Trade‐offs in integer data envelopment analysis

• Author: Mohammadreza Rafiee Sani,Mohammadreza Alirezaee
• DOI: http://doi.org/10.1111/itor.12255
• Date: 01 November 2018
• Published date: 01 November 2018

Intl. Trans. in Op. Res. 25 (2018) 1997–2007

DOI: 10.1111/itor.12255

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Trade-offs in integer data envelopment analysis

Mohammadreza Alirezaeea,b and Mohammadreza Rafiee Sania

aSchool of Mathematics, Iran University of Science and Technology (IUST), Tehran, Iran

bCenter for Management of Technology and Entrepreneurship(CMTE), University of Toronto, Ontario, Canada

E-mail: mralirez@iust.ac.ir [Alirezaee]; mr_rafiee@iust.ac.ir [Rafiee Sani]

Received 31 December 2014; receivedin revised form 22 August 2015; accepted 23 November 2015

Abstract

If production trade-offs—which represent simultaneously feasible exchanges in the inputs and outputs of

decision-making units (DMUs)—are added to an integer production possibility set (IPPS), a new IPPS is

produced; conventional axioms of production do not generate a new IPPS, however. This paper develops

the axiomatic foundation for data envelopment analysis (DEA) for integer-value inputs and outputs in the

presence of production trade-offs by introducing a new axiom of “natural trade-offs.” First, a mixed-integer

linear programmingformula called an integer DEA trade-off (IDEA-TO) is presented for computing efficiency

scores and reference points. The numeration algorithm (NA) method presented in this concept is improved,

and an improved numeration algorithm (INA) method for solving integer DEA (IDEA) models is developed.

Finally, comparison between the two methods and a generalized INA method for solving the IDEA-TO

model are presented.

Keywords:data envelopment analysis; trade-offs; integer data; reference point

1. Introduction

In data envelopment analysis(DEA), the efficiency of decision-making units (DMUs) is assessed by

solving two models that contain dual linear programming problems. These problems are referred to

as the envelopment and multiplier forms of DEA models (Cooper et al., 2000; Thanassoulis, 2001).

Often, in order to improve the discrimination of the analysis, additional weight restrictions are

incorporated in the multiplier form of DEA models. In most cases, the construction of weight

restrictions is based on value judgments concerning the importance that the decision maker places

on the inputs and outputs (Podinovski,2004). Another approach to improving DEA models is based

on incorporating production trade-offsin the envelopment form of DEA models (Podinovski, 2004,

2005). A trade-off is a decision-makers’ judgment between inputs and outputs, and it is feasible for

all DMUs. In addition, trade-offsrepresent all technologically possible simultaneous changes to the

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