Set partitioning approach to the Multiple Depot Vehicle Scheduling Problem

We address the problem of scheduling a fleet of vehicles, stationed in different depots, in such a way to perform a set of time-tabled trips and to minimize a given objective function. We consider the constraint that requires each vehicle to return to the starting depot. This problem, known as Multiple Depot Vehicle Scheduling (MD-VSP), is NP-hard. In this paper we formulate the MD-VSP as a Set Partitioning Problem with side constraints (SP). We describe a procedure that, without using the SP matrix, computes a lower bound to the MD-VSP by finding a heuristic solution to the dual of the continuous relaxation of SP. The dual solution obtained is used to reduce the number of variables in the SP in such a way that the resulting SP problem can be solved by usual branch and bound techniques. The computational results show the effectiveness of the proposed method.