Contract carriers in the trucking industry are known to offer shippers a per mile rate that decreases stepwise as the shipper’s route lengthens, with a mileage band designated for each rate. While the use of quantity-based pricing discounts in supply chains has been well studied, there has been no research on how shippers should route under such a pricing scheme or how carriers should set such bands. In this paper, we provide methods for both. Route construction is complicated by the fact that the per mile rate cannot be determined until after the route has been created. With this consideration, we develop a model of this problem and then an algorithm for solving it that assists the shipper in constructing the lowest cost route. It is beneficial for the shipper to extend the length of certain routes to incur a lower per mile cost, and we find that most of these routes can be constructed to equal any mileage required to receive the lower rate. As an extended route generates unnecessary expense and energy use for the carrier, theoretical and analytical insights provide guidelines for a carrier to use in developing better mileage bands. These guidelines assist a carrier in constructing bands that maximize profit and minimize the cost associated with a shipper extending a route.
Loyola University Chicago