A Bi-Reference Procedure for Interactive Multiple Criteria Programming

The paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem. The procedure requires the decision maker to specify the worst outcome. Then, the ideal outcome is identified, and the improvement direction from the worst to ideal outcomes is constructed. A trial solution is found by moving from a current solution along the improvement direction, while maximizing the step size. For a trial solution, the decision maker is requested to partition the set of objective functions into three categories: those to be improved, those which may remain unchanged, those which may be relaxed. Based on this partition, the procedure displaces the worst and ideal outcomes, calculates the new improvement direction, and the entire process is repeated. The method terminates when two successive trial solutions are reasonably similar.

[1]  J. March.  Bounded rationality, ambiguity, and the engineering of choice , 1978 .

[2]  Wojtek Michalowski,et al.  A procedure for worst outcomes displacement in multiple criteria decision making , 1989, Comput. Oper. Res..

[3]  Ram Narasimhan,et al.  An Experimental Evaluation of Articulation of Preferences in Multiple Criterion Decision‐Making (MCDM) Methods , 1988 .

[4]  W. Edwards,et al.  Decision Analysis and Behavioral Research , 1986 .

[5]  Stanley Zionts,et al.  Multiple criteria mathematical programming: an updated overview and several approaches , 1988 .

[6]  Andrzej P. Wierzbicki,et al.  Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds , 1988 .

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

[8]  Pekka Korhonen,et al.  A Careful Look at Efficiency in Multiple Objective Linear Programming , 1989 .

[9]  Jyrki Wallenius,et al.  A Progressive Algorithm for Modeling and Solving Multiple-Criteria Decision Problems , 1986, Oper. Res..

[10]  Wojtek Michalowski.  Use of the displaced worst compromise in interactive multiobjective programming , 1988, IEEE Trans. Syst. Man Cybern..

[11]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[12]  G. W. Evans,et al.  An Overview of Techniques for Solving Multiobjective Mathematical Programs , 1984 .

[13]  Mark Gershon,et al.  Techniques for multiobjective decision making in systems management , 1986 .

[14]  Simon French,et al.  Multi-Objective Decision Analysis with Engineering and Business Applications , 1983 .

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

[16]  Robert J. Reilly,et al.  Preference Reversal: Further Evidence and Some Suggested Modifications in Experimental Design , 1982 .

[17]  Theodor J. Stewart,et al.  An aspiration-level interactive model for multiple criteria decision making , 1992, Comput. Oper. Res..

[18]  D. E. Bell,et al.  Decision making: Descriptive, normative, and prescriptive interactions. , 1990 .

[19]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[20]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[21]  B. Roy.  Meaning and validity of interactive procedures as tools for decision making , 1987 .

[22]  Wojtek Michalowski,et al.  Evaluation Of A Multiple Criteria Interactive Programming Approach: An Experiment , 1987 .

[23]  Hirotaka Nakayama,et al.  Satisficing Trade-off Method for Multiobjective Programming , 1984 .

[24]  J. Wallenius,et al.  Using qualitative data in multiple objective linear programming , 1990 .

[25]  James P. Ignizio,et al.  Linear Programming in Single- and Multiple-Objective Systems , 1984 .

[26]  R. Hogarth,et al.  BEHAVIORAL DECISION THEORY: PROCESSES OF JUDGMENT AND CHOICE , 1981 .

[27]  Jyrki Wallenius,et al.  Comparative Evaluation of Some Interactive Approaches to Multicriterion Optimization , 1975 .

[28]  Ewa Konarzewska-Gubała.  On the Use of Bipolar Reference Objectives in Multiple Criteria Decision Making , 1987 .

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

[30]  O. I. Larichev,et al.  Analytical Survey of Procedures for Solving Multicriteria Mathematical Programming Problems (MMPP) , 1987 .

[31]  Pekka Korhonen,et al.  A Visual Interactive Method for Solving the Multiple-Criteria Problem , 1986 .