Advances in Decision Sciences
Volume 2013 (2013), Article ID 354509, 9 pages
http://dx.doi.org/10.1155/2013/354509
Research Article

Efficiency in the Worst Production Situation Using Data Envelopment Analysis

Md. Kamrul Hossain,1 Anton Abdulbasah Kamil,1 Adli Mustafa,2 and Md. Azizul Baten3

1School of Distance Education, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia
2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia
3Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia, 01610 Sintok, Kedah, Malaysia

Received 28 June 2012; Accepted 10 January 2013

Academic Editor: Graham Wood

Copyright © 2013 Md. Kamrul Hossain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data. The least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study. Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution. Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating the effectiveness of this SDEA model.