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.
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References
Benayoun, R., de Montgolfier, J., Tergny, J., and Larichev, O., “Linear Programming with Multiple Objective Functions: Step Method (STEM),” Mathematical Programming, 1, 1971, 615.
Breslawski, S., A Study in Multiple Objective Linear Programming, Unpubl ished Doctoral Dissertation, School of Management, State University of New York, Buffalo, New York, 1986.
Charnes, A. and Cooper, W. W., Management Models and Industrial Applications of Linear Programming, John Wiley and Sons, New York, 1961.
Charnes, A. and Cooper, W. W., “Goal Programming and Multiple Objective Optimization — Part 1,” European Journal of Operations Research, 1, 1977, 39.
Chung, H. W., Investigation of Discrete Multiple Criteria Decision Making and an Application to Home Buying, Unpublished Doctoral Dissertation, School of Management, State University of New York, Buffalo, 1986.
Deshpande, D., Investigations in Multiple Objective Linear Programming-Theory and an Application, Unpublished Doctoral Dissertation, School of Management, State University of New York at Buffalo, 1980.
Dyer, J., “A Time-Sharing Computer Program for the Solution of the Multiple Criteria Problem,” Management Science, 19, 1973, 349.
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, Multiple Criteria Decision Making, University of South Carolina Press, 1973.
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, 357.
Haimes, Y. Y., and Hall, W. A., “Multiobjectives in Water Resources Systems Analysis: The Surrogate Worth Trade Off Method,” Water Resources Research, 10, 1974, 615.
Ijiri, Y., Management Goals and Accounting for Control, North-Holland Publishing Co., Amsterdam, and Rand McNally, Chicago, 1965.
Kallio, M., Lewandowski, A., and Orchard-Hays, W., “An Implementation of the Reference Point Approach for Multiobjective Optimization,” Working Paper No. 80–35, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1980.
Karwan, M. H. Zionts, S., Villareal, B., and R. Ramesh, “An Improved Interactive Multicriteia Integer Programming Algorithm,” in Haimes, Y. Y. and Chan Kong, V., Decision Making with Multiple Objectives, Proceedings, Cleveland, Ohio, 1984, Lecture Notes in Economics and Mathematical Systems, Vol. 242, Springer-Verlag, (Berlin), 1985, pp. 261–271.
Keeney, R. L. and Raiffa, H., Decisions with Multiple Objectives Preferences and Value Tradeoffs, John Wiley and Sons, New York, 1976.
Koksalan, M., Karwan, M. H., and Zionts, S., “An Improved method for Solving Multicriteria Problems Involving Discrete Alternatives,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 14, No. 1, January 1984, 24–34.
Korhonen, P. J., and Laakso, J., “A Visual Interactive Method for Solving the Multiple Criteria Problem,” European Journal of Operational Research, 24, 1986, 277–287.
Korhonen, P. J., and Wallenius, J., A Pareto Race, Unpublished Paper, Helsinki School of Economics, 1987. Forthcoming in Naval Research Logistics.
Korhonen, P., Wallenius, J., and Zionts, S., “Solving the Discrete Multiple Criteria Problem Using Convex Cones,” Management Science, 30, 11, 1984, 1336–1345.
Lee, S. M., Goal Programming for Decision Analysis, Auerbach, Philadelphia, 1972.
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.
Miller, G., “The Magical Number Seven Plus or Minus Two: Some Limits on Our Capacity For Processing Information,” in Psychological Review, 63, 1956, 81.
Ramesh, R., Multicriteria Integer Programming, Unpublished Doctoral Dissertation, Department of Industrial Engineering, State University of New York at Buffalo, 1985.
Roy, B., “Partial Preference Analysis and Decision Aid: The Fuzzy Criterion Concept,” in Bell, D. E., Keeney, R. L. and Raiffa, H., eds., Conflicting Objectives in Decisions, International Series on Applied Systems Analysis, John Wiley and Sons, 1977, 442.
Steuer, R. E., “Multiple Objective Linear Programming with Interval Criterion Weights,” Management Science, 23, 1977, 305.
Steuer, R. E., Multiple Criteria Optimization Theory, Computation, and Application, John Wiley and Sons, New York, 1986
Steuer, R. E., and, 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.
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, 159.
Villareal, B., Multicriteria Integer Linear Programming, Doctoral Dissertation, Department of Industrial Engineering, State University of New York at Buffalo, 1979.
Wallenius, H., Wallenius, J., and Vartia, P., “An Approach to Solving Multiple Criteria Macroeconomic Policy Problems and an Application,” Management Science, 24, 1978, 1021.
Wierzbicki, A. P., “The Use of Reference Objectives in Multiobjective Optimization,” in G. Fandel and T. Gal (Eds.), Multiple Criteria Decision Making Theory and Application, Springer-Verlag, New York, 1980.
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, 430.
Zionts, S., “Integer Linear Programming with Multiple Objectives”,Annals of Discrete Mathematics, 1, 1977, 551.
Zionts, S. and Wallenius, J., “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science, 22, 1976, 652.
Zionts, S. and Wallenius, J., “An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions,” Management Science, 29, 1983, 519.
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Zionts, S. (1988). Multiple Criteria Mathematical Programming: an Updated Overview and Several Approaches. In: Mitra, G., Greenberg, H.J., Lootsma, F.A., Rijkaert, M.J., Zimmermann, H.J. (eds) Mathematical Models for Decision Support. NATO ASI Series, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83555-1_7
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DOI: https://doi.org/10.1007/978-3-642-83555-1_7
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