Identification of Congestion in DEA

Abstract

Productivity is a common descriptive measure for characterizing the resource-utilization performance of a production unit, or decision making unit (DMU). The challenge of improving productivity is closely related to a particular form of congestion, which reflects waste (overuse) of input resources at the production unit level. Specifically, the productivity of a production unit can be improved not only by reducing some of its inputs but also simultaneously by increasing some of its outputs, when such input congestion is present. There is thus a need first for identifying the presence of congestion, and then for developing congestion-treatment strategies to enhance productivity by reducing the input wastes and the output shortfalls associated with such congestion. Data envelopment analysis (DEA) has been considered a very effective method in evaluating input congestion. Because the assumption of strong input disposability precludes congestion, it should not be incorporated into the axiomatic modeling of the true technology involving congestion. Given this fact, we first develop a production technology in this contribution by imposing no input disposability assumption. Then we define both weak and strong forms of congestion based on this technology. Although our definitions are made initially for the output-efficient DMUs, they are well extended in the sequel for the output-inefficient DMUs. We also propose in this contribution a method for identifying congestion. The essential tool for devising this method is the technique of finding a maximal element of a non-negative polyhedral set. To our knowledge, our method is the only reliable method for precisely detecting both weak and strong forms of congestion. This method is computationally more efficient than the other congestion-identification methods developed in the literature. This is due to the fact that, unlike the others, our method involves solving a single linear program. Unlike the other methods, the proposed method also deals effectively with the presence of negative data, and with the occurrence of multiple projections for the output-inefficient DMUs. Based on our theoretical results, three computational algorithms are developed for testing the congestion of any finite-size sample of observed DMUs. The superiority of these algorithms over the other congestion-identification methods is demonstrated using four numerical examples, one of which is newly introduced in this contribution.