Congestion and non-congestion areas: identify and measure congestion in DEA

Department of mathematics, Yadegar-e-Imam Khomeini (RAH), Shahre Rey Branch, Islamic Azad University, Tehran, Iran

^* Corresponding author: muosavi.s.r1982@gmail.com; s_r_ muosavi@yahoo.com

Received: 1 March 2021
Accepted: 31 May 2022

Abstract

Detecting the weak and strong congestion statuses of decision-making units (DMUs) and measuring them via data envelopment analysis (DEA) is an important issue that has been discussed in several studies and with different views. The efficiency frontier is a concept derived from the underlying production possibility set (PPS), and the congestion concept is related to them. Still, researchers have defined congestion for each DMU in many previous studies and ignored that congestion is linked with the underlying production technology. In the congestion measurement matter, this paper presents two new insights into a congestion area and non-congestion area for production technology and two new mathematical definitions of congestion based on the PPS properties and detecting the weak and strong congestion status of DMUs (CSOD). We prove our definitions are equal to the original definition of congestion. First, we describe the congestion and non-congestion areas based on the PPS; then provide full details of how to measure congestion built on these new insights. Our approaches are very accurate and fast to calculate; they are theoretically elementary and efficient in performance. Our proposed methods can deal with both non-negative and negative data. Finally, an empirical example is provided to illustrate our approaches.