Exact algorithms for the multi-depot vehicle scheduling problem based on multicommodity network flow type formulations

We compare the linear programming relaxation of different mathematical formulations for the multi-depot vehicle scheduling problem. As a result of this theoretical analysis, we select for development a tree search procedure based on a multicommodity network flow formulation that involves two different types of decision variables: one type is used to describe the connections between trips, in order to obtain the vehicle blocks, while the other type is related to the assignment of trips to depots. We also develop a branch and bound algorithm based on the linear relaxation of a more compact multicommodity network flow formulation, in the sense that it contains just one type of variable and fewer constraints than the previous model. Computational experience is presented to compare the two algorithms.