# American Institute of Mathematical Sciences

July  2012, 8(3): 623-637. doi: 10.3934/jimo.2012.8.623

## A common set of weight approach using an ideal decision making unit in data envelopment analysis

 1 Department of Mathematics, Tehran-North Branch, Islamic Azad University, P.O. Box 19585-936, Tehran, Iran 2 Louvain School of Management, Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, L1.03.01, B-1348 Louvain-la-Neuve, Belgium, Belgium 3 Management Information Systems, Lindback Distinguished Chair of Information Systems, La Salle University, Philadelphia, PA19141, United States

Received  September 2011 Revised  January 2012 Published  June 2012

Data envelopment analysis (DEA) is a common non-parametric frontier analysis method. The multiplier framework of DEA allows flexibility in the selection of endogenous input and output weights of decision making units (DMUs) as to cautiously measure their efficiency. The calculation of DEA scores requires the solution of one linear program per DMU and generates an individual set of endogenous weights (multipliers) for each performance dimension. Given the large number of DMUs in real applications, the computational and conceptual complexities are considerable with weights that are potentially zero-valued or incommensurable across units. In this paper, we propose a two-phase algorithm to address these two problems. In the first step, we define an ideal DMU (IDMU) which is a hypothetical DMU consuming the least inputs to secure the most outputs. In the second step, we use the IDMU in a LP model with a small number of constraints to determine a common set of weights (CSW). In the final step of the process, we calculate the efficiency of the DMUs with the obtained CSW. The proposed model is applied to a numerical example and to a case study using panel data from 286 Danish district heating plants to illustrate the applicability of the proposed method.
Citation: Saber Saati, Adel Hatami-Marbini, Per J. Agrell, Madjid Tavana. A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial & Management Optimization, 2012, 8 (3) : 623-637. doi: 10.3934/jimo.2012.8.623
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##### References:
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