Nonparametric Model of Preferred Efficiency for Interval Scale Data (DEA)
محورهای موضوعی : Data Envelopment Analysis
حسین عباسیان
1
(استادیار دانشکده ریاضی، دانشگاه آزاد اسلامی، واحد علی آباد کتول، علی آباد کتول، ایران)
کلید واژه: DEA, Preferred Efficiency, Interval Scale, Common Weights, Returns to Scale.,
چکیده مقاله :
The obtained benchmarks and preferred efficiency scores are strongly dependent on the selected Most Preferred Solution (MPS) units. The new directional value-based measures are more general than the existing preferred-based measures. We examine the use of interval scale (IS) variables, particularly when the IS variable represents the difference between two variables (such as sales) that serve as inputs and/or outputs. Data Envelopment Analysis models are widely used in commercial firms to assess their technical, cost, and revenue efficiencies. The new models that are introduced in this study are based on inverse DEA, which helps to preserve cost and revenue efficiency. we use a metric called Preferred Efficiency (PE) to measure the efficiency of Decision Making Units (DMUs) that have negative data derived from IS variables. PE is a concept that takes into account the DM's preferences while searching for the Most Preferred combination of DMU inputs and outputs that are efficient in DEA. Moreover, we approximate the indifference contour of the unknown Preferred Function (PF) at the MPS by using a supporting hyper plane on the production possibility set (PPS) at MPS. We propose to assume that it is tangent on the indifference contour of PF. We use radial DEA problems with Variable Returns to Scale (VRS), specifically BCC models, at the combination orientation where both outputs are maximized and inputs are minimized. We also decompose each IS variable into two Ratio Scale (RS) variables. Then, we use a compromise solution approach to generate Common Weights (CW) for the decomposed input/output variables. We will be introducing an MOLP model that uses input and output variables as objective functions. Moreover, the resulting performance evaluation scores and the corresponding methodology can be utilized to address practical issues with the aforementioned models.
The obtained benchmarks and preferred efficiency scores are strongly dependent on the selected Most Preferred Solution (MPS) units. The new directional value-based measures are more general than the existing preferred-based measures. We examine the use of interval scale (IS) variables, particularly when the IS variable represents the difference between two variables (such as sales) that serve as inputs and/or outputs. Data Envelopment Analysis models are widely used in commercial firms to assess their technical, cost, and revenue efficiencies. The new models that are introduced in this study are based on inverse DEA, which helps to preserve cost and revenue efficiency. we use a metric called Preferred Efficiency (PE) to measure the efficiency of Decision Making Units (DMUs) that have negative data derived from IS variables. PE is a concept that takes into account the DM's preferences while searching for the Most Preferred combination of DMU inputs and outputs that are efficient in DEA. Moreover, we approximate the indifference contour of the unknown Preferred Function (PF) at the MPS by using a supporting hyper plane on the production possibility set (PPS) at MPS. We propose to assume that it is tangent on the indifference contour of PF. We use radial DEA problems with Variable Returns to Scale (VRS), specifically BCC models, at the combination orientation where both outputs are maximized and inputs are minimized. We also decompose each IS variable into two Ratio Scale (RS) variables. Then, we use a compromise solution approach to generate Common Weights (CW) for the decomposed input/output variables. We will be introducing an MOLP model that uses input and output variables as objective functions. Moreover, the resulting performance evaluation scores and the corresponding methodology can be utilized to address practical issues with the aforementioned models.
Dimitris K. Despotis and Dimitris Sotiros, (2017), Value-based data envelopment analysis: A piece-wise linear programming approach, International Journal of Multicriteria Decision Making 4(1):47 – 68.#
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.#
Gerami J., Mozafari M.R., Wanke P.F., Improving information reliability of non-radial value efficiency analysis: An additive shacks based measure approach, European Journal Operational Research, 298(3) (2022) 967-978.#
Halme M., Joro J., Korhonen P., Salo S., Wallenius J., A value efficiency approach to incorporating preference information in data envelopment analysis, Management Science, 45(1999) 103-115.#
Hosseinzadeh Lotfi, F., Ebrahimnejad A., Vaez-Ghasemi M., Moghaddas Z. (2020). Data envelopment analysis with R, Springer International Publishing.#
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.#
Joro T., Korhonen P., Zionts S., An interactive approach to improve estimates of value efficiency in data envelopment analysis, European Journal Operational Research, 149(2003) 688-699.#
Khosro Soleimani-Chamkhorami, F. Lotfi, G. Jahanshahloo, M. Rostamy-Malkha, (2020) Preserving cost and revenue efficiency through inverse data envelopment analysis models, nformation systems and operational research, 58(4):1-18.#
Korhonen P., Syrjanen M.J., on the interpretation of value efficiency, Journal Productivity Analysis, 24(2005) 197-201.#
S. Stanek, D. Kuchta, (2020), Increasing earned value analysis efficiency for IT projects, Journal of Decision Systems, 29(1):1-9.#
Tajik Yabr A.H., Najafi S.E., Moghaddas C., Shahnazaei P., Interval cross efficiency measurement for general two-stage systems, Mathematical preblems in Enginnring Hindawi,(2022) Article ID 5431358, 19 pages.#
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.#
Zohrabandan M., Using Zionts-Wallenius method to improve estimate of value efficiency in DEA, Applied Mathematical Modeling, 35(2011) 3769-3776.#
