Linear Programming for a Single Objective

Chapter

Abstract

This chapter is dedicated in its entirety to Linear Programming, a well-known mathematical procedure which has an enormous diffusion in hundreds of applications around the world. This technique, using a practical example, is explained in a way for everybody to understand it. It aims at making the DM aware of how to use this tool, and more important, how to interpret its results. Linear Programming as is explained here deals with a sole objective which is common in many applications and in different fields. Its greatest advantage can be synthesized on three counts: (a) It permits one to approximately represent an actual situation – no matter its nature – in a mathematical context, that allows for applying an algorithm to solve it, (b) it yields a unique and optimal solution, and (c) it lets to perform an extensive analysis of “What if….?” scenarios which is a valuable tool for sensitivity analysis.

Keywords

Linear programming Graphic solution Simplex method Multicriteria Objective function 

References

  1. *  Indicates suggested reading material not mentioned in text.Google Scholar
  2. *  Avriel, M., & Golany, B. (1996). Mathematical programming for industrial engineers. New York: Marcel Dekker.Google Scholar
  3. Ballestero, E. (2007). Compromise programming: A utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions. European Journal of Operational Research, 182(3), 1369–1382.CrossRefGoogle Scholar
  4. *  Calderón, S., & González, A. (1995). Programación matemática. Spain: Universidad de Málaga Departamento de Economía Aplicada (Matemáticas). Retrieved January 9, 2010, from http://www.uma.es/
  5. Charnes, A., & Cooper, W. (1961). Management models and industrial applications of linear programming. New York: Wiley.Google Scholar
  6. *  Conde Sánchez, E., Fernández García, F., & Puerto Albandoz, J. (1994). Análisis interactivo de las soluciones del problema lineal múltiple ordenado. Question, 18(3), 397–415.Google Scholar
  7. *  Diwekar, U. (2007). Introduction to applied optimization (2nd ed.). Dordrecht: Springer.Google Scholar
  8. Dodgson, J., Spackman, M., & Pearman, A. (2002). DTLR (Department of Transportation, Local Government and Regions). Multicriteria analysis manual. London: National Economic Research Associates and DTLR members.Google Scholar
  9. *  Elliott, D. (1978). Planning investments in water resources by mixed integer programming: The Vardar-Axios River Basin. Massachusetts: Massachusetts Institute of Technology. Paper OR 072-78.Google Scholar
  10. *  Fernández Lechón, R., Soto, M. D., Garcillán, J. J. (1990). Optimización multicriterio en el contexto de la programación matemática. Anales de estudios económicos y empresariales, 5, 147–160, ISSN 0213-7569.Google Scholar
  11. *  Hansen, B. (1996). Fuzzy logic and linear programming find optimal solutions for meteorological problems, term paper for Fuzzy Logic course. Nova Scotia: Technical University of Nova Scotia. Retrieved February 3, 2010, from http://www.webindia123.com/career/studyabroad/Canada/details.asp?uname=Technical+University+Nova+Scotia
  12. Kuhn, K., Tucker, A. (1950). Non-linear programming. In: Jerzy Neyman (Ed.), Proceedings of the second Berkeley symposium on mathematical statistics and probability (pp. 481–492). Berkeley: University of California Press.Google Scholar
  13. Lee, S. (1972). Goal programming for decision analysis. Philadelphia: Auerbach Publishers.Google Scholar
  14. Malczewski, J. (1999). GIS and multicriteria decision analysis. New York: Wiley.Google Scholar
  15. *  Nijkamp, P., & Spronk, J. (1978). Interactive multiple goal programming, Research Memorandum 3. Amsterdam: Department of Economics, Free University Amsterdam.Google Scholar
  16. *  Schrage, L. (1984). Linear, integer and quadratic programming with Lind (3rd ed.). San Francisco: Scientific Press.Google Scholar
  17. Steuer, R. (1986). Multiple criteria optimization: Theory, computation and application. New York: Wiley.Google Scholar
  18. Weingartner, H. (1966). Capital budgeting of interrelated projects: Survey and synthesis. Management Science, XII(7), 485–516.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.ValenciaSpain

Personalised recommendations