Document Type

Journal Article

Publication Date


Subject Area

operations - scheduling, planning - methods, planning - route design, mode - bus


Scheduling, Route time constraints, Optimization, Optimisation, Mathematical models, Large cities, Intracity bus transportation, Heuristic methods, Bus transit, Baltimore (Maryland)


A procedure is presented for solving real-world large-scale multiple depot vehicle scheduling (MDVS) problems considering the route time constraints (RTCs). The procedure is applied to some test problems and then to a real-world problem. The real-world problem is the transit bus scheduling problem of the mass transit administration (MTA) in Baltimore, Maryland. The RTCs are added to the MDVS problem to account for real-world operational restrictions such as fuel consumption. Formulation of the MDVS problem, the set of constraints for considering the time restriction, and a heuristic procedure for solving the MDVS problems with RTCs are discussed. Application of the proposed procedures in solving bus scheduling problems in large cities requires a reduction in size of those problems in terms of number of variables and constraints. Two techniques are proposed to decrease the size of the real-world problems. Combining these techniques results in a strategy to reduce the MTA problem size into a manageable and solvable size. The solutions to the reduced size problems are further improved by solving a series of single depot vehicle scheduling problems for each of the MTA depots. The final results from the proposed model are compared with the MTA's January 1998 schedule. The comparison indicates that the proposed model improves on the MTA schedules in all aspects. The improvements are 7.90% in the number of vehicles, 4.66% in the operational time, and 5.77% in the total cost.