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A graphical subroutine for multiobjective linear programming

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Zusammenfassung

In diesem Artikel wird ein Algorithmus zur Erstellung von Computergraphiken für den Fall der linearen Optimierung bei mehrfacher Zielsetzung vorgestellt. Das Verfahren beruht auf der klassischen einparametrischen linearen Optimierung und bestimmt ein Spektrum effizienter Kriterienwerte, die mit Hilfe stückweise linearer Funktionen dargestellt werden können. Beispielhaft wird gezeigt, wie sich jedes Standard-LP-Paket mit dem vorgestellten Verfahren in einfacher Weise für eine flexible graphische Multikriteria-Analyse erweitern läßt.

Summary

This paper is concerned with multiobjective linear programming and presents an algorithm for displaying computer graphics. The method is based on the classical oneparametric linear programming. It determines a spectrum of efficient criteria values, which can be visualized by means of piecewise linear functions. By some examples it is shown how to use the new algorithm for extending standard LP-packages to a flexible graphical multicriteria analysis.

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References

  1. Achilles A, Elster KH, Nehse R (1979) Bibliographie zur Vektoroptimierung (Theorie und Anwendung). Mathematische Operationsforschung und Statistik, Serie Optimization 10, 2:277–321

    Article  Google Scholar 

  2. Dinkelbach W (1969) Sensitivitätsanalysen und parametrische Programmierung. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  3. Ecker JG, Hegner NS, Kouada IA (1980) Generating all maximal efficient faces for multiple objective linear programs. J Optimization Theory Appl 30:353–381

    Article  Google Scholar 

  4. Gal T (1977) A general method for determining the set of all efficient solutions to a linear vector maximum problem. Eur J Oper Res 1:307–322

    Article  Google Scholar 

  5. Gal T (1979) Postoptimal analyses, parametric programming, and related topics. McGraw-Hill, New York

    Google Scholar 

  6. Geoffrion AM, Dyer JS, Feinberg A (1972) An interactive approach for multicriterion optimization, with an application to the operation of an academic department. Manag Sci 19:357–368

    Article  Google Scholar 

  7. Hwang CL, Masud ASM (1979) Multiple objective decision making — methods and applications — a state of the art survey. Lecture Notes in Economics and Mathematical Systems No. 164. Springer, Berlin Heidelberg New York

    Google Scholar 

  8. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications — a state of the art survey. Lecture Notes in Economics and Mathematical Systems No. 186. Springer, Berlin Heidelberg New York

    Google Scholar 

  9. Ignizio JP (1978) A review of goal programming: a tool for multiobjective analysis. J Oper Res Soc 29:1109–1119

    Article  Google Scholar 

  10. Isermann H (1977) The enumeration of the set of all efficient solutions for a linear multiple objective program. Oper Res Qu 28:711–725

    Article  Google Scholar 

  11. Isermann H (1979) Strukturierung von Entscheidungsprozessen bei mehrfacher Zielsetzung. OR Spektrum 1:3–26

    Article  Google Scholar 

  12. Kornblut JSH (1973) A survey of goal programming. Omega 1:193–205

    Article  Google Scholar 

  13. Nožička F, Guddat J, Hollatz H, Bank B (1974) Theorie der linearen parametrischen Optimierung. Akademie-Verlag, Berlin

    Google Scholar 

  14. Roy B (1971) Problems and methods with multiple objective functions. Math Programming 1:239–266

    Article  Google Scholar 

  15. Roy B (1981) The optimization problem formulation: criticism and overstepping. J Oper Res Soc 32:427–436

    Article  Google Scholar 

  16. Soland RM (1979) Multicriteria optimization: a general characterization of efficient solutions. Decision Sci 10:26–38

    Article  Google Scholar 

  17. Wallenius J (1975) Comparative evaluation of some interactive approaches to multicriterion optimization. Manag Sci 21:1387–1396

    Article  Google Scholar 

  18. Winkels HM (1979) Interaktive Lösungsverfahren für lineare Probleme mit mehrfacher Zielsetzung. In: Henn R, Schips B, Stähly P (Hrsg) Quantitative Wirtschafts- und Unternehmensforschung. Springer, Berlin Heidelberg New York, pp 560–585

    Google Scholar 

  19. Winkels HM (1980) Complete efficiency analysis: theoretical background and an algorithm. Document du LAMSADE No. 13. Université Paris IX-Dauphine

  20. Winkels HM (1982) A flexible decision aid method for linear multicriteria systems. In: Grauer M, Lewandowski A, Wierczbicki AP (eds) Multiobjective and stochastic optimization, Proceedings of an IIASA Task Force Meeting November 30–December 4, 1981, International Institute for Applied Systems Analysis, Laxenburg, Austria pp 377–410

    Google Scholar 

  21. Winkels HM, Colman R (1982) Visualization of five dimensional polyhedra. Working Paper on Economathematics No. 8209, Abteilung für Wirtschaftswissenenschaft und Abteilung für Mathematik, Ruhr-Universität, D-4630 Bochum

    Google Scholar 

  22. Winkels HM, Meika M (1982) An integration of efficiency projections into the GEOFFRION-approach for multiobjective linear programming. Working Paper on Economathematics No. 8207, Abteilung für Wirtschaftwissenschaft und Abteilung für Mathematik, Ruhr-Universität, D-4630 Bochum and Eur J Oper Res (to appear 1984)

    Google Scholar 

  23. Yu PL, Zeleny M (1975) The set of all nondominated solutions in linear cases and a multicriteria simplex method. J Math Analysis Appl 49:430–468

    Article  Google Scholar 

  24. Yu PL, Zeleny M (1976) Linear multiparametric programming by multicriteria simplex method. Manag Sci 23:159–170

    Article  Google Scholar 

  25. Zeleny M (1974) Linear multiobjective programming. Lecture Notes in Economics and Mathematical Systems — Operations Research No. 95. Springer, Berlin Heidelberg New York

    Google Scholar 

  26. Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New York

    Google Scholar 

Download references

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Authors and Affiliations

  1. Institut für Unternehmungsführung und Unternehmensforschung der Ruhr-Universität, D-4630, Bochum

    H. -M. Winkels

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  1. H. -M. Winkels
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Winkels, H.M. A graphical subroutine for multiobjective linear programming. OR Spektrum 5, 175–192 (1983). https://doi.org/10.1007/BF01720242

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  • DOI: https://doi.org/10.1007/BF01720242

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