Optimal location of transshipment depots

A number of agricultural commodities are either transported once harvested to a destination outside the production region or processed (or consumed) at a centrally located facility within the production region. One or more depots (or assembly points) can be located optimally within the harvesting region to reduce the overall shipment costs when transshipment at a lower freight rate can be achieved from the depot. Processing at the depot to concentrate the commodity, or to select desired fractions from the raw material, can achieve additional reductions in freight costs and increase the economic benefit. A model based on a circular harvesting region with uniform production per hectare and a linear transport function was used to define the optimal location of the depots. In the case of transshipment out of the supply region, a single depot was considered. A transshipment depot can be placed within the supply region for a net reduction in transport costs as long as the transshipment freight rate is less than approximately 85% of the collection freight rate. For transshipment to a central processing facility, the supply region was divided into uniform sectors and the optimal depot placement in a sector was located. Given a non-negative transshipment freight rate and that all production passes through the depot, the optimal depot placement cannot lie beyond 70.7% of the radius. A minimum reduction in the ratio of the freight rates is also required for the shipment point to move from the centre of the region to within a sector. Division of the production region into an infinite number of sectors was examined and it was found that convergence to the maximum benefit (at infinite number) was rapid so that, with just eight or nine sectors, 80% of the limiting benefit was obtained. The model was developed with the harvesting of milk in mind, but appears to relate to a wide range of harvestable low value bulky agricultural commodities. For a circular harvesting region, it was found that the economic benefit varied as the cube of the radius of the production region and linearly with the production intensity, regardless of whether transshipment was internal or external. The economic benefit was quantified for both variants of the model using selected parameters pertinent to milk harvesting.