On the equivalence between compromise programming and the use of composite compromise metrics.

This paper analyzes the relationship between Compromise Programming and a close relative called Composite Programming that is based on the use of composite metrics. More specifically, it focuses on the possibility that the results of Compromise Programming are equivalent to those obtained with a particular case of Composite Programming in which a linear combination between the two bounds of the compromise set is established. Several situations, depending on the number of criteria involved and the mathematical structure of the efficient set, are studied. The most relevant result is obtained when two criteria are involved and the efficient set is continuously differentiable. In this case, it is possible to find a unique equivalent value of the control parameter in Composite Programming for each metric in Compromise Programming. It is remarked that this particular case is very relevant in many economic scenarios. On the other hand, it turns out that the equivalence between both approaches can not be extended to the case with more than two criteria.