Generating Well-Behaved Utility Functions for Compromise Programming 1. M. A. MORON, 2 C. ROMERO, 3 AND F. R. RuIz DEL PORTAL 4. Communicated by ...
JOURNAL OF OPTIMIZATIONTHEORY AND APPLICATIONS: Vol. 91, No. 3, pp. 643~549, DECEMBER 1996
Generating Well-Behaved Utility Functions for Compromise Programming1 M . A. MORON, 2 C. ROMERO, 3 AND F. R. R u I z DEL PORTAL 4
Communicated by P. L. Yu
Abstract. The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programruing. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum. Key Words. Compromise programming, utility theory, multicdteria analysis, choice theory, economic optimization.
1. Introduction Compromise programming (CP) is a well-known approach o f operations research/management science, developed by Yu and Zeleny in the early seventies (see Refs. 1-3). The original approach has led to experimentally important theoretical developments as well as many practical applications; see Ref. 4, Chapter 4 for a review. The structure o f a CP problem for a
due to the reviewers for their helpful suggestions. The English editing by Ms. Christine M6ndez is appreciated. The authors have been supported by the Comisi6n Interministerial de Ciencia y Tecnologia (CICYT), Madrid, Spain. 2AssociateProfessor, Unidad Docente de Matem~ticas, EscuelaT6cnicaSuperiorde Ingenieros de Montes, Universidad Polit6cnicade Madrid, Madrid Spain. 3professor, Departamento de Economia y Gesti6n, Escuela T6cnica Superior de Ingenieros de Montes, Universidad Polit6cnicade Madrid, Madrid, Spain. 4Associate Professor, Departamento de Geometda y Topologia, Facultad de Ciencias Matem~ticas, Universidad Complutense de Madrid, Madrid, Spain. IThanks are
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bicriterion case can be summarized as follows: min
L,~= (coT(x* - xl) '~+ co'~'x* 2~ z-Xz)~) 1/~,
(la)
s.t.
T(xl, x2) =k, 0 < x l
