Measuring a Dynamic Efficiency Based on MONLP Model under DEA Control

Subject Areas : International Journal of Data Envelopment Analysis

K. Gholami ¹ , Z. Ghelej Beigi ²

1 - Department of Science, Bushehr Branch, Islamic Azad University, Bushehr, Iran
2 - Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Isfahan, Iran

Received: 2017-01-12 Accepted : 2017-06-17 Published : 2017-09-01

Keywords: Data Envelopment Analysis‎, ‎Decision Making‎ ‎Unit‎, ‎Multi-Objective Programming P, ‎Goal Programming‎. ‎,

Abstract :

Data envelopment analysis (DEA) is a common technique in measuring the relative efficiency of a set of decision making units (DMUs) with multiple inputs and multiple outputs. ‎‎Standard DEA models are ‎‎quite limited models‎, ‎in the sense that they do not consider a DMU ‎‎at different times‎. ‎To resolve this problem‎, ‎DEA models with dynamic ‎‎structures have been proposed‎.‎In a recent paper by afarian-Moghaddam and Ghoseiri [Jafarian-Moghaddam, A.R., Ghoseiri k., 2011. Fuzzy dynamic multi-objective Data Envelopment Analysis model. Expert Systems with Applications, 38 (1), 850-855.] they contribute to an interesting topic by presenting a ‎‎fuzzy dynamic multi-objective DEA model to evaluate DMUs in which ‎‎data are changing with time‎. However, this paper finds that their approach has some problems in the proposed models. In this paper, we first stress the present shortcomings in their modeling and then we propose a new DEA method for improving fuzzy dynamic multi-objective DEA model. The proposed model is a ‎‎multi-objective non-linear programming (MONLP) problem and there are ‎‎several methods for solving it; We use the goal programming (GP) method‎. ‎The proposed model calculates the efficiency scores of DMUs by‎‎ solving only one linear programming problem‎. ‎Finally‎, ‎we present an ‎‎example with ten DMUs at three times to illustrate the applicability the proposed model.

References:

[1] Amin, G.R., Toloo, M., (2007) Finding the most efficient DMUs in DEA: an improved integrated model. Computers & Industrial Engineering, 52, 71-77.

[2] Amirteimoori A., (2006) Data envelopment analysis in dynamic framework. Applied Mathematics and Computation, 181 (1), 21-28.

[3] Chankong, V., Haimes, Y.Y., (1983) Multiobjective decision making: Theory and methodology, Elsevier Science Publishing, New York.