Best partial flow aggregation in transportation cost functions

Full description of transportation output as a vector of flows would make the estimation of transportation cost functions unfeasible in most real cases. In this paper the authors generate procedures to aggregate flows in an optimal way (i.e. such that a pseudo cost function specified in terms of aggregates, best approximates a true cost function in a previously defined manner). The problem is stated and solved in terms of the search for an aggregation matrix that fulfills the required properties. The case of disjoint aggregation, where each componet of the flow vector contributes to the generation of only one aggregated variable, is particularly analyzed. The approach is applied using previously reported data, comparing the results with those obtained with other forms of partial aggregation.