Skip to main content
SpringerLink
Log in
Book cover

Multiple Criteria Decision Methods and Applications pp 85–128Cite as

Multiple Criteria Mathematical Programming: an Overview and Several Approaches

  • Chapter

Abstract

Multiple Criteria Decision Making (MCDM) refers to making decisions in the presence of multiple, usually conflicting, objectives. Multiple criteria decision problems pervade all that we do and include such public policy tasks as determining a country’s policy, developing a national energy plan, as well as planning national defense expenditures, in addition to such private enterprise tasks as new product development, pricing decisions, and research project selection. For an individual, the purchase of an automobile or a home exemplifies a multiple criteria problem. Even such routine decisions as the choice of a lunch from a menu, or the assignment of job crews to jobs constitute multiple criteria problems. All have a common thread — multiple conflicting objectives.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Benayoun, R., de Montgolfier, J., Tergny, J. and Larichev, O, ‘Linear programming with multiple objective functions: step method (STEM)’ Mathematical Programming, 1, 1971, pp. 366–375.

    Article  Google Scholar 

  • Charnes, A. and Cooper, W.W., Management Models and Industrial Applications of Linear Programming, John Wiley and Sons, New York, 1961.

    Google Scholar 

  • Charnes, A. and Cooper, W.W., ‘Goal programming and multiple objective optimization-Part l’, European Journal of Operations Research, 1, 1977, pp. 39–54.

    Article  Google Scholar 

  • Deshpande, D., ‘Investigations in multiple objective linear programming-theory and an application’, Unpublished Doctoral Dissertation, School of Management, State University of New York at Buffalo, 1980.

    Google Scholar 

  • Dyer, J., ‘A time-sharing computer program for the solution to the multiple criteria problem’, Management Science, 19, 1973, pp. 1379–1383.

    Article  Google Scholar 

  • Evans, J.P. and Steuer, R.E., ‘Generating efficient extreme points in linear multiple objective programming: two algorithms and computing experience’, in Cochrane and Zeleny (1973), pp. 349–365.

    Google Scholar 

  • Geoffrion, A.M., Dyer, J.S. and Feinberg, A., ‘An interactive approach for multicriterion optimization with an application to the operation of an academic department’, Management Science, 19, 1972, pp. 357–368.

    Article  Google Scholar 

  • Haimes, Y.Y. and Hall, W.A., ‘Multiobjectives in water resources systems analysis: the surrogate worth tradeoff method’, Water Resources Research, 10, 1974, pp. 615–623.

    Article  Google Scholar 

  • Ijiri, Y., Management Goals and Accounting for Control, North Holland Publishing Co., Amsterdam and Rand McNally, Chicago, 1965.

    Google Scholar 

  • Kallio, M., Lewandowski, A. and Orchard-Hays, W., ‘An implementation of the reference point approach for multiobjective optimization’, Working Paper no. 30–35, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1980.

    Google Scholar 

  • Karwan, M.H., Zionts, S. and Villareal, B., ‘An improved interactive multicriteria integer programming algorithm’, Working Paper no. 530, School of Management, State University of New York at Buffalo, Revised February 1983.

    Google Scholar 

  • Karwan, M.H. and Zionts, S., ‘On finding starting feasible solutions for some specifally structured linear programming problems’, Working Paper no. 445, School of Management, State University of New York at Buffalo, 1980.

    Google Scholar 

  • Keefer, D.L., ‘Allocation planning for R&D with uncertainty and multiple objectives’, IEEE Transactions on Engineering Management’, EM-25, 1973a, pp. 8–14.

    Google Scholar 

  • Keefer, D.L., ‘Applying multiobjective decision analysis to resource allocation planning problems’, in Zionts (1978), pp. 299–320.

    Google Scholar 

  • Keeney, R.L., ‘Multiplicative utility functions’, Operations Research, 22, 1974, pp. 22–34.

    Article  Google Scholar 

  • Keeney, R.L. and Raiffa, H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs, John Wiley and Sons, New York, 1976.

    Google Scholar 

  • Lee, S.M., Goal Programming for Decision Analysis, Auerbach, Philadelphia, 1972. 128

    Google Scholar 

  • Manheim, M.L. and Hall, F., ‘Abstract representation of goals: A method for making decisions in complex problems’, in: Transportation: A Service, Proceedings of the Sesquicentennial Forum, New York Academy of Sciences American Society of Mechanical Engineers, New York, 1967.

    Google Scholar 

  • Miller, G., ‘The magical number seven plus or minus two: some limits on our capacity for processing information’, Psychological Review, 63, 1956, pp. 81–97.

    Article  Google Scholar 

  • Roy, B., ‘Partial preference analysis and decision aid: the fuzzy outranking relation concept’, in Bell, Keeney and Raiffa (1D77).

    Google Scholar 

  • Steuer, R.E., ‘Multiple objective linear programming with interval criterion weights’, Management Science, 23, 1977, pp. 305–316.

    Article  Google Scholar 

  • Steuer, R.E. and Schuler, A.T., ‘An interactive multiple objective linear programming approach to a problem in forest management’, Working Paper No. BA2, College of Business and Economics, University of Kentucky, 1976.

    Google Scholar 

  • Steuer, R.E. and Wallace, M.J. Jr., ‘An interactive multiple objective wage and salary administration procedure’, in Lee, S.M. and Thorp, C.D. Jr. (eds), Personnel Management: A Computer-Based System, Petrocelli, New York, 1978, pp. 159–176.

    Google Scholar 

  • Villareal, B., Multicriteria Integer Linear Programming, Doctoral Dissertation, Department of Industrial Engineering, State University of New York at Buffalo, 1979.

    Google Scholar 

  • Villareal, B., Karwan, M.H. and Zionts, S., ‘An interactive branch and bound procedure for multicriterion integer linear programming’, in Fandel and Gal, 1930a.

    Google Scholar 

  • Villareal, B., Karwan, M.H. and Zionts, S., ‘A branch and bound approach to interactive multicriteria integer linear programming’, Paper presented at the Joint National Meeting TIMS/ORSA, Washington, DC, 1980b.

    Google Scholar 

  • Wallenius, H., Wallenius, J. and Vartia, P., ‘An approach to solving multiple criteria macroeconomic policy problems and an application’, Management Science, 24, 1978, pp. 1021–1030.

    Article  Google Scholar 

  • Wierzbicki, A.P., ‘The use of reference objectives in multiobjective optimization’, Working Paner 79–66, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1979.

    Google Scholar 

  • Yu, P.L. and Zeleny, M., ‘The set of all nondominated solutions in the linear cases and a multicriteria simplex method’, Journal of Mathematical Analysis and Applications, 49, 1975, pp. 430–468.

    Article  Google Scholar 

  • Zionts, S., ‘Integer linear programming with multiple objectives’, Annals of Discrete Mathematics, 1, 1977, pp. 551–562.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zionts, S. and Wallenius, J., ‘An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions’, Management Science, vol. 29, no. 5, May 1933, pp. 529–529.

    Google Scholar 

Download references

Authors
  1. S. Zionts
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Lehrstuhl für Betriebswirtschaft, Fernuniversität Hagen, Roggenkamp 6, D-5800, Hagen 1, Germany

    Günter Fandel

  2. Department of Business Finance and Portfolio Investment, Erasmus University, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands

    Jaap Spronk

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zionts, S. (1985). Multiple Criteria Mathematical Programming: an Overview and Several Approaches. In: Fandel, G., Spronk, J. (eds) Multiple Criteria Decision Methods and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70583-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70583-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70585-4

  • Online ISBN: 978-3-642-70583-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation