Theories and an exact interactive paired-comparison approach for discrete multiple-criteria problems

An interactive approach is developed to help decision-makers (DMs) find the best alternatives with few questions without making stringent assumptions about their behavior. Theories and procedures are developed for ranking alternatives and eliminating suboptimal ones, assuming that the DM can respond to tradeoff- and paired-comparison questions. It is assumed that the DM wishes to maximize an unknown quasiconcave utility function for discrete multiple-criteria decision-making (MCDM) problems. Several tests are developed based on convex dominating cones. Optimality conditions for discrete MCDM problems are given for extreme, nonextreme, and convex-dominated points without requiring the DM to enumerate the remaining set of discrete alternatives. These optimality conditions are based on a branching technique which converts nonextreme points to extreme points. This substantially reduces the number of questions asked of the DM. Finally, an exact discrete MCDM method is developed. >

[1]  S. Zionts,et al.  An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions , 1983 .

[2]  Joseph J. Talavage,et al.  A Tradeoff Cut Approach to Multiple Objective Optimization , 1980, Oper. Res..

[3]  S. Zionts,et al.  Approaches for Discrete Alternative Multiple Criteria Problems for Different Types of Criteria , 1986 .

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

[5]  Behnam Malakooti,et al.  A decision support system and a heuristic interactive approach for solving discrete multiple criteria problems , 1988, IEEE Trans. Syst. Man Cybern..

[6]  Behnam Malakooti,et al.  Identifying nondominated alternatives with partial information for multiple-objective discrete and linear programming problems , 1989, IEEE Trans. Syst. Man Cybern..

[7]  Stanley Zionts,et al.  An improved method for solving multiple criteria problems involving discrete alternatives , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  Behnam Malakooti,et al.  An exact interactive method for exploring the efficient facets of multiple objective linear programming problems with quasi-concave utility functions , 1988, IEEE Trans. Syst. Man Cybern..

[9]  Jyrki Wallenius,et al.  Identifying Efficient Vectors: Some Theory and Computational Results , 1980, Oper. Res..

[10]  Sowmyanarayanan Sadagopan,et al.  Interactive algorithms for multiple criteria nonlinear programming problems , 1986 .

[11]  K. Arrow,et al.  QUASI-CONCAVE PROGRAMMING , 1961 .

[12]  Behnam Malakooti.  Ranking multiple criteria alternatives with half-space, convex, and non-convex dominating cones: quasi-concave and quasi-convex multiple attribute utility functions , 1989, Comput. Oper. Res..

[13]  Hanif D. Sherali,et al.  A Convergent Interactive Cutting-Plane Algorithm for Multiobjective Optimization , 1987, Oper. Res..

[14]  S. Zionts,et al.  Solving the Discrete Multiple Criteria Problem using Convex Cones , 1984 .

[15]  R. Soland,et al.  An interactive branch-and-bound algorithm for multiple criteria optimization , 1986 .

[16]  Behnam Malakooti,et al.  Selection of acceptance sampling plans with multi - attribute defects in computer-aided quality control , 1987 .