Characteristics of multi-shop/ multi-termal delivery routes, with backghauls and unique items

This paper creates and evaluates spatial models for multiple stop delivery routes that are allowed to begin and end at separate terminals. Each terminal must deliver a set of unique items. These deliveries can be coordinated with deliveries from other terminals to form back-haul loops. The paper assumes that stops are uniformly distributed over a large region and that a strip-routing strategy is followed. Among the findings are that the optimal orientation of a delivery district is defined by the ellipse passing through the routing district and having the terminals as foci. The paper also determines optimal district shape, and determines which districts should be traveled in a single pass (entering and exiting at opposite ends), and which should be traversed in two passes (entering and exitin from the same end).