Outcome space partition of the weight set in multiobjective linear programming

Approaches for generating the set of efficient extreme points of the decisi on set of a multiple-objective linear program (P) that are based upon decom positions of the weight set W-0 suffer from one of two special drawbacks. E ither the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for prob lem (P) can be decomposed into a partition based upon the outcome set Y of the problem, where the elements of the partition are in one-to-one correspo ndence with the efficient extreme points of Y. As a result, the drawbacks o f the decompositions of W-0 based upon the decision set of problem (P) disa ppear. The article explains also how this new partition offers the potentia l to construct algorithms for solving large-scale applications of problem ( P) in the outcome space, rather than in the decision space.