A study on the hierarchical collection/distribution system with economies of scale

This paper analyzes the optimal hierarchical collection/distribution system for many-to-one (or one-to-many) transport demand using a criterion of transport cost minimization. We consider the continuous terminal locations and define the parameters which are scale economy in weight, scale economy in distance and demand volume. We find that logarithmic function of demand volume mainly determines hierarchical levels, and that the number of hierarchical levels and the number of intermediate terminals of the optimal system become larger as scale economy in weight gets smaller, scale economy in distance gets larger or demand volume gets larger. The actual postal and parcel systems are compared with our theoretically optimal systems.