Two-level national-regional planning and mathematical programming decomposition applied to spatial price equilibrium models2

This paper is concerned with computation strategies related with the quantitative analysis of only a sector of a global economy (e.g. agriculture or energy). Under a ceteris paribus condition on the environment of the sector, and within the hypothetical context of the neoclassical economic theory, it is well known a type of partial equilibrium model that can be cast mathematically into an optimization framework. We attempt here to a typical specification which considers spatially separated markets, that has been called spatial price equilibrium model and that has contained within it many classical transportation problems (one for each commodity). The model is specially suitable for mathematical programming decomposition, resulting regional sybsystems whose coupling variables are the transportation flows. We explore here this structure, discussing two decomposition algorithms with economic interpretations that suggest decentralized procedures for planning. The first—of the price coordination type—is a variant of the Dantzig-Wolfe's principle which is expected to have a low number of cycles of information flow between the master level and the sub-problems (at each cycle it is calculated a series of regional production-consumption responses to alternative prices generated by transhipment problems at the central planning level). The second algorithm specializes the Geoffrion's projection/feasible directions technique, so interpreting the problem solution within the context of a net-output target coordination.