Undesirable Component Set and Duality Theory

The purpose of this paper is to introduce an undesirable component set. Physically, this set depicts all possible inputs and bad outputs combinations that can produce desirable outputs. Literature about traditional combined environmental and productive performance studies consider specific situations focusing on desirable and undesirable outputs. Therefore, there is a room to define a new vision focusing on the undesirable components. The main goal of this methodological contribution is to show that the earlier standard combined environmental and productive performance measures can be implemented in an undesirable component-oriented case. The innovative undesirable component efficiency measure leads to a new duality results between an undesirable component directional distance function and the combined environmental and productive cost function