Generalized spatial price equilibria with semicontinuous market structures
The spatial price equilibrium model is widely used to analyze interregional trade patterns. Many large-scale applications involve the solution of linear programming subproblems to define the regional supply and demand functions. However, the use of such LP's gives rise to discontinuous supply and demand functions. This dissertation develops new concepts, theory and solution methods for spatial price equilibrium when such discontinuous functions are present. We first estended the traditional concept of spatial price equilibrium to a more general concept to allow discontinuous market functions which we call the generalized spatial price equilibrium. We then developed an existence theory for such generalized spatial price equilibrium. Furthermore, we developed a formulation technique. Using it, a spatial price equilibrium problem with step supply or/and step demand functions can be transformed into a nonlinear complementarity problem (NCP). This formulation technique saves the trouble of developing new algorithms for the solution of generalized spatial price equilibrium problems with step market functions, since any existing algorithm for the nonlinear complementarity problems can be employed. Finally, we studied the electric power industry which is undergoing deregulation. We demonstrated how the generalized spatial price equilibrium model can be used as a tool to forecast bulk power transactions and prices to assist in searching for the best investment decision such as where and when to carry out a capacity expansion or retirement on either generation or transmission networks.
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