Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 78))

Abstract

We provide an introduction to the use of interactive methods in multiple objective programming. We focus on discussing the principles to implement those methods. Our purpose is not to review existing procedures, but some examples are picked to illustrate the main ideas behind those procedures. Furthermore, we discuss two available software systems developed to implement interactive methods. Abstract

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. C.H. Antunes and J.N. Clìmaco. Sensitivity analysis in MCDM using the weight space. Operations Research Letters, 12: 187–196, 1992.

    Article  MathSciNet  Google Scholar 

  2. A. Arbel and P.J. Korhonen. Using objective values to start multiple objective linear programming algorithms. European Journal of Operational Research, 128: 587–596, 2001.

    Article  MathSciNet  Google Scholar 

  3. C.A. Bana e Costa and J.C. Vansnick. MACBETH — An interactive path towards the construction of cardinal value functions. International Transactions in Operational Research, 1: 387–500, 1994.

    Article  Google Scholar 

  4. M.S. Bazaraa, J.J. Jarvis, and H.D. Sherali. Linear Programming and Network Flows. John Wiley & Sons, Chichester, 1990.

    Google Scholar 

  5. V. Belton and M. Elder. Visual interactive modeling. European Journal of Operational Research, 54: 273–273, 1991.

    Article  Google Scholar 

  6. V. Belton and S.P. Vickers. V.I.S.A. — VIM for MCDM. In G. Lockett and G. Islei, editors, Improving Decisions Making in Organisations, volume 335 of Lecture Notes in Economics and Mathematical Systems, pages 287–304. Springer Verlag, Berlin, 1988.

    Google Scholar 

  7. R. Benayoun, J. de Montgolfier, J. Tergny, and O. Larichev. Linear programming with multiple objective functions: Step method (Stem). Mathematical Programming, 1: 366–375, 1971.

    Article  Google Scholar 

  8. A.R. Borges and C.H. Antunes. A weight space-based approach to fuzzy multipleobjective linear programming. Decision Support Systems, 34: 427–443, 2003.

    Article  Google Scholar 

  9. A. Charnes and W.W. Cooper. Management Models and Industrial Applications of Linear Programming (Appendix B), Vol. I. John Wiley & Sons, Chichester, 1961.

    Google Scholar 

  10. A. Charnes, W.W. Cooper, and R.O. Ferguson. Optimal estimation of executive compensation by linear programming. Management Science, 1: 138–151, 1955.

    MathSciNet  Google Scholar 

  11. J.N. Clìmaco and C.H. Antunes. Implementation of a user-friendly software package — A guided tour of TRIMAP. Mathematical and Computer Modelling, 12: 1299–1309, 1989.

    Google Scholar 

  12. C. Coello, D. Van Veldhuizen, and G. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems, volume 5 of Genetic Algorithms and Evolutionary Computation. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  13. J. Dyer. A time-sharing computer program for the solution of the multiple criteria problem. Management Science, 19: 1379–1383, 1973.

    MATH  MathSciNet  Google Scholar 

  14. L.R. Gardiner and R.E. Steuer. Unified interactive multiple-objective programming — An open-architecture for accommodating new procedures. Journal of the Operational Research Society, 45: 1456–1466, 1994.

    Google Scholar 

  15. A. Geoffrion, J. Dyer, and A. Feinberg. An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Management Science, 19: 357–368, 1972.

    Google Scholar 

  16. J.P. Ignizio. Goal Programming and Its Extensions. D.C. Heath, Lexington, MA, 1976.

    Google Scholar 

  17. J.P. Ignizio, editor. Computers & Operations Research, volume 10. 1983. Special Issue on Generalized Goal Programming.

    Google Scholar 

  18. A. laszkiewicz and R. Slowinski. The light beam search approach — An overview of methodology and applications. European Journal of Operational Research, 113: 300–314, 1999.

    Google Scholar 

  19. D. Kahneman and A. Tversky. Prospect theory: An analysis of decisions under risk. Econometrica, 47: 262–291, 1979.

    Google Scholar 

  20. I. Kaliszewski and W. Michalowski. Efficient solutions and bounds on tradeoffs. Journal of Optimization Theory and Applications, 94: 381–394, 1997.

    Article  MathSciNet  Google Scholar 

  21. E.K. Karasakal and M. Koksalan. A simulated annealing approach to bicriteria scheduling problems on a single machine. Journal of Heuristics, 6: 311–327, 2000.

    Article  Google Scholar 

  22. R. Keeney and H. Raiffa. Decisions with Multiple Objectives. John Wiley & Sons, New York, 1976.

    Google Scholar 

  23. R. Klimberg. GRADS — A new graphical display system for visualizing multiple criteria solutions. Computers & Operations Research, 19: 707–711, 1992.

    Article  MATH  Google Scholar 

  24. T. Koopmans. Analysis of production as an efficient combination of activities. In T. Koopmans, editor, Activity Analysis of Production and Allocation, volume 13 of Cowles Commission Monograph, pages 33–97. John Wiley & Sons, New York, 1951.

    Google Scholar 

  25. P.J. Korhonen. VIG — A visual interactive support system for multiple criteria decision making. Belgian Journal of Operations Research, Statistics and Computer Science, 27: 3–15, 1987.

    Google Scholar 

  26. P.J. Korhonen. Using harmonious houses for visual pairwise comparison of multiple criteria alternatives. Decision Support Systems, 7: 47–54, 1991.

    Article  MathSciNet  Google Scholar 

  27. P.J. Korhonen and J. Karaivanova. An algorithm for projecting a reference direction onto the nondominated set of given points. IEEE Transactions on Systems, Man, and Cybernetics — Part A: Systems and Humans, 29(5):429–435, 1999.

    Google Scholar 

  28. P.J. Korhonen and J. Laakso. A visual interactive method for solving the multiple criteria problem. European Journal of Operational Research, 24: 277–287, 1986.

    MathSciNet  Google Scholar 

  29. P.J. Korhonen, H. Moskowitz, and J. Wallenius. Choice behavior in interactive multiple criteria decision-making. Annals of Operations Research, 23: 161–179, 1990.

    Article  MathSciNet  Google Scholar 

  30. P.J. Korhonen, H. Moskowitz, and J. Wallenius. Multiple criteria decision support — A review. European Journal of Operational Research, 63: 61–375, 1992.

    Article  Google Scholar 

  31. P.J. Korhonen and J. Wallenius. A Pareto race. Naval Research Logistics, 35: 615–623, 1988.

    Google Scholar 

  32. P.J. Korhonen and J. Wallenius. Observations regarding choice behavior in interactive multiple criteria decision-making environments: An experimental investigation. In A. Lewandowski and I. Stanchev, editors, Methodology and Software for Interactive Decision Support, pages 163–170. Springer Verlag, Berlin, 1989. Proceedings of the Workshop sponsored by IIASA.

    Google Scholar 

  33. P.J. Korhonen, J. Wallenius, and S. Zionts. A computer graphics-based decision support system for multiple objective linear programming. European Journal of Operational Research, 60: 280–286, 1992.

    Article  Google Scholar 

  34. O.I. Larichev and H.M. Moshkovich. Limits to decision-making ability in direct multiattribute alternative evaluation. Organizational Behavior And Human Decision Processes, 42: 217–233, 1988.

    Article  Google Scholar 

  35. A. Lewandowski and M. Granat. Dynamic BIPLOT as the interaction interface for aspiration based decision support systems. In P.J. Korhonen, A. Lewandowski, and J. Wallenius, editors, Multiple Criteria Decision Support, pages 229–241. Springer-Verlag, Heidelberg, 1991. Proceedings of the Workshop organized by IIASA and sponsored by IIASA.

    Google Scholar 

  36. B. Mareschal and J.P. Brans. Geometrical representations for MCDA. European Journal of Operational Research, 34: 69–77, 1988.

    Article  MathSciNet  Google Scholar 

  37. W. Michalowski and T. Szapiro. A bi-reference procedure for interactive multiple criteria programming. Operations Research, 40: 247–258, 1992.

    Google Scholar 

  38. K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston, 1999.

    Google Scholar 

  39. D. Olson. Decision Aids for Selection Problems. Springer Series in Operations Research. Springer Verlag, New York, 1996.

    Google Scholar 

  40. V. Pareto. Manuel d’Economie Politique. Marcel Giard, Paris, 1909.

    Google Scholar 

  41. B. Roy. Problems and methods with multiple objective functions. Mathematical Programming, 1: 239–266, 1972.

    Google Scholar 

  42. T. Saaty. The Analytic Hierarchy Process. McGraw-Hill, New York, 1980.

    Google Scholar 

  43. A.A. Salo and R.P. Hämäläinen. Preference assessment by imprecise ratio statements. Operations Research, 40: 1053–1061, 1992.

    Google Scholar 

  44. W.S. Shin and A. Ravindran. Interactive multiple objective optimization: Survey I — Continuous case. Computers & Operations Research, 18: 97–114, 1991.

    Article  MathSciNet  Google Scholar 

  45. R.E. Steuer. An interactive multiple objective linear programming procedure. TIMS Studies in the Management Sciences, 6: 225–239, 1977.

    Google Scholar 

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

    Google Scholar 

  47. R.E. Steuer and E.-U. Choo. An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming, 26: 326–344, 1983.

    MathSciNet  Google Scholar 

  48. M. Weber and K. Borcherding. Behavioral-influences on weight judgments in multiattribute decision-making. European Journal of Operational Research, 67: 1–12, 1993.

    Article  Google Scholar 

  49. A. Wierzbicki. The use of reference objectives in multiobjective optimization. In G. Fandel and T. Gal, editors, Multiple Objective Decision Making, Theory and Application, volume 177 of Lecture Notes in Economics and Mathematical Systems. Springer Verlag, Berlin, 1980.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  51. S. Zionts and J. Wallenius. An interactive programming method for solving the multiple criteria problem. Management Science, 22: 652–663 1976.

    Google Scholar 

  52. S. Zionts and J. Wallenius. An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Management Science, 29: 519–529, 1983.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science + Business Media, Inc.

About this chapter

Cite this chapter

Korhonen, P. (2005). Interactive Methods. In: Multiple Criteria Decision Analysis: State of the Art Surveys. International Series in Operations Research & Management Science, vol 78. Springer, New York, NY. https://doi.org/10.1007/0-387-23081-5_16

Download citation

Publish with us

Policies and ethics