A DEA production technology and its usage for incorporation of collaboration in efficiency analysis: an axiomatic approach

• DOI: http://doi.org/10.1111/itor.12325
• Published date: 01 May 2019
• Date: 01 May 2019
• Author: Mojtaba Ghiyasi

Intl. Trans. in Op. Res. 26 (2019) 1118–1134

DOI: 10.1111/itor.12325

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A DEA production technology and its usage for incorporation

of collaboration in efficiency analysis: an axiomatic approach

Mojtaba Ghiyasia,b

aFaculty of Industrial Engineering and Management Sciences, Shahrood Universityof Technology, Shahrood, Semnan

68259, Iran

bDepartment of Business and Economics, Centreof Health Economics Research (COHERE), University of Southern

Denmark, Odense, Denmark

Received 14 August2015; received in revised form 13 March 2016; accepted 27 May 2016

Abstract

Data envelopment analysis (DEA) is a method used to estimate the relative efficiency of decision-making

units (DMUs) that use multiple inputs to produce multiple outputs. A number of different production

possibility sets are defined from a dual point of view in the DEA literature; the convex cone, convex hull,

free disposal hull, free replicability hull, and free coordination hull, each having different properties. This

article introduces a novel DEA production technology that considers the possibility of aggregating units,

so it assesses the performance of each unit compared with both individual and aggregated units. Hence,

this technology provides a more competitive environment for DMUs to achieve an efficient frontier. On the

other hand, possible collaboration between DMUs can be considered using this technology. The strength

and practical relevance of the proposed technology is shown in the efficiency analysis of Danish hospitals

in a collaborative environment. This yields a bi-classification of hospitals, namely resistant and nonresistant

hospitals. The proposed technologyhas a general framework, and the associated model is easy to solve using

standard DEA software. It follows that the current article could potentially be used in other theoretical and

empirical research in the future.

Keywords:data envelopment analysis; hospital performance; collaboration; additivity

1. Introduction

Efficiency analysis plays an important role in decision-making processes and has been a subject

of great interest as organizations have struggled to improve productivity. Consequently, several

different methodologies have been investigated to deal with different aspects of efficiency analysis.

Farrell (1957) published a comprehensive article on frontier efficiency analysis for the single output

case. Based on this technology, Charnes et al. (1978) developed data envelopment analysis (DEA),

a mathematical programming technique used to estimate the efficiency of decision-making units

(DMUs) for multiple input and multiple output case. After many years of development, this model

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M. Ghiyasi / Intl. Trans. in Op. Res. 26 (2019) 1118–1134 1119

has become a useful tool for management and policy making. Since its conception three decades

ago, several different reference technologies have been introduced into DEA literature, allowing the

technology to assess different aspects of the real world. However, in order to properly benchmark

and assess the performance of a set of units, an appropriate production possibility set (PPS) must

be defined.

After the first paper on DEA developed byCharnes et al. (1978), which assumed constant returns-

to-scale (CRS) for reference technology, in order to estimate both technical and scale efficiencies,

Banker et al. (1984) proposed another model that has variable returns-to-scale (VRS) properties.1

They proposed a PPS based on the convex hull of individual units and strong disposability as-

sumption. Later, Fare et al. (1985) employed nonincreasing (decreasing) returns-to-scale (DRS)

technology in efficiency estimation. In a different framework from DEA models, Koopmans (1977)

proposed another form of nonincreasing returns-to-scale technology. Grosskopf (1986) showed

Koopman’s technology in DEA framework and pointed out that it includes the sum of the individ-

ual units and comprises Fare et al.’s technology. Free disposal hall (FDH),2which is a nonconvex

PPS, was introduced by Deprins et al. (1984). This model is equivalent to the model of Banker et al.

(1984), if only binary intensity variables are considered. Recently, Green and Cook (2004) were

inspired by Koopman and proposed a nonconvex PPS known as free coordination hall (FCH),3

where a given DMU’s performance is assessed not only againstthe individual DMUs included in the

sample but also against composite DMUs obtained by aggregation. As Bogetoft and Otto (2010)

mention, additivity is an appealing assumption because one might, for example, imagine that the

two original production sites were built next door and were run under independent managements.

There may be potential possibility of merging two different production sites, although they run

under independent managements before merging. Using the original inputs, the sites should there-

fore be able to produce the same output, and the firm should be able to produce the sum. Some of

the current reference technologies accept additivity assumption, but these technologies presuppose

restrictive properties on returns to scale of the technology.4It is worth pointing out that in the real

world, as long as we do not have specific knowledge about the returns to scale of technology, we

cannot impose any specific property about the returns to scale of the reference technology. There-

fore, scale of production unit plays an important role in efficiency analysis. Asmild et al. (2013)

show the importance of scale in efficiency analysis of Canadian public hospitals.

In order to overcome the aforementioned drawbacks, this article introduces a new PPS and

provides an axiomaticapproach to construct this PPS, which does not require the presupposition of

the returns to scale. This enables decision makers to distinguish the technical and scale efficiencies

of each DMU. In the proposed technology, namely semiadditive (SA) technology hereafter,5each

unit has to compete not only with individual units but also with aggregated units, providing a more

competitive efficient frontier. Moreover, this is a generalized technology from which traditional

DEA technologies can be derived.

1For more details aboutVRS property, see Banker et al. (1984).

2For more details, see Deprins et al. (1984).

3For more details, see Green and Cook (2004).

4This is explained in detail in the next section.

5Section 3.2 explains why we use this appellation.

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