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Implementing the Tchebycheff Method in a Spreadsheet

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Essays In Decision Making

Abstract

The Tchebycheff Method [29] is one of a group of interactive procedures [e.g., 3–7, 10, 13–14, 16–19, 21, 23, 25-27, 30–31] for solving multiple objective programming problems. While the procedures in this group represent a diversity of Solution strategics, the implementations of most of these procedures posses remarkable similarities [8, 9], with most of these procedures being essentially supervisory routines designed to call commercial-grade linear, integer and nonlinear programming codes as their workhorse Software. That is, to probe the Solution set at each iteration, one or more (single objective) mathematical programs must be solved, at which point in earlier Computing environments, an appropriate solver such as MINOS (Murtagh and Saunders [1977]) for linear problems, MPSX (IBM [1979]) for integer problems, or GRG2 (Lasdon and Waren [1986]) for nonlinear problems would be called.

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References

  1. Agrell, P. J. (1995). “A Multicriteria Framework for Inventory Control,” International Journal of Production Economics 41, 59–70.

    Article  Google Scholar 

  2. Agrell, P. J. and J. Wikner (1997). “An MCDM Framework for Dynamic Systems,” International Journal of Production Economics, forthcoming.

    Google Scholar 

  3. Benayoun, R., J. de Montgolfier, J. Tergny and O. Larichev (1971). “Linear Programming with Multiple Objective Functions: Step Method (STEM),” Mathematical Programming 1/3, 366–375.

    Article  Google Scholar 

  4. Chankong, V. and Y. Y. Haimes (1978). “The Interactive Surrogate Worth Trade-Off (ISWT) Method for Multiobjectivc Decision-Making.” In: Multiple Criteria Problem Solving (S. Zionts, ed.), Lecture Notes in Economics and Mathematical Systems, Vol. 155, 42–67.

    Google Scholar 

  5. Climaco, J.C.N. and C.H. Antunes (1987). “TRIMAP-An Interactive Tricriteria Linear Programming Package,” Foundations of Control Engineering 12/3, 101–120.

    Google Scholar 

  6. Franz, L. S. and S. M Lee (1981), “A Goal Programming Based Interactive Decision Support System.” In: Organizations: Multiple Agents with Multiple Criteria (J. N. Morse, ed.), Lecture Notes in Economics and Mathematical Systems, Vol. 190, 110–115.

    Google Scholar 

  7. Gabbani, D. and M. Magazine (1986). “An Interactivc Heuristic Approach for Multi-Objective Integer-Programming Problems,” Journal of the Operational Research Society 37, 285–291.

    Google Scholar 

  8. Gardiner, L. R. and R. E. Steuer (1994). “Unified Interactive Multiple Objective Programming,” European Journal of Operational Research 74/3, 391–406.

    Article  Google Scholar 

  9. Gardiner, L. R. and R. E. Steuer (1994). “Unified Interactive Multiple Objective Programming: An Open Architecture for Accommodating New Procedures,” Journal of the Operational Research Society, 45/12, 1456–1466.

    Google Scholar 

  10. Geoffrion, A. M., J. S. Dyer and A. Feinberg (1972). “An Interactive Approach for Multicriterion Optimization, with an Application to the Operation of an Academic Department,” Management Science 19/4, 357–368

    Article  Google Scholar 

  11. Heyman, M. S. (1995). Essential Visual Basic 4, SAMS Publishing, Indianapolis, Indiana.

    Google Scholar 

  12. IBM Document No. GH19-1091-1 (1979). “IBM Mathematical Programming System Extended/370: Primer”, IBM Corporation, Data Processing Division, White Plains, New York.

    Google Scholar 

  13. Karaivanova, J. N, S.C. Narula and V. Vassilev, (1993). “An Interactive Procedure for Multiple Objective Integer Linear Programming Problems,” European Journal of Operational Research 68/3, 344–351.

    Article  Google Scholar 

  14. Korhonen, P. J. and J. Wallenius (1988). “A Pareto Race,” Naval Research Logistics 35/6, 615–623.

    Article  Google Scholar 

  15. Lasdon, L. S. and A. D. Waren (1986). “GRG2 Userís Guide,” University of Texas, Austin, Texas.

    Google Scholar 

  16. Lewandowski, A., T. Kreglewski, T. Rogowski and A. P. Wierzbicki (1987). “Decision Support Systems of DIDAS Family (Dynamic Interactive Decision Analysis and Support),” Archiwum Automatyki i Telemechaniki 32/4, 221–246.

    Google Scholar 

  17. Lotov, A. V. (1989). “Generalized Reachable Sets Method in Multiple Criteria Problems.” In: Methodology and Software for Interactive Decision Support (A. Lewandowski and I. Stanchev, eds.), Lecture Notes in Economics and Mathematical Systems, Vol. 337, 65–73.

    Google Scholar 

  18. Marcotte, O. and R. M. Soland (1986). “An Interactive Branch-and-Bound Algorithm for Multiple Criteria Optimization,” Management Science 32/1, 61–75.

    Article  Google Scholar 

  19. Michalowski, W. and T. Szapiro (1992). “A Bi-Reference Procedure for Interactive Multiple Criteria Programming,” Operations Research 40/2, 247–258.

    Article  Google Scholar 

  20. Microsoft Document No. XL57927-0694 (1994). Visual Basic Userís Guide: Automating, Customizing, and Programming in Microsoft Excel, Microsoft Corporation.

    Google Scholar 

  21. Mikhalevich, V. S. and V. L. Volkovich (1987). “Methods for Constructing Interactive Procedures in Multiobjective Optimization Problems.” In: Toward Interactive and Intelligent Decision Support Systems, Volume 1 (Y. Sawaragi, K. Inoue and H. Nakayama, eds.), Lecture Notes in Economics and Mathematical Systems, Vol. 285, 105–113.

    Google Scholar 

  22. Murtagh, B. A. and M. A. Saunders (1987). “MINOS 5.1 Userís Guide,” Report SOL 83-20R, Department of Operations Research, Stanford University, Stanford, California.

    Google Scholar 

  23. Nakayama, H. (1991). “Interactive Multi-Objective Programming and Its Applications.” In: Methodology, Implementation and Applications of Decision Support Systems (A. Lewandowski, P. Serafini, and M. G. Speranza, eds ), Springer-Verlag, Vienna, 75–197.

    Google Scholar 

  24. Ragsdale, C. T. (1995). Spreadsheet Modeling and Decision Analysis, Course Technology, Inc., Cambridge, Massachusetts.

    Google Scholar 

  25. Reeves, G. R. and L. S. Franz (1985). “A Simplified Interactive Multiple Objective Linear Programming Procedure,” Computers & Operations Research 12/6, 589–601.

    Article  Google Scholar 

  26. Sakawa, M. and H. Yano (1990). “An Interactive Fuzzy Satisfying Method for Generalized Multiobjective Programming Problems with Fuzzy Parameters,” Fuzzy Sets and Systems 35/2, 125–142.

    Article  Google Scholar 

  27. Spronk, J. (1981). Interactive Multiple Goal Programming, Martinus Nijhoff, Boston.

    Google Scholar 

  28. Steuer, R. E. (1986). Multiple Criteria Optimization. Theory, Computation, and Application, John Wiley & Sons, New York.

    Google Scholar 

  29. Steuer, R. E. and E.-U. Choo (1983). “An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming,” Mathematical Programming 26/1, 326–344.

    Article  Google Scholar 

  30. Zionts, S. and J. Wallenius (1976). “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science 22/6, 652–663.

    Article  Google Scholar 

  31. Zionts, S. and J. Wallenius (1983). “An Interactive Multiple Objective Linear Programming Method for Class of Underlying Nonlinear Utility Functions,” Management Science, 29/5, 519–529.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Management Science, Brooks Hall, University of Georgia, 30602-6255, Athens, Georgia, USA

    Ralph E. Steuer

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  1. Ralph E. Steuer
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Editor information

Editors and Affiliations

  1. School of Engineering and Applied Sciences, State University of New York at Buffalo, 412 Bonner Hall, Buffalo, NY, 14260, USA

    Mark H. Karwan

  2. Department of Finance, Erasmus University Rotterdam, P. O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    Jaap Spronk

  3. Helsinki School of Economics and Business Administration, Runeberginkatu 14–16, 00100, Helsinki, Finland

    Jyrki Wallenius

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© 1997 Springer-Verlag Berlin Heidelberg

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Steuer, R.E. (1997). Implementing the Tchebycheff Method in a Spreadsheet. In: Karwan, M.H., Spronk, J., Wallenius, J. (eds) Essays In Decision Making. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60663-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-60663-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64499-3

  • Online ISBN: 978-3-642-60663-2

  • eBook Packages: Springer Book Archive

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