A PARAMETRIC PROGRAMMING SOLUTION TO THE VECTOR MAXIMUM PROBLEM, WITH APPLICATIONS TO DECISIONS UNDER UNCERTAINTY

Some relationships between decision criteria for decision-making under uncertainty and risk are demonstrated. It is suggested that several criteria should be considered simultaneously so as to yield a vector maximum problem to be solved. It is shown that under certain conditions such a vector maximum problem can be reformulated as an equivalent parametric concave programming problem of the form Maximize ab x 1-a c x subject to d x or 0 i1,...,m for each fixed value of a in the unit interval, where fb and c are strictly concave functions of the decision vector x, the constraint functions are concave, and certain additonal regularity conditions are satisfied. A class of computational algorithms, based on maintaining a solution to the relevant Kuhn-Tucker conditions as a varies, is given for solving such programs. It is to be noted that the present algorithms also provide a deformation method for nonparametric concave programming. Illustrative examples are presented.