Upgrading inefficient decision making units (with negative data) towards common weights (using DEA)
Subject Areas : Operation Research
1 - Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
Keywords: Data envelopment analysis, Negative data, Common weights, Inefficient Units, SORM,
Abstract :
The main purpose of this paper is to upgrade and improve inefficient units by common weights obtained from all units studied. In fact, we consider the common weight vector as the direction in which inefficient units rise. The methodology of this research is to consider the semi-essential radial model and we want to use the duality of this model to find the common weights of inputs and outputs, some of which are negative. For this purpose, we present a multi-objective problem of generating common weights and use ideal programming to solve it, which leads to the production of a nonlinear problem, which for this particular problem, by a linearization method, is called We turn a linear programming problem. Since the necessary and sufficient condition for the boundary of the semi-essential radial model in the nature of input (output) is that there is an input (output) with at least one positive value, so we observe this condition here. Finally, we will explain our method with an example and the remarkable thing about the promotion method in the present study is that negative data is promoted and improved as negative data.
Amin G R and Toloo, M (2007). Finding the most efficient DMUs in DEA: an improved integrated model. Computer & Industrial Engereeing, 52, 71-77.
Briec, W and Kerstens, K (2009). Infeasibilities and directional distance functions with application to the determinateness of the Luenberger productivity indicator. Journal Optimization Theory and Applications, 141, 55-73.
Cooper, W W, Park, K S and Pastor, J T (1999). RAM: a range measure of inefficiency for use with additive models, and relations to other models and measures in DEA. Journal of Productivity Analysis, 11, 5-42.
Davoodi, A and Rezai, H ZH R (2012). Common set of weights in data envelopment analysis: a linear programming problem. Centeral European Journal of Operations Research, Springer Science. 20, 355-365.
Emrouznejad, A, Anouze, A L and Thanassoulis, E (2010). A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. European Journal of Operational Research, 200(1), 297-304.
Franklin, Liu F-H and Hsuan Peng H (2008). Ranking of units on the DEA frontier with common weights. Computer.Operational Research. 35, 1624-1637.
FarzipoorSaen. Moghaddas Z., Vaez-Ghesemi, M., Hosseinzadeh Lotfi F. (2020). Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants. R. scientia iranica. DOI.10.24200/SCI.2020.55350.4184.
Jahanshahloo, G R Hossinzadeh Lotfi F Khanmohammadi M Kazemimanesh M and Rezai V (2010). Ranking of units by positive idea DMU with common weights. Expert System Applications, 37(12), 7483-7488.
Jahanshahloo, G R Zohrebandian, M Alinezhad A Abbasian H Abbasian Naghneh, S Kiani Mavi, R (2010). Finding common weights based on the DM’s preference information. Journal of the Operational Research Society, 1796-1800.
Hosseinzadeh Lotfi, F., Ebrahimnejad A., Vaez-Ghasemi M., Moghaddas Z. (2020). Data envelopment analysis with R, Springer International Publishing.
Makui, A., et al (2008). A goal programming method for finding common weights in DEA with an improved discriminating power for efficiency. Journal of Industrial and Systems Engiereeing, 1(4), 293-303.
Pastor, J Ruiz, J (2007). Variables with negative values in DEA. Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, 63-84.
Portela, M.C.A.S Thanassoulis E Simpson G (2004). A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of the Operational Research Society, 55(10), 1111-1121.
sharp, J A, Liu, W B, Meng, W (2007). A modified slacks-based measure model for data envelopment analysis with 'natural' negative putputs and inputs. Journal of the Operational Research Society, 58, 1672-1677.
Tajik Yabr A. H., Najafi S. E., Moghaddas Z., Shahnazari Shahrezaei P (2022). Interval Cross Efficiency Measurement for General Two-Stage Systems. Mathematical Problems in Engineering. Hindawi
Vaez-Ghasemi M., Moghaddas, Z., Farzipoor Saen R. (2021). Cost efficiency evaluation in sustainable supply chains with marginal surcharge values for harmful environmental factors: a case study in a food industry. Operational Research (Springer Berlin Heidelberg). 1-16