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

Abstract

Quantitative information on land use can be confronted with social, economic and environmental objectives in interactive multiple-goal linear programming (IMGLP) models to explore land use options. For various reasons, quantitative information on land use (input-output combinations) and resources is often aggregated to administrative units when integrated in the IMGLP model. In this paper, consequences of aggregating spatial units in an IMGLP model are analyzed for both 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 tend to be 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 many complicated interacting effects, the aggregation error is difficult to predict. Therefore, in land use studies using IMGLP, the motto is '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.