## Outcome space partition of the weight set in multiobjective linear programming.(English)Zbl 1028.90051

Summary: Approaches for generating the set of efficient extreme points of the decision set of a multiple-objective linear program (P) that are based upon decompositions of the weight set $$W^0$$ suffer from one of two special drawbacks. Either the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for problem (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 correspondence with the efficient extreme points of $$Y$$. As a result, the drawbacks of the decompositions of $$W^0$$ based upon the decision set of problem (P) disappear. The article explains also how this new partition offers the potential to construct algorithms for solving large-scale applications of problem (P) in the outcome space, rather than in the decision space.

### MSC:

 90C29 Multi-objective and goal programming 90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)