MULTI OBJECTIVE LINEAR PROGRAMMING
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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A linear program is considered with several objective functions. The traditional approach has been either to trade off by weighting each function, or if a trade off vector cannot be provided to ignore all but the most significant. The author is interested in classes of programs whose members possess some common characteristics. Examples are sequences of production, refining, inventory problems over time at one installation. If sufficient conditions exist an estimate of a trade-off vector can be made. This estimate improves over the sequence. A set X exists which contains the solutions obtained by optimizing with respect to all nonnegative combinations of objective functions. A decision maker is not indifferent to these solutions but can characterize preferred solutions. A method is presented whereby he can direct a finite sequence of solutions over X towards a preferred solution. As the estimate of the trade-off vector improves, the expected length of the sequence diminishes, and the efficiency of solution increases.
- Operations Research