Weakly disposable production technology set with undesirable products

The weak disposability assumption within the framework of data envelopment analysis shows how the level of undesirable outputs scales down when the activity level decreases. In the classic weak disposability assumption, all desirable and undesirable outputs are proportionally reduced as a result of activity level reduction. In some real occasions, although all undesirable outputs are directly related to the activity level, some of them should be reduced by reducing the activity level, while others should not. This contribution builds on the weak disposability assumption with non-uniform abatement factors and introduces the directional weak disposability assumption, which reduces the level of undesirable outputs by decreasing the activity level in a specific user-defined direction. It has been demonstrated that the traditional weak disposability assumption is a special case of directional weak disposability assumption. To demonstrate the practical application of the proposed method, we used data from 22 power plants over 7 years. The analysis revealed that the choice of direction plays an important role in evaluating efficiency because it dictates how much weight is given to desirable outputs and how undesirable outputs are taken into account. As a result, different directions yield varying efficiency scores, reflecting the diverse perspectives used to measure the companies' productivity and performance.