Abstract
In this paper we present an interactive method for ranking items subject to an (initially) unspecified linear utility function. The method is economical on the number of paired judgements that must be made by the decision maker and leads to the identification of the desired ranking and the space of weights for the corresponding linear utility functions which would lead to this ranking. In the simulation tests on random data it is shown that the number of comparisons that must be made at each stage tends to be less than n+1 where n is the number of criteria being used.
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References
J.L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, University of South Carolina Press, Columbia, South Carolina, (1973).
J.P. Evans, “Connectedness of the Efficient Extreme Points in Linear Multiple Objective Problems”, Graduate School of Business Administration and Operations Research and Systems Analysis Curriculum, University of North Carolina, Chapel Hill, (July 1972).
J.P. Evans and R.E. Steuer, “A Revised Simplex Algorithm for Linear Multiple Objective Programs”, Mathematical Programming, Vol. 5, No. 1, pp. 54–72, (1973).
D.E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching, Addison Wesley Publishing Co., (1973).
J.S.H. Kornbluth, “Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming”, Operations Research Quarterly, Vol. 25, pp. 599–614, (1974).
H. Lorin, Sorting and Sort Systems, Addison Wesley Publishing Co., (1975).
J. Philip, “Algorithms for the Vector Maximization Problem”, Mathematical Programming, Vol. 2, pp. 207–229, (1972).
B. Roy, “Problems and Methods with Multiple Objective Functions”, Mathematical Programming, Vol. 1, pp. 239–266, (1971).
V. Srinivasan and A.D. Shocker, “Linear Programming Techniques for Multi-dimensional Analysis of Preference”, Psychometrika, Vol. 38, No. 3, pp. 337–369, (September 1973).
V. Srinivasan and A.D. Shocker, “Estimating the Weights for Multiple Attributes in a Composite Criterion Using Pairwise Judgements”, Psychometrika, Vol. 38, No. 4, pp. 473–493, (December 1973).
R.E. Steuer, “Interval Criterion Weights Programming”, University of Kentucky (1974).
M. Zeleny, “A Concept of Compromise Solutions and the Method of the Displaced Ideal”, Computers and Operations Research Vol. 1, pp. 479–496, (1974).
S. Zionts and J. Wallenius, “An Interactive Programming Method for Solving the Multiple Criteria Problem”, Management Science, Vol. 22, No. 6, pp. 652–663, (February 1976).
S. Zionts and J. Wallenius, “Identifying Efficient Vectors: Some Theory and Computational Results”, Working Paper, No. 257, School of Management, State University of New York at Buffalo, (November 1976).
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© 1978 Springer-Verlag Berlin Heidelberg
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Kornbluth, J.S.H. (1978). Ranking with Multiple Objectives. In: Zionts, S. (eds) Multiple Criteria Problem Solving. Lecture Notes in Economics and Mathematical Systems, vol 155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46368-6_17
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DOI: https://doi.org/10.1007/978-3-642-46368-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08661-1
Online ISBN: 978-3-642-46368-6
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