Identification of congestion in data envelopment analysis under the occurrence of multiple projections: A reliable method capable of dealing with negative data

To detect the weak and strong congestion statuses of decision making units (DMUs) via data envelopment analysis (DEA), first, a technology is constructed under the assumptions of convexity and strong output disposability. Then, the congestion of any inefficient DMU is defined at its projection on the efficient frontier of this technology. It has, however, been argued that this definition is not precise under the occurrence of multiple projections. In this paper, therefore, we propose a single-stage linear programming (LP) model to recognize the evidence of congestion. Our model precisely distinguishes between the DMUs exhibiting weak—but not strong—congestion and those suffering from strong congestion, and identifies the full-efficient DMUs as well. To cope effectively with the occurrence of multiple projections, we first prove that all relative interior points of a face exhibit the same type of congestion. Based on this finding, we define the congestion of an inefficient DMU at its MAX-projection—a projection that lies in the relative interior of the corresponding minimum face. Then, by showing that the global reference set spans the minimum face, we propose an LP model for identifying the MAX-projection. We highlight a theoretically interesting and practically useful consequence of our results that the congestion status of an inefficient DMU can be determined based on those of its reference DMUs. Furthermore, our proposed method can deal with negative data, and is also computationally more efficient than the existing approaches. Finally, three numerical examples are presented to illustrate the use of our proposed method.