A proof of the relationship between optimal vehicle size, haulage length and the structure of distance-transport costs

This paper deals with two interrelated questions, namely the optimum size of a vehicle or vessel, and the structure of transport costs with respect to haulage distance. The relationship between these two questions has not been coherently dealt with previously in the literature, and the heuristic attempts at doing so have led to both theoretical and empirical anomalies. This paper adopts an inventory optimisation approach in order to show that both of these questions can be treated in a unified manner and this allows us to show, first, that under very general conditions the optimum size of a ship increases with the haulage distance and haulage weight, and second, that the observed structure of transport costs with respect to the haulage distance and quantity is itself a result of this optimisation problem.