Intl. j. Basic. Sci. Appl. Res. Vol., 2 (12), 996-1001, 2013
996
International Journal of Basic Sciences & Applied Research. Vol., 2 (12), 996-1001, 2013
Available online at http://www.isicenter.org
ISSN 2147-3749 ©2013
Several Modes for Assessment Efficiency Decision Making Unit in Data Envelopment
Analysis with Integer Data
Balal Karemi
1
, Ardeshir Bazrkar
2*
, Mahdi Eyni
3
, Ali Abdali
4
1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2
Department of Industrial Management, University of East Azerbaijan Research and Science, Tabriz, Iran
3
Department of Mathematics, Payame Noor University, Tehran, Iran
4
Deputy of Ghavamin Bank, Tehran, Iran
*
Corresponding Author Email: Ardeshir.13@gmail.com
Abstract
The purpose of this study is to use integer data in the DEA model. In the first stage, we
introduced a radial model in which the image was an integer point. Next, we applied this
concept to non-radial models. Finally we used a numerical example with the integer data
which indicated the importance of this concept.
Keyword: DEA, Integer efficiency, Integer additive, Integer SBM, Integer data.
Introduction
Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the relative efficiency of
decision making units (DMUs) with multiple inputs and multiple outputs, where every unit characterized by a pair of non-negative
(j=1,…, n) for real input and output vectors (Cooper et al., 2003; Charnels et al., 1978). The traditional models of
DEA, the data real amount, but in some cases the data has been limited to the integer value. First Lozano and Villa (2006) with an
example highlighted the difference between the two scenarios (Integer & Real) and with the integer constraints on the model
calculated efficiency units. Next the Kuosmanen and Kazemi Matin (2009) introduced the basic principles and proposed a produce
possibility set (PPS) and an integer model to calculate the efficiency integer units. In the following, Kazemi-Matin and Kuosmanen
(2009) with regard to assumption of variable returns to scale and extend principle developed their previous work. In this paper, was
provides a radial integer model to calculate the performance units, integer additive model and then non radial integer model to
calculate the unit's efficiency.
The remaining structure of this study is organized as follows: In section 2 we provided prerequisite of DEA by the integer
data. In section 3, we proposed a radial model and an additive model with integer data and then a non-radial model to calculate the
efficiency of integer units. In section 4, an example from real world is given to address the importance of topic. Section 5 contains
conclusions.
Prerequisites
Supposes are given n decision making units as , that and
are the vectors of non-negative input and output of j units, also and
are the input and output matrices, respectively. In standard DEA models we assumed that all data to be real
values. But the worlds around us, some data has been limited to be integer. First Lozano and Villa (2007) due to these differences
and introducing integer constraints in the context of DEA, introduced a mixed integer linear programming model for performance
units. After them Kuosmanen and Kazemi Matin (2009) by introducing axioms:
1. Envelopment:
2. Natural disposability: