The transportation problem and a doubly constrained gravity model with a power deterrence function are used to find predictions of a number of 134 × 134 freight matrices detailing tonnages moved in Great Britain in 1972. The matrices detail movements by thirty commodity groups, and predictions are obtained for movements by road for all but one of the commodities and for the principal items carried by rail. These predicted matrices are used to examine a number of questions. The relationships between some alternative goodness-of-fit statistics are examined to establish which commodities are best modelled by each technique and to point out empirically which statistics give unreliable rankings. Various summary measures of the actual matrices are examined to see if it is possible to predict which matrices will be best modelled by each technique. The modelling techniques are compared to indicate which provides the best predictions for each matrix, and some conclusions are offered on the absolute efficiency of the best models.
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