Multiple Depot Vehicle Scheduling Problem: A New Heuristic Based on Quasi-Assignment Algorithms

Abstract

This work is concerned with the multiple depot vehicle scheduling problem where one has to group timetabled trips into chains and, at the same time, assign those chains to depots in order to minimize fleet size costs and dead-heading time. A new mathematical programming formulation is presented for such problem which is known to be NP-hard (Bertossi et al, 1987). Lagrangean relaxation is used, with the corresponding relaxed problem being decomposed into: a semi-assignment problem; a multiple depot vehicle scheduling problem without the requirement that each vehicle must return to the source depot. This last problem is solved by an adaptation of the quasi-assignment algorithm for the multiple depot vehicle scheduling problem (Branco,1989), which takes into account the depots capacities. Computational experience is reported for problems randomly generated according to real life data.