Delivery itineraries and distribution capacity of a freight network with time slots

The paper focuses on the distribution problem of delivering goods to medium size stores in a Central Business District (CBD) having limited off-street parking which can accommodate only restricted space and time for parking, loading/unloading operations. In this scenario, freight distribution can be addressed from two perspectives: (i) from the viewpoint of delivery/pick-up firms, delivery itineraries need to be coordinated with consideration of the delivery capacities and times at store sites for parking, and loading/unloading operations; (ii) from the viewpoint of transportation and city planners, the ‘distribution capacity’ in the CBD must be determined, including the average cost of distribution routes, the maximum number of routes that can be simultaneously coordinated, the total number of stores that can be served, etc., much in the way traffic engineers are interested in the ‘traffic capacity’ of a transportation network under which the vehicles move efficiently. Both the above viewpoints are addressed in this paper by solving the following problem: what delivery itineraries are available so that parking, loading/unloading capacities and associated time windows are respected and the itineraries are ‘balanced’ in a way that costs and number of deliveries fall in given ranges. This problem is studied and a mathematical programming formulation is developed. To evaluate exactly the freight distribution capacity, a branch-and-bound approach is developed, where the relaxation of the formulation provides good bounds. Subsequently, a heuristic is presented that is useful from an operational point of view. In fact, the latter algorithm exploits the results provided by the exact approach and maximizes the efficiency of the system.