Handling Uncertainties in Linear Programming Models

A frequently used approach to linear programming problems with only vaguely known coefficients of the objective function is to treat these coefficients as random variables; this means that the lack of knowledge is described by a distribution function. For the case in which such a procedure cannot be justified, S.Ya. Chernavsky and A.D. Virtzer of the working Consultative Group for the President of the Academy of Sciences of the USSR developed a decision theoretical approach, some aspects of which are described here for pedagogical purposes. In this paper first the problem of handling uncertainties in linear programming models is outlined, and the decision criteria to be used are explained. Thereafter, a method of finding optimal strategies under uncertain values of the objective function coefficients is described. Finally, the method is applied to a simple uncertainty case of the MESSAGE model