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A New Decomposition Method for Multiregional Economic Equilibrium Models

Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong, China
Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3
mswchung{at}cityu.edu.hk
dfuller{at}engmail.uwaterloo.ca
jwu{at}ryerson.ca

This paper discusses decomposition of a multiregional economic equilibrium model that is characterized by a cost minimizing, linear programming (LP) model of the supply side and a vector-valued function that gives demand prices as functions of the quantities demanded. Our motivation is to ease model development and maintenance by a solution method that links separately developed regional models only when a consistent multiregion solution is desired. A heuristic strategy is described to extend any existing (LP) decomposition principle to a procedure for decomposing an equilibrium model by region. This strategy is applied to extend Dantzig-Wolfe decomposition to the multiregional economic equilibrium model, and several theoretical results are derived for the resulting algorithm. The central result is a proof of asymptotic convergence, under usefully general conditions. The extended Dantzig-Wolfe procedure is illustrated with an existing, two-region model of Canadian energy supplies and demands.

Subject classifications: natural resources, energy: multiregional economic equilibrium models; programming: decomposition, variational inequalities.
History: Received December 2000; revision received May 2005; accepted May 2005.