Linear programming as a forecasting device for interregional freight flows in Great Britain

Abstract

This paper reports some experiments testing the efficacy of linear programming (LP) as a method for predicting flows of commodities between regions of Great Britain.

‘Transportation problem’ solutions were found for the annual movement by road of eleven commodity categories between 78 origin and destination zones in 1964. Road distances were used as a surrogate for freight costs. Data on actual flows of these commodities in that year were available for comparison. For the more homogeneous commodity classes the LP solutions replicated the actual pattern quite well.

Another experiment was carried out using the same commodities, on a subset of zones which were more homogeneous with respect to areal extent - namely the 24 major cities in Great Britain: the correspondence between LP solutions and actual flows was much closer than for all 78 zones.

A further test involved finding LP solutions for total road plus rail traffic with six commodities which might be described as ‘heavy’ and which use the rail system extensively. These solutions for total flows proved to correlate with actual flows better than solutions for road movements alone.

These results would appear to justify continuation of investigations of this kind using a finer commodity - and if possible zonal - breakdown. It is hoped that data on actual flows for 1967/68, which have a more disaggregated commodity classification, will be available soon.

The ‘shadow prices’ of the minimizing dual of the transportation problem were produced and examined to see if they made sense in terms of notions of geographical comparative cost advantage variations for production and consumption.