Decomposition approach for solving large-scale spatially disaggregated economic equilibrium problems

Abstract

This paper employs the Dantzig-Wolfe decomposition procedure to solve large-scale economic equilibrium problems formulated as nonlinear programs with block-diagonal linear constraints, where each block characterizes the supply possibilities in a region, and a set of unifying constraints that characterize the supply-demand balances. We derive lower and upper bounds for the value of the objective function at each step of the decomposition procedure, and use the percentage deviation between the two bounds as guidance for terminating the iterations to obtain an approximation of the equilibrium solution. Our computational results with moderate-size problems show that the decomposition procedure can reduce the solution time substantially compared to the direct solution approach without using decomposition. We present a large-scale empirical application where the impacts of the US biofuel mandates on agricultural and transportation fuel sectors were analyzed. Two powerful optimization solvers could not handle the problem due to the sheer size of the model and nonlinearity involved in the objective function, whereas we could solve the economic equilibrium successfully using the decomposition approach.