DISTRIBUTING NONSTORABLE ITEMS WITHOUT TRANSSHIPMENTS

The research reported in this paper attempted to find optimal strategies for distributing items from one depot to many demand points without transshipments and within a limited amount of time. The objective was to find a near optimal partition of the region supplied by the depot into districts (the zones containing the points visited by one delivery route) and corresponding shipment sizes and costs. Initially, the average distribution cost per demand point on a single delivery route was studied using expressions that relate route length to the dimensions of a delivery district. Two routing strategies were considered: one that generates tours with nearly minimal local distance per point and another that generates tours with nearly minimal line-haul distance per point. Formulas were derived to estimate the optimal shipment size, district shape, and cost when the strategy yielding the least cost per point is used. Finally, the results were applied to develop guidelines for partitioning a whole supply region into nearly optimal districts; an example is given. For a constant demand density, an optimal district partition of the supply region should have bigger and fatter districts near the depot and smaller and thinner ones along the boundary of the region.