Modified MAJ model for ranking decision making units in data envelopment analysis

Abstract

Efficiency Data Envelopment Analysis (DEA) models assessing decision making units (DMUs) are unable to discriminate between efficient DMUs. From experience, we know that usually plural DMUs are efficient. To discriminate between these efficient DMUs is an interesting subject. To this aim, super-efficiency models are proposed. In this paper we study a super-efficiency model, namely MAJ. Each time an efficient DMU is excluded from the set of the observed DMUs, a new production possibility set (PPS) is obtained. In this model, ranking is done based on the position of each excluded efficient DMU in relation to its corresponding new PPS. If the efficient DMUs and the new PPSs remain unchanged, it is expected that the ranking, also, remain unchanged. But, in this paper, we show that the technique used for rendering this model unit-invariant causes the ranking to change when some inputs of some inefficient DMUs change, without causing any change in the new PPS. In this paper, we modify this model so that this problem will not occur.