Skip to main content
SpringerLink
Log in

Reference Point Approaches

  • Chapter
Multicriteria Decision Making

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 21))

Abstract

This chapter presents a summary of reference point methodology in vector optimization and decision support. The methodology has been developed at the International Institute for Applied Systems Analysis (IIASA) since 1980 and found numerous applications, both in IIASA and elsewhere. The chapter presents methodological foundations, basic concepts and notation, reference points and achievement functions, neutral and weighted compromise solutions, issues of modeling for multi-objective analysis, some basic applications of reference point methods and a discussion of a decision process type supported by reference point methodology.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoine, J., G. Fischer and M. Makowski: Multiple Criteria Land Use Analysis. Applied Mathematics and Computation 83(1997)195–215

    Article  Google Scholar 

  2. Bisschop, J., R. Entriken: AIMMS, The Modeling System. Paragon Decision Technology Haarlem, The Netherlands 1993

    Google Scholar 

  3. Brooke, A., D. Kendrick and A. Meeraus GAMS, A User’s Guide. The Scientific Press Redwood City 1988

    Google Scholar 

  4. Charnes, A., W. W. Cooper: Goal programming and multiple objective optimization. J. Oper. Res. Soc. 1(1977)39–54.

    Article  Google Scholar 

  5. Dinkelbach, W., H. Isermann: “On decision making under multiple criteria and under incomplete information.” In: J. L. Cochrane, M. Zeleny (eds.): Multiple Criteria Decision Making. University of South Carolina Press Columbia SC 1973, pp. 302–312

    Google Scholar 

  6. Ermolev, Yu., R. J-B. Wets: Numerical Techniques for Stochastic Optimization. Springer Berlin etc. 1988

    Google Scholar 

  7. Fodor, J., M. Roubens: Fuzzy Preference Modeling and Multicriteria Decision Support. Kluwer Academic Publishers Dordrecht 1994

    Google Scholar 

  8. Fourer, R., D. M. Gay and B. W. Kernighan: AMPL, A Modeling Language for Mathematical Programming. The Scientific Press San Francisco 1993

    Google Scholar 

  9. Gal, T.: A general method of determining the set of all efficient solutions to a linear vectormaximum problem. European Journal of Operational Research 1(1977)307–322

    Article  Google Scholar 

  10. Geoffrion, A. M.: An Introduction to Structured Modeling. Operations Research 37(1987)30–51

    Article  Google Scholar 

  11. Granat, J., M. Makowski: “ISAAP — Interactive Specification and Analysis of Aspiration-based Preferences.” Interim Report IR-98-52, International Institute for Applied Systems Analysis, Laxenburg, Austria 1998

    Google Scholar 

  12. Granat, J., A. P. Wierzbicki: Interactive Specification of DSS User Preferences in Terms of Fuzzy Sets. Archives of Control Sciences 5(1996)185–201

    Google Scholar 

  13. Granat, J., T. Krȩglewski, J. Paczyński and A. Stachurski:“IAC-DIDAS-N++ Modular Modeling and Optimization System. Part I: Theoretical Foundations, Part II: Users Guide.” Internal Report, Institute of Automatic Control, Warsaw University of Technology, Warsaw, Poland 1994

    Google Scholar 

  14. Griewank, A.: Computational Differentiation and Optimization. In: J. R. Birge, K. G. Murty (eds.): Mathematical Programming: State of the Art 1994. University of Michigan Press Ann Arbor 1994, pp. 102–131

    Google Scholar 

  15. Haimes, Y. Y., W. A. Hall: Multiobjectives in Water Resources Systems Analysis: The Surrogate Worth Trade-Off Method. Water Resources Research 10(1974)615–623

    Article  Google Scholar 

  16. Henig, M.: Proper efficiency with respect to cones. JOTA 22(1982)618–630.

    Google Scholar 

  17. Janssen, R.: Multiobjective Decision Support for Environmental Management. Kluwer Academic Publishers Dordrecht 1992

    Google Scholar 

  18. Jaszkiewicz, A., R. Slowiński: “The LBS package — a microcomputer implementation of the Light Beam Search method for multi-objective nonlinear mathematical programming.” Working Paper WP-94-07, International Institute for Applied Systems Analysis, Laxenburg, Austria 1985

    Google Scholar 

  19. Kaliszewski, I.: Quantitative Pareto Analysis by Cone Separation Techniques. Kluwer Academic Publishers Dordrecht 1994

    Google Scholar 

  20. Kallio, M., A. Lewandowski and W. Orchard-Hays: “An Implementation of the Reference Point Approach for Multi-Objective Optimization.” Working Paper WP-80-35, International Institute for Applied Systems Analysis, Laxenburg, Austria 1980

    Google Scholar 

  21. Kok, M., F. A. Lootsma: Pairwise comparison methods in multiple objective programming. European Journal of Operational Research 22(1985)44–55.

    Article  Google Scholar 

  22. Korhonen, P. and J. Laakso: A Visual Interactive Method for Solving the Multiple Criteria Problem. European Journal of Operational Research 24(1985)277–287.

    Article  Google Scholar 

  23. Korhonen, P., S. Salo and R. E. Steuer: A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming. Operations Research 45(1997)751–757

    Article  Google Scholar 

  24. Krȩglewski, T., J. Paczyński, J. Granat and A. P. Wierzbicki:“IAC-DIDAS-N: A Dynamic Interactive Decision Support System for Multicriteria Analysis of Nonlinear Models with a Nonlinear Model Generator Supporting Model Analysis.” Working Paper WP-88-112, International Institute for Applied Systems Analysis, Laxenburg, Austria 1988

    Google Scholar 

  25. Lewandowski, A., A. P. Wierzbicki (eds.): Aspiration Based Decision Support Systems. Lecture Notes in Econ. and Math. Syst. No 331, Springer Berlin etc. 1989

    Google Scholar 

  26. Lootsma, F. A.: Scale sensitivity in multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 2(1993)87–110.

    Article  Google Scholar 

  27. Makowski, M.: “LP-DIT, Data Interchange Tool for Linear Programming Problems, (version 1.20).” Working Paper WP-94-36, International Institute for Applied Systems Analysis, Laxenburg, Austria, Laxenburg 1994

    Google Scholar 

  28. Makowski, M., L. Somlyódy and D. Watkins: Multiple Criteria Analysis for Water Quality Management in the Nitra Basin. Water Resources Bulletin 32(1996)937–951

    Article  Google Scholar 

  29. Makowski, M., J. Sosnowski: “HYBRID: Multicriteria Linear Programming System for Computers under DOS and UNIX.” In: J. Wessels, A. P. Wierzbicki (eds.): User-Oriented Methodology and Techniques for Decision Analysis and Support. Lecture Notes in Econ. and Math. Syst. No 397, Springer Berlin etc. 1991, pp. 223–233

    Google Scholar 

  30. Matsuhashi, K.: “Application of Multi-Criteria Analysis to Urban Land-Use Planning.” Interim Report IR-97-091, International Institute for Applied Systems Analysis, Laxenburg, Austria 1997

    Google Scholar 

  31. Nakayama, H. and Y. Sawaragi:“Satisficing trade-off method for multiobjective programming.” In: M. Grauer, A. P. Wierzbicki (eds.): Interactive Decision Analysis. Lecture Notes in Econ. and Math. Syst. No 229, Springer Berlin etc. 1983, pp. 113–122

    Google Scholar 

  32. Ogryczak, W., K. Studziński and K. Zorychta: “A generalized reference point approach to multiobjective transshipment problem with facility location.” In: A. Lewandowski, A. P. Wierzbicki (eds.): Aspiration Based Decision Support Systems. Lecture Notes in Econ. and Math. Syst. No 331, Springer Berlin etc. 1989, pp. 230–250

    Google Scholar 

  33. Osyczka, A.: C Version of Computer Aided Multicriterion Optimization System (CAMOS). Workshop on Advances in Methodology and Software in DSS, IIASA, Laxenburg 1994

    Google Scholar 

  34. Polak, E.: “On the approximation of solutions to multiple criteria decision making problems.” In: M. Zeleny (ed.): Multiple Criteria Decision Making. Springer New York 1976, pp. 271–282

    Google Scholar 

  35. Rios, S.: Decision Theory and Decision Analysis: Trends and Challenges. Kluwer Academic Publishers Boston etc. 1994

    Google Scholar 

  36. Roy, B., Ph. Vincke: Multicriteria Analysis: Survey and New Directions. European Journal of Operational Research 8(1981)207–218.

    Article  Google Scholar 

  37. Saaty, T.: The Analytical Hierarchy Process. McGraw-Hill New York 1980

    Google Scholar 

  38. Sawaragi, Y., H. Nakayama and T. Tanino: Theory of Multiobjective Optimization. Academic Press New York 1985

    Google Scholar 

  39. Seo, F., M. Sakawa: Multiple Criteria Decision Analysis in Regional Planning. Reidel Publishing Company Dordrecht 1988

    Google Scholar 

  40. Simon, H. A.: Models of Man. Macmillan New York 1957

    Google Scholar 

  41. Smierzchalski, R., J. Lisowski: “Computer simulation of safe and optimal trajectory avoiding collision at sea.” Joint Communication, WSM Gdynia and Hochschule Bremerhaven 1994

    Google Scholar 

  42. Steuer, R. E., E. V. Choo: An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming 26(1983)326–344

    Article  Google Scholar 

  43. Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation, and Application. J.Wiley & Sons New York 1986

    Google Scholar 

  44. Vincke, Ph.: Multicriteria Decision Aid. Wiley Chichester etc. 1989

    Google Scholar 

  45. Wierzbicki, A. P.: “The use of reference objectives in multiobjective optimization.” In: G. Fandel, T. Gal (eds.): Multiple Criteria Decision Making; Theory and Applications. Lecture Notes in Econ. and Math. Syst. No 177, Springer Berlin etc. 1980, pp. 468–486

    Google Scholar 

  46. Wierzbicki, A. P.: A mathematical basis for satisficing decision making. Mathematical Modeling 3(1983)391–405.

    Article  Google Scholar 

  47. Wierzbicki, A. P.: Models and Sensitivity of Control Systems. Elsevier-WNT Amsterdam 1984

    Google Scholar 

  48. Wierzbicki, A. P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR-Spektrum 8(1986)73–87.

    Article  Google Scholar 

  49. Wierzbicki, A. P.: Dynamic Aspects of Multi-Objective Optimization. In: A. Lewandowski, V. Volkovich (eds.): Multiobjective Problems of Mathematical Programming. Lecture Notes in Econ. and Math. Syst. No 351 Springer Berlin etc. 1988, pp. 154–174

    Google Scholar 

  50. Wierzbicki, A. P.: Multiple Criteria Games: Theory and Applications. Working Paper WP-92-079, International Institute for Applied Systems Analysis, Laxenburg, Austria 1992

    Google Scholar 

  51. Wierzbicki, A. P.: On the Role of Intuition in Decision Making and Some Ways of Multicriteria Aid of Intuition. Multiple Criteria Decision Making 6(1996)65–78.

    Article  Google Scholar 

  52. Wierzbicki, A. P.: “Convergence of Interactive Procedures of Multiobjective Optimization and Decision Support.” In: M. H. Karwan, J. Spronk, J. Wallenius (eds): Essays in Decision Making. Springer Berlin etc. 1997, pp. 19–47

    Google Scholar 

  53. Zadeh, L. A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1(1978)3–28

    Article  Google Scholar 

  54. Zeleny, M.: A concept of compromise solutions and the method of the displaced ideal. Comput. Oper. Res. 1(1974)479–496

    Article  Google Scholar 

  55. Zimmermann, H.-J., H.-J. Sebastian: “Fuzzy Design — Integration of Fuzzy Theory with Knowledge-Based System Design.” In: Fuzzy-IEEE 94 Proceedings, Orlando Florida, Pergamon Press 1994, pp. 352–357

    Google Scholar 

Download references

Authors
  1. Andrzej P. Wierzbicki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fern Universität, Hagen, Germany

    Tomas Gal  & Thomas Hanne  & 

  2. University of Cape Town, Rep. of South Africa

    Theodor J. Stewart

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Wierzbicki, A.P. (1999). Reference Point Approaches. In: Gal, T., Stewart, T.J., Hanne, T. (eds) Multicriteria Decision Making. International Series in Operations Research & Management Science, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5025-9_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5025-9_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7283-7

  • Online ISBN: 978-1-4615-5025-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation