Negative valuation of undesirable outputs in evaluating the efficiency of production systems

This paper extends a data envelopment analysis (DEA) model that considers only desirable outputs in measuring efficiencies to incorporate undesirable outputs by requiring the associated multipliers to be negative. It is shown that the proposed model is the ratio-measure counterpart of the difference-measure model existed in the literature. It has the technology of variable returns to scale, and the modification made to it means that it also has the property of null-jointness, satisfies the axiom of weak disposability, and has positive shadow prices, considered as pitfalls in modeling undesirable outputs. In addition to the economic interpretation, the ratio-measure of efficiency of the proposed model better shows the relative performance of a unit than the difference-measure does, and its simpler form also provides a clearer geometric interpretation of efficiency measurement with undesirable outputs