Measuring congestion by anchor points in DEA

Abstract

One of the most important issues in microeconomics is congestion. In general, an increase in inputs will result in an increase in outputs. However, in some cases, it does not happen. Hence, in these situations congestion occurs. The existence of the congestion reduces efficiency of Decision Making Units (DMUs), so determination of congestion is highly regarded. Some studies suggested methods to determine the congestion via solving conventional Data Envelopment Analysis (DEA) models, in which first an inefficient unit was depicted on the BCC frontier. However, sometimes, some optimal projections are obtained, where some previous models encounter problems. In this paper, according to S-shape form of the production function and with respect to the geometric features of anchor points, we have developed an algorithm by the connection between the anchor points and congestion definition. In this algorithm, with no need for efficiency value and projecting the inefficient DMUs on BCC efficiency frontier, only by determining the anchor point with the largest output and comparing inefficient units with it, with an easier calculation, and solving conventional DEA models, congested DMUs and their status of congestion are obtained and their values are calculated. At the end, the proposed algorithm is illustrated by some examples and the results are compared to those of the existing methods.