A full investigation of the directional congestion in data envelopment analysis

Abstract

One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs re- sult in increases (decreases) in some outputs without worsening (im- proving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional de nition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or de- creases the inputs dis-proportionally. This means that, the traditional de nition of congestion in DEA may be unable to measure the con- gestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two di erent scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear pro- gramming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two nu- merical examples.

A new method of determining decision-making unit congestion under inter-temporal dependence

“…Mehdiloozad et al (2020) specified the congestion using a maximal element of a non-negative polyhedral set and by solving a linear programming model. Khezri et al (2019) obtained directional congestion in a situation where at least one input or output direction is not known but still did not study dynamic DEA congestion with inter-temporal dependence between input and output levels. In this paper, congestion calculation method of dynamic DEA under inter-temporal dependence of input and output levels is studied.…”

A New Method for Recognizing the Input Congestion in Data Envelopment Analysis

“…For example, in the case of strong or weak congestion, the precise direction, along which the congestion occurs, cannot be recognized. To tackle this drawback, Yang (2015), Khezri et al (2021) considered the definition of the directional congestion along certain input and output directions. This paper concentrates on offering a method to recognize the congestion of units so that the DM may decide about increasing or decreasing the size of a particular DMU.…”

New Method of Determining Decision Making Unit Congestion under Inter-Temporal Dependence

“…Mehdiloozad et al (2020) specified the congestion using a maximal element of a non-negative polyhedral set and by solving a linear programming model. Khezri et al (2019) obtained directional congestion in a situation where at least one input or output direction is not known but still did not study dynamic DEA congestion with inter-temporal dependence between input and output levels. In this paper, congestion calculation method of dynamic DEA under inter-temporal dependence of input and output levels is studied.…”