-based model, ii) integrating CG with IDCA, and iii) applying HDD. Together, the these techniques yield an average speed up factor of 12.4 compared to CG alone applied to a schedule-based model, with only marginal degradation in the solution cost.

, 18 pages

Ce cahier a été révisé en janvier 2026

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