Kuhn-Tucker multipliers as trade-offs in multiobjective decision-making analysis

Useful relationships between the optimal Kuhn-Tucker multipliers and trade-offs in the multiobjective decision-making problems are developed based on the sensitivity interpretation of such multipliers. Practical and theoretical applications of these results are discussed. The results provide a convenient way for obtaining necessary (trade-off) information for continuing into the analyst-decision-maker interactive phase of the multiobjective decision-making process. This paper further extends the theoretical basis of the Surrogate Worth Trade-off (SWT) Method; a multiobjective optimization method which first appeared in the scientific literature in 1974.

[1]  BenayounR.,et al.  Linear programming with multiple objective functions , 1971 .

[2]  Bernard Roy,et al.  Problems and methods with multiple objective functions , 1971, Math. Program..

[3]  Yacov Y. Haimes,et al.  Hierarchical analyses of water resources systems : modeling and optimization of large-scale systems , 1977 .

[4]  Heinz Isermann,et al.  Technical Note - Proper Efficiency and the Linear Vector Maximum Problem , 1974, Oper. Res..

[5]  Yacov Y. Haimes,et al.  Integrated System Identification and Optimization , 1973 .

[6]  Robert W. Reid,et al.  On the noninferior index approach to large-scale multi-criteria systems , 1971 .

[7]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[8]  Y. Haimes,et al.  Multiobjectives in water resource systems analysis: The Surrogate Worth Trade Off Method , 1974 .

[9]  J. Cohon Multiobjective optimization in water resources systems , 1976 .

[10]  S. Zionts,et al.  An Interactive Programming Method for Solving the Multiple Criteria Problem , 1976 .

[11]  R. Benayoun,et al.  Linear programming with multiple objective functions: Step method (stem) , 1971, Math. Program..

[12]  H. P. Benson,et al.  The Vector Maximization Problem: Proper Efficiency and Stability , 1977 .

[13]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[14]  Arthur M. Geoffrion,et al.  An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department , 1972 .

[15]  A. M. Geoffrion Proper efficiency and the theory of vector maximization , 1968 .

[16]  Russell L. Ackoff,et al.  Fundamentals of operations research , 1968 .

[17]  E. Polak Introduction to linear and nonlinear programming , 1973 .