An Approach to Vehicle Scheduling with Depot Capacity Constraints

Multiple-depot vehicle scheduling in public transport can be formulated as an integral multicommodity flow problem in a time-space network. Using a Lagrangean relaxation and subgradient optimization, an improved lower bound and, in many cases, the optimal solution of that problem can be determined. An algorithm is introduced to maintain multicommodity flow conservation of a solution of the Lagrangean relaxation in order to obtain a feasible solution of the original multicommodity flow problem.