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Electrical power pricing with technical externalities
Omega, VoL 3, No. 4
Nonconvex All-Quadratic Programming REEVES GR (1973) A global minimizationalgorithmfor nonconvex all-quadraticplrogrammiDg problems. D S Dissertation,WashhtgtonUniversity.Copiesavailablefrom UniversityMicrofilms, Ann Arbor, Michigan,U.S.A. THIS dissertation presents a branch and bound algorithm for the global minimization of a quadratic objective function subject to quadratic constraints and upper and lower bounds on the variables. No assumptions are made regarding the convexity of either the objective function or the constraints. An iteration of the algorithm consists of three basic steps: (1) Determine a local minimum, X*. (2) Eliminate a region surrounding X* over which X* is global. This involves partitioning and verifying that the Kuhn-Tucker conditions hold for bounding convex envelope approximations to the original problem in all partitioned subregions of the elimination region. Due to the special structure of all-quadratic problems, verification is accomplished using linear, rather than nonlinear or even convex, programming techniques. (3) Partition any remaining regions into subregions and solve bounding convex envelope approximating problems globally over each. Eliminate subregions with global bounds greater than the best local minimum objective value. Successive iterations take place over the current remaining subregion with the lowest bound. The algorithm terminates when all subregions are eliminated. The algorithm is convergent in that it identifies a global minimum point or a point with objective value arbitrarily close to a global convex envelope approximating bound in a finite number of iterations. Computational results are included for problems up to 25 variables and 30 constraints. For problems tested the algorithm identified a good local minimum rapidly. As problem size increased, the majority of time was spent not in identifying a local minimum, but in verifying that the minimum was global. Abstracted by Gary R Reeves, Department of Business Analysis, Miami University, Oxford, Ohio 45056, U.S.A.
Electrical Power Pricing SCHERER CR (1974) Electrical power In'icing with tedmical externalities. Copies available from Charles R Scherer, Engineetlag Systems Departmem, University of California, Los Angeles,
California 90024, U.S.A.
THE STANDARD theoretical basis for decreasing block rate structures in e!ectric power pricing is reviewed with emphasis on necessary assumptions, in 497
Abstracts
particular that technical externalities and "'second best" problems associated with power production are negligible. Both of these assumptions are questioned. Concentrating on the external effects of air and water pollution, and recognizing that these externalities may not be negligible, an approach is suggested whereby it can be determined whether or not decreasing rates are still appropriate in view of these externalities. Basically, the approach recognizes that some level of pollution might co-exist with an optimal allocation of society's resources to power production. The long-run average cost curve is then estimated e x a n t e for levels of pollution outputs ranging from minimum technically possible to totally unabated conditions. This is done using a mixed-integer mathematical programming model of the electric power system under consideration. The results from an application of the technique to the New York State Gas and Electric Corporation's System show that system average costs decrease when nuclear-fueled new plants are used in the system, and rise when coal-fired plants arc used, regardless of the pollution level. Hence, since decreasing block rates depend on the existence of decreasing costs, the results suggest that whether or not decreasing block rates are appropriate depends more on the type of fuel burned in new steam-electric plants than on the level of emission controls on these plants. A note on damage function estimation is included. Abstracted by Charles R Schetcr, Universityof California, Los Angeles, U.S.A.
498
Nonconvex All-Quadratic Programming REEVES GR (1973) A global minimizationalgorithmfor nonconvex all-quadraticplrogrammiDg problems. D S Dissertation,WashhtgtonUniversity.Copiesavailablefrom UniversityMicrofilms, Ann Arbor, Michigan,U.S.A. THIS dissertation presents a branch and bound algorithm for the global minimization of a quadratic objective function subject to quadratic constraints and upper and lower bounds on the variables. No assumptions are made regarding the convexity of either the objective function or the constraints. An iteration of the algorithm consists of three basic steps: (1) Determine a local minimum, X*. (2) Eliminate a region surrounding X* over which X* is global. This involves partitioning and verifying that the Kuhn-Tucker conditions hold for bounding convex envelope approximations to the original problem in all partitioned subregions of the elimination region. Due to the special structure of all-quadratic problems, verification is accomplished using linear, rather than nonlinear or even convex, programming techniques. (3) Partition any remaining regions into subregions and solve bounding convex envelope approximating problems globally over each. Eliminate subregions with global bounds greater than the best local minimum objective value. Successive iterations take place over the current remaining subregion with the lowest bound. The algorithm terminates when all subregions are eliminated. The algorithm is convergent in that it identifies a global minimum point or a point with objective value arbitrarily close to a global convex envelope approximating bound in a finite number of iterations. Computational results are included for problems up to 25 variables and 30 constraints. For problems tested the algorithm identified a good local minimum rapidly. As problem size increased, the majority of time was spent not in identifying a local minimum, but in verifying that the minimum was global. Abstracted by Gary R Reeves, Department of Business Analysis, Miami University, Oxford, Ohio 45056, U.S.A.
Electrical Power Pricing SCHERER CR (1974) Electrical power In'icing with tedmical externalities. Copies available from Charles R Scherer, Engineetlag Systems Departmem, University of California, Los Angeles,
California 90024, U.S.A.
THE STANDARD theoretical basis for decreasing block rate structures in e!ectric power pricing is reviewed with emphasis on necessary assumptions, in 497
Abstracts
particular that technical externalities and "'second best" problems associated with power production are negligible. Both of these assumptions are questioned. Concentrating on the external effects of air and water pollution, and recognizing that these externalities may not be negligible, an approach is suggested whereby it can be determined whether or not decreasing rates are still appropriate in view of these externalities. Basically, the approach recognizes that some level of pollution might co-exist with an optimal allocation of society's resources to power production. The long-run average cost curve is then estimated e x a n t e for levels of pollution outputs ranging from minimum technically possible to totally unabated conditions. This is done using a mixed-integer mathematical programming model of the electric power system under consideration. The results from an application of the technique to the New York State Gas and Electric Corporation's System show that system average costs decrease when nuclear-fueled new plants are used in the system, and rise when coal-fired plants arc used, regardless of the pollution level. Hence, since decreasing block rates depend on the existence of decreasing costs, the results suggest that whether or not decreasing block rates are appropriate depends more on the type of fuel burned in new steam-electric plants than on the level of emission controls on these plants. A note on damage function estimation is included. Abstracted by Charles R Schetcr, Universityof California, Los Angeles, U.S.A.
498