Abstract
This chapter presents the Bounded Dual Simplex Algorithm, which is one of the most frequently used linear programming algorithms for solving real-world problems. A solution structure of the bounded dual simplex method (used to solve linear programming problems) is presented. The main advantage of this algorithm is its use in finding solutions for large-scale problems, and its robustness and efficiency are identified in this chapter. One application of this algorithm in the area of electrical engineering is provided: namely, solving the transmission network expansion planning where the normal operation conditions of the system are continually evaluated by solving linear programming problems. The method is explained step-by-step, so that the methodology can be adapted to other problems. Finally, some conclusions are drawn.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Garfinkel, R.S., Nemhauser, G.L.: Integer Programming. John Wiley and Sons, New Jersey (1972)
Bazaraa, M.S., Jarvis, J.J.: Linear Programming and Network Flows. John Wiley and Sons, New York (1977)
Gallego, R.A., Escobar, A.H., Romero, R.: Optimización en Sistemas Eléctricos I - Programación Lineal. Ed. Universidad Tecnológica de Pereira, Colombia (2003) (in Spanish)
Koberstein, A., Suhl, U.H.: Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms. Comput. Optim. Appl. 37, 49–65 (2007)
Romero, R., Monticelli, A., Garcia, A., Haffner, S.: Test systems and mathematical models for transmission network expansion planning. IEE. Proc., Gen. Trans. Distrib. 149(1), 27–36 (2002)
Hashimoto, S.H.M.: Phd. Dissertation, Análise de desenvolvimento de algoritmos eficientes para programacão linear para o problema de planejamento de sistemas de transmissão a longo prazo”, Universidade Estadual Paulista - UNESP, Faculdade de Engenharia Elétrica, Campus Ilha Solteira, Brasil (in Portuguese)
Hashimoto, S.H.M., Romero, R., Mantovani, J.R.S.: Efficient linear programming algorithm for the transmission network expansion planning problem. IEE. Proc. Gen. Trans. Distrib. 150(5), 536–542 (2003)
Gallego, R.A., Romero, R.: Programación Lineal Entera. Ed. Universidad Tecnológica de Pereira, Colombia (2007) (in Spanish)
Nemhauser, G.L., Rinnooy, A.H.G., Todd, M.J.: Handbooks in Operations Research and Management Science - Optimization. Elsevier Science, The Netherlands (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Garcés, L.P., Gallego, L.A., Romero, R. (2013). Bounded Dual Simplex Algorithm: Definition and Structure. In: Zelinka, I., Snášel, V., Abraham, A. (eds) Handbook of Optimization. Intelligent Systems Reference Library, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30504-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-30504-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30503-0
Online ISBN: 978-3-642-30504-7
eBook Packages: EngineeringEngineering (R0)