Design of multiple-vehicle delivery tours—III valuable goods

For the delivery of valuable goods (such as people in a van pool), we assume that it costs cv per unit time during a round trip time of a vehicle and it costs cu/C per unit time for each of C items being delivered only during the travel time from the source to the point of delivery. The objective is to design delivery routes so as to minimize the (expected) total cost of delivery in some region containing N >> C delivery points. With nearly rectangular shaped delivery zones for each vehicle route it is shown that if cu/2 cv, however, one should deliver only on the outbound leg and deadhead back from the far end of the zone. In each case there is an optimal width and orientation of the rectangular zone relative to the local grid of roads and the travel-time contours from the source.