A DSS oriented method for multiobjective linear programming problems

Abstract Most of practical linear programming problems involve multiple and conflicting objectives. The paper presents an interactive method to approach this kind of problems. The main original aspect of this method lies in the fact that it combines the advantageous features of both the paradigms of Satisfactory Goals and Multiattribute Utility Assesment. It is a DSS oriented approach providing a ‘two level’ interaction: 1. (1) interactive assessment of the decision maker's utility function using the UTA ordinal regression model; 2. (2) interactive modification of the satisfaction levels. Piecewise linear optimazation techniques are used to determine, at each iteration, a new compromise solution over the set of efficient solutions.

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

[2]  M. Tawfik Jelassi.  MCDM: From ‘Stand-Alone’ Methods to Integrated and Intelligent DSS , 1987 .

[3]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[4]  Jyrki Wallenius,et al.  Interactive Multiple Criteria Decision Methods: An Investigation and an Approach , 1976 .

[5]  M. Shakun,et al.  Decision support systems for semi-structured buying decisions , 1984 .

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

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

[8]  R. Słowiński,et al.  Molp with an interactive assessment of a piecewise linear utility function , 1987 .

[9]  Eng Ung Choo,et al.  An interactive algorithm for multicriteria programming , 1980, Comput. Oper. Res..

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

[11]  D. H. Marks,et al.  A review and evaluation of multiobjective programing techniques , 1975 .

[12]  Robert Fourer,et al.  A simplex algorithm for piecewise-linear programming I: Derivation and proof , 1985, Math. Program..

[13]  J. Siskos.  Assessing a set of additive utility functions for multicriteria decision-making , 1982 .

[14]  D. J. White.  Multi-Objective Interactive Programming , 1980 .

[15]  T. Gal.  On Efficient Sets in Vector Maximum Problems — A Brief Survey , 1986 .

[16]  Constantin Zopounidis,et al.  The evaluation criteria of the venture capital investment activity: An interactive assessment , 1987 .

[17]  Tom Hemming,et al.  Guide Lines for Testing Interactive Multicriterion Methods by Simulation , 1987 .

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

[19]  Tom Hemming.  Multiobjective decision making under certainty , 1978 .

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

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

[22]  Denis Yannacopoulos.  Mise en place et expérimentation d'un système interactif d'aide à la décision multicritère , 1985 .

[23]  Herbert A. Simon,et al.  The new science of management decision , 1960 .