Aggregation of spatial units in linear programming models to explore land use options.

Consequences of aggregating spatial units in an interactive multiple-goal linear programming (IMGLP) model are analysed for a schematized and an existing IMGLP model (GOAL) exploring land use options for the European Union. A discrimination was made between effects on objective functions for the system as a whole, and effects on related optimum land use allocation within the system. In GOAL, effects on land use allocation are more important than effects on the value of objective functions. Several rules or factors were identified that determine the effect of aggregation, among which the degree in curvilinearity in input-output relations and the method of aggregation are important ones. However, because of complicated interacting effects, the aggregation error is difficult to predict. Therefore, in land use studies using IMGLP it is important to first optimize the linear programming model at the non-aggregated level and then aggregate to the appropriate policy level. If aggregation is inevitable because LP models become too big, aggregation according to agro-ecological criteria, i.e., aggregation of units with similar output-input ratios and constraints, results in the smallest errors