MOLP with an interactive assessment of a piecewise linear utility function. (English) Zbl 0636.90083

Jacquet-Lagrèze, Eric; Meziani, Rachid; Slowinski, Roman

Eur. J. Oper. Res. 31, 350-357 (1987).

The paper presents a methodology for Multi-Objective Linear Programming (MOLP) problems. It relies on three steps: (1) Generation of a subset of feasible efficient solutions (from 10 to 50) as representative as possible of the efficient set. (2) Assessment of an additive utility function using an interactive method (PREFCALC). (3) Optimization of the additive utility function on the original set of feasible alternatives. Following this methodology enables the user to find compromise solutions which can be different from the vertices. It is particularly adapted for large scale linear programs where traditional multiobjective methods would be too costly to use, since the interactive phase is limited to step 2, using PREFCALC on a micro-computer. A micro-computer version of the method (PREFCHAT) is available.

MSC:

90C31	Sensitivity, stability, parametric optimization
90B50	Management decision making, including multiple objectives

Keywords:

utility function; Multi-Objective Linear Programming; interactive method; compromise solutions; large scale linear programs

Software:

UTA Plus

References:

[1]	Bazarra, M. S.; Shetty, C. M., Nonlinear Programming (1979), Wiley: Wiley New York
[2]	Choo, E. U.; Atkins, D. R., An interactive algorithm for multicriteria programming, Computers & Operations Research, 7, 81-87 (1980)
[3]	Fourer, R., Piecewise linear programming, (Report (March 1983), Dept. of Industrial Engrg. and Management Sci., Northwestern University: Dept. of Industrial Engrg. and Management Sci., Northwestern University Evanston, IL)
[4]	Goicoechea, A.; Hansen, Don R.; Duckstein, L., Multiobjective Decision Analysis with Engineering and Business Applications (1982), Wiley: Wiley New York · Zbl 0584.90045
[5]	Iserman, H., The enumeration of the set of all efficient solutions for a linear multiple objective program, Operational Research Quarterly, 28, 3 (1977)
[6]	Jacquet-Lagrèze, E., Prefcalc—Evaluation et décision multicritères, Euro-Décision (1983)
[7]	Jacquet-Lagrèze, E.; Shakun, M., Decision support systems for semi-structured buying decisions, European Journal of Operational Research, 16, 1, 48-58 (1984)
[8]	Jacquet-Lagrèze, E.; Siskos, J., Assessing a set of additive utility functions for multicriteria decision-making, the Uta method, European Journal of Operational Research, 10, 2, 151-164 (1982) · Zbl 0481.90078
[9]	Kornbluth, J. S.; Steuer, R. E., Multiple objective linear fractional programming, Management Science, 27, 1024-1039 (1981) · Zbl 0467.90064
[10]	Miller, C. E., The simplex method for local separable programming, (Graves, R. L.; Wolfe, P., Recent Advances in Mathematical Programming (1963), McGraw-Hill: McGraw-Hill New York), 89-100
[11]	Morse, J. N., Reducing the size of the nondominated set: Prunning and clustering, Computers & Operations Research, 7, 55-66 (1980)
[12]	Siskos, J., Analyses de régression et programmation linéaire, (Cahier du LAMSADE no. 54, Université de Paris-Dauphine, May 1984. Cahier du LAMSADE no. 54, Université de Paris-Dauphine, May 1984, Revue de Statistique Appliquée, 33 (1985)), 1 · Zbl 0562.62054
[13]	Slowinski, R., A review of multiobjective linear programming methods (in Polish), Przeglad Statystyczny, 31 (1984), Part I - No. 1/2, Part II - No. 3/4
[14]	Torn, A., A sampling-search-clustering approach for exploring the feasible/effcient solutions of MCDM problems, Computers & Operations Research, 7, 67-80 (1980)
[15]	Vincke, Ph., Présentation et analyse de neuf méthodes multicritères interactives, (Cahier du LAMSADE no. 42, Université de Paris-Dauphine (Dec. 1982))
[16]	Wierzbicki, A. P., On the completness and constructivness of parametric characterizations to vector optimization problems, OR Spectrum B (1986) · Zbl 0592.90084
[17]	Winkels, H.-M., Complete efficiency analysis for linear vector maximum systems: Theoretical background and an algorithm, (Document du LAMSADE No. 13 (1980), Université de Paris-Dauphine: Université de Paris-Dauphine Paris)
[18]	Yu, P. L.; Zeleny, M., Linear multiparametric programming by multicriteria simplex method, Management Science, 23, 2 (1976) · Zbl 0357.90034