Congestion: Relation between traditional DEA congestion and two-stage processes congestion

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

^* Corresponding author: hadi_bagherzadeh@yahoo.com

Received: 1 June 2022
Accepted: 30 December 2023

Abstract

Congestion is a kind of inefficiency because it causes the decision-making units (DMUs) to be inefficient and reduces their output. Identifying inefficient DMUs and determining the cause of their inefficiencies has been one of the most important reasons for referring to the internal structure of DMUs and analyzing the effect of intermediate products on the subDMU’s (or stages) performance. In this paper, to characterize the cause of the DMU’s congestion, we refer to its internal structure as a two-stage network data envelopment analysis (DEA) and decompose the DMU’s congestion into black-box (BB) and two-stage structure congestion. Also, inputs have two separate and simultaneous roles; black-box inputs role and stage1’s input role, so three congestion types occur. Thus, we sought to analyze the relation between two types of initial inputs congestion, intermediate products congestion, and express their effects on BB congestion. Finally, we define three congestion definitions and model the relation between two types of input congestion, intermediate products congestion, and BB inputs congestion. Finally, a practical example illustrates the proposed method.