Méthode d’estimation d’utilités additives concaves en programmation linéaire multiobjectifs. (An estimation method for concave additive utilities in linear multiobjective programming). (French) Zbl 0712.90066

Despotis, D. K.; Yannacopoulos, D.

RAIRO, Rech. Opér. 24, No. 4, 331-349 (1990).

Summary: In an important class of multiobjective linear programming methods the determination of a satisfactory solution is realized by the maximization of the decision maker’s utility function. Several methods have been proposed for the assessment of utility functions. These methods require different types of information (cardinal or ordinal) and rely on different assumptions for the utility function, such as linearity, additivity and concavity. The latter property, although restrictive for the decision maker’s preferences, provides a sufficient condition for a global optimum.
In this paper an extension of the algorithm UTASTAR to the assessment of concave utility functions is presented. The new algorithm is illustrated by a numerical example. Finally, the degree to which the concavity restriction influences the results of the assessment process is studied and discussed.

MSC:

90C29	Multi-objective and goal programming
91B16	Utility theory
90B50	Management decision making, including multiple objectives
90C05	Linear programming

Keywords:

concave additive utility functions; multiobjective linear programming; assessment of concave utility functions