Expected Distances in Distribution Problems

In many problems in distribution management it is necessary to take account of the expected distances that result from dispatching vehicles to meet customer demand. For example, in mathematical models for determining the optimal location of depots, the sum of radial distances (between customers and the depot), or the sum of the weighted distances, is used as a measure of the delivery "costs". Since actual delivery operations from the depot usually consist of truck-routes with each truck delivering to more than one customer at a time, it is important to know to what extent the above simplification is valid, namely to find a relationship between the actual route-distances and the sum of the radial distances.This paper makes use of an algorithm which plans optimal or near optimal routes to estimate this relationship by solving a large number of randomly generated problems. The discrepancies between the two methods are shown to be significant under certain circumstances.