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LINEAR PROGRAMMING WITH MULTIPLE OBJECTIVE . FUNCTIONS

R. BENAYOUN, О. I. LARITCHEV, J. DE MONTGOLFIEn, J. TEHONY

This paper describes a method of .solving linear programming problems with mul-• tiple objective functions. In this type of problems it is often necessary to replace the concept of (optimum by that of <best compromise. Three major classes of problems are investigated: those where the relative importance of the objective functions is quan­tified; those where it is known but is unquantifiable and thoso where it is completely unknown. The method described involves a sequential investigation of the solutions. This investigation is to some extent guided by the decision maker who intervenes by means of definite responses to the questions posed by the algorithm. The method is il­lustrated by an application of Manpower Management