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Mathematical Problems in Engineering
Volume 2014, Article ID 675895, 6 pages
Research Article

Undesirable Outputs’ Presence in Centralized Resource Allocation Model

Department of Mathematics, Islamic Azad University, Central Branch, Tehran, Iran

Received 15 July 2014; Revised 25 August 2014; Accepted 28 August 2014; Published 15 September 2014

Academic Editor: Vikas Kumar

Copyright © 2014 Ghasem Tohidi 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.


Data envelopment analysis (DEA) is a common nonparametric technique to measure the relative efficiency scores of the individual homogenous decision making units (DMUs). One aspect of the DEA literature has recently been introduced as a centralized resource allocation (CRA) which aims at optimizing the combined resource consumption by all DMUs in an organization rather than considering the consumption individually through DMUs. Conventional DEA models and CRA model have been basically formulated on desirable inputs and outputs. The objective of this paper is to present new CRA models to assess the overall efficiency of a system consisting of DMUs by using directional distance function when DMUs produce desirable and undesirable outputs. This paper initially reviewed a couple of DEA approaches for measuring the efficiency scores of DMUs when some outputs are undesirable. Then, based upon these theoretical foundations, we develop the CRA model when undesirable outputs are considered in the evaluation. Finally, we apply a short numerical illustration to show how our proposed model can be applied.