Design of multiple-vehicle delivery tours--I a ring-radial network
Certain aspects of what is commonly described as the "Vehicle Routing Problem" are discussed. We wish to deliver items to a large number of points randomly distributed over some region by means of vehicles, each of which can deliver to only C points. The key to any detailed routing to minimize the cost of delivery (by hand or computer) is first to partition the region into zones in which individual vehicles make deliveries. We assume here that there are many such zones, an average density of points [delta], that the "unit of length" [delta]-1/2 is large compared with the spacing between roads, and C >> 1. To minimize the delivery cost, zones should be approximately rectangular in shape with a width comparable with [delta]-1/2 and length comparable with C[delta]-1/2. In order to illustrate some numerical methods of approximation, we will first analyze, in considerable detail, the routing of vehicles on an idealized ring-radial network including how one would distort the shape of the zones near the origin and at boundaries. In Part II we will generalize this to other network geometries, and in Part III consider modifications in strategy if the items (people, for example) are valuable. In contrast with presently available computer programs for which the accuracy may decrease with increasing number of points in the region, the methods described here are essentially asymptotic approximations; the more points there are in the region, the more accurate are the results.
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Volume (Year): 20 (1986)
Issue (Month): 5 (October)
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