A review of Dynamic Data Envelopment Analysis: state of the art and applications

• Author: Fernanda B.A.R. Mariz,Mariana R. Almeida,Daniel Aloise
• Published date: 01 March 2018
• Date: 01 March 2018
• DOI: http://doi.org/10.1111/itor.12468

Intl. Trans. in Op. Res. 25 (2018) 469–505

DOI: 10.1111/itor.12468

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

A review of Dynamic Data Envelopment Analysis: state of the

art and applications

Fernanda B.A.R. Mariza, Mariana R. Almeidaband Daniel Aloisec

aFederal Institute of Education Science and Technology of Rio Grande do Norte, Logistics, S˜

ao Gonc¸alos, Rio Grande do

Norte, Brazil

bDepartment of Industrial Engineering, Federal University of Rio Grande do Norte, Natal, Rio Grande do Norte, Brazil

cDepartment of Computer Engineering, ´

Ecole Polytechnique de Montr´

eal, Montr´

eal, Canada

E-mail: rocha_fernanda@outlook.com [Mariz]; almeidamariana@yahoo.com [Almeida];

daniel.aloise@polymtl.ca [Aloise]

Received 9 January 2017; received in revised form16 August 2017; accepted 23 August 2017

Abstract

This article reports the evolution of the literature on Dynamic Data Envelopment Analysis (DDEA) models

from 1996 to 2016. Systematic searches in the databases Scopus and Webof Science were performed to outline

the state of the art. The resultsenabled the establishment of DDEA studies as the scope of this article,analyzing

the transition elements to represent temporal interdependence. The categorization of these studies

enabled the mapping of the evolution of the DDEA literature and identification of the relationships between

models. The threemost widely adopted studies to conduct DDEA research were classified as structuring mod-

els. Mapping elucidated the literature behavior through three phases and showed an increase in publications

with applications in recent years. The analysis of applications indicatedthat most studies address evaluations

in the agriculture and farming, banking and energy sectors and consider the facilities as transition elements

between analysis periods.

Keywords:data envelopment analysis; structuring models; dynamic DEA; efficiency

1. Introduction

Measuring efficiency has become a key indicatorto control and plan the performance of production

units. The dissemination of quantitative methods to assess this measure and to assist managerial

decision-making has been especially driven by the development of Data Envelopment Analysis

(DEA). DEA measures the efficiency of a series of Decision-Making Units (DMUs) using linear

programming models (Charnes et al., 1978).

For over three decades of studies, DEA has evolved considerably in an attempt to improve

its modeling to include new analysis criteria and to represent the complexity of current systems

(Emrouznejad et al., 2008; Cook and Seiford, 2009; Kao, 2014). This evolution also enabled a large

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Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

USA.

470 F. Mariz et al. / Intl. Trans.in Op. Res. 25 (2018) 469–505

number of real applications in various sectors and further stimulated the interest of academics and

professionals in conducting research studies (Liu et al., 2013a, 2013b).

Dynamic DEA (DDEA) results from this search work toward refining the DEA model with the

aim of measuring the efficiency of DMUs over time. The main difference and specificity of the struc-

ture of dynamic models are the inclusion of transition elements between subsequent observations

of activities, which establish the interdependence between periods (Tone and Tsutsui, 2010).

First introduced by F¨

are and Grosskopf (1996), DDEA modeling encompasses 20 years of

development, with different approaches and applications to measure dynamic efficiency in real

problems through the contribution of several authors worldwide. The first overview of the state of

the art of dynamic models was conducted by Fallah-Fini et al. (2014) and aimed at discussing the

similarities and differences between dynamic nonparametric approaches that focus on measuring

the performance of companies and aspects of production processes.

Subsequently, Kao (2014) reviewed the DEA network models, particularly discussing modeling

structures, whichalso covered several DDEA studies. The dynamicmodeling contemplates different

configurations and structures. The most used structure is the type of the series structure (Kao,

2014). Dynamic models measure the efficiency in an aggregated perspective, where a link variable

interconnects the periods. With the advances of hybrid modeling, the Dynamic Network DEA

(DNDEA) has emerged as a tool to evaluate the efficiency considering the dependence between

internal evaluation periods and sub-processes (Kao, 2014; Tone and Tsutsui, 2014).

The study by Fallah-Fini et al. (2014), in particular, differs from the present study because it

covers dynamic models devised by methods beyond the scope of DEA. The present study focuses

exclusively on DDEA models in different compositions, especially with the presenceof inter mediate

elements in the modeling structure.

Accordingly, the present study contributes to previous reviews by Fallah-Fini et al. (2014) and

Kao (2014) by reporting the evolution of the literature on dynamic models within DEA through the

organization of the state of the art from 1996 to 2016. The contributions of this review include the

following: (a) evaluation of the design of DDEA models over time; (b) outlining of the phases of

the DDEA literature; (c) identification of the structuring dynamic models; and (d) analysis of the

main characteristics of modeling applications.

In the section that follows, we first introduce the basic concepts of DDEA. Section 3 describes the

dataset and the method of analysis. Section 4 shows the evolution of the DDEA literature through

the following elements: literature phases, structuring models and applications. Section 5 presents

future research directions. Finally, the last section draws conclusions, including insights from the

analysis frameworks that could be helpful to researchers and practitioners interested in applying

DDEA models.

2. Dynamic DEA

Consider a set of “n” units to be evaluated. Each unit uses different quantities of “m” types of input

to produce “s” types of outputs. One DMUjuses the quantity xij of input “i”(i=1, ...,m)and

produces the quantity yrj of output “r”(r=1, ...,s).

Figure 1 represents the structure of a conventional efficiency evaluation system of any “j”DMU

for three time periods (t–1; t;t+1). Each period is analyzed separately with its inputs and

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F. Mariz et al. / Intl. Trans.in Op. Res. 25 (2018) 469–505 471

Period t Period t + 1Period t -1

Fig. 1. Static comparison of a DMU’s performance in three periods. [Colour figure can be viewedat

wileyonlinelibrary.com]

outputs, showing no DMUjrelationship between periods. The efficiency measure using classical

DEA modeling is calculated by tmodels to assess the DMU performance year by year.

However, there are several limitations of classical modeling that must be considered in their

application (Dyson et al., 2001; Jafarian-Moghaddam and Ghoseiri, 2012; Toneand Tsutsui, 2014).

DEA models overlook the effects of the use of inputs and of managerial decisions in a specific

period on the level of outputs in the following periods. This oversight assumes that the production

capacity of the DMU is immediately adjusted and thatthere are no medium- and long-term impacts

resulting from decisions. Therefore, models with such characteristics are termed static (Fallah-Fini

et al., 2014).

Evaluations of DMUs’ efficiency subject to temporal interdependence are aimed at optimizing

performance based on the resource allocationand production decisions of the units over time. Under

these conditions, a dynamic modeling structure must be considered for the analysis of DMUs.

The DDEA model measures the interdependence between different periods (Sueyoshi and

Sekitani, 2005) because it incorporates transition activities between periods, establishing the per-

formance relationships of the DMU over time (Tone and Tsutsui, 2010; Kao, 2013). DDEA uses

specific elements to represent and quantify the dependence between periods resulting from the dy-

namics of factors, including information,the characteristics of organizational systems, their physical

structure, etc. (Fallah-Fini et al., 2014).

Accordingly, Fallah-Fini et al. (2014) claim that temporal interdependence between different

periods results from the isolated or concomitant presence of elements, including the following: (a)

inventories; (b) production delays; (c) capital or quasi-fixed points; (d) adjustment costs; and (e)

incremental development.

Figure 2 shows the dynamic structure of performance evaluation for three periods of time

(t–1;t;t+1). The intermediates zt

fj

, which were not observed in the previous structure (Fig. 1),

represent the variables accounting for the temporal relationships of the DMUs. Each DMUjhas

“g” intermediates zt

fj ∈Rg

+(f=1,...,g) remaining from period “t” that are used as inputs in the

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies