Estimation of efficiency of two-stage processes using a fully fuzzy range-adjusted measure approach and strong complementary slackness conditions

Document Type : Original Article

Authors

1 PhD student, Department of Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran

2 Professor, Department of Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran

3 Professor, Department of Mathematics, Faculty of Basic Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

4 Assistant Professor, Department of Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran

Abstract

In recent decades, the topic of performance measurement has been one of the popular topics for large companies and manufacturers managers . The range - adjusted measurement ( RAM ) model in data envelopment analysis (DEA) is a non - radial model used to evaluate the performance of firms. Due to the presence of uncertain data in many investigations, a fully fuzzy range-adjusted measurement model with strong complementary slackness conditions to find efficient two-stage systems in a reference set is presented in this paper and it is used to evaluate airline . Given that we have a multi-objective network model of fully fuzzy range - adjusted measurement with strong complementary slackness conditions, the proposed model is solved using the lexicograph method . We also compare it with the existing fully fuzzy network DEA - range adjusted measurement model. Finally, we apply this model using the data of 14 Iranian airlines.

Keywords


[1]    Charnes, A., W.W. Cooper, and E. Rhodes, Measuring the efficiency of decision making units. European journal of operational research, 1978. 2(6): p. 429-444.
[2]    Ruggiero, J., Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research, 1998. 111(3): p. 461-469.
[3]    Seiford, L.M. and J. Zhu, Profitability and marketability of the top 55 US commercial banks. Management science, 1999. 45(9): p. 1270-1288.
[4]    Lewis, H.F. and T.R. Sexton, Network DEA: efficiency analysis of organizations with complex internal structure. Computers & Operations Research, 2004. 31(9): p. 1365-1410.
[5]    Yu, M.-M. and E.T. Lin, Efficiency and effectiveness in railway performance using a multi-activity network DEA model. Omega, 2008. 36(6): p. 1005-1017.
[6]    Amirteimoori, A., S. Kordrostami, and H. Azizi, Additive models for network data envelopment analysis in the presence of shared resources. Transportation Research Part D: Transport and Environment, 2016. 48: p. 411-424.
[7]    Kao, C. and S.-N. Hwang, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European journal of operational research, 2008. 185(1): p. 418-429.
[8]    Tone, K. and M. Tsutsui, Network DEA: A slacks-based measure approach. European journal of operational research, 2009. 197(1): p. 243-252.
[9]    Kao, C. and S.-N. Hwang, Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems, 2010. 48(3): p. 437-446.
[10]    Amirteimoori, A. and S. Kordrostami, Production planning in data envelopment analysis. International Journal of Production Economics, 2012. 140(1): p. 212-218.
[11]    Kongar, E.A. and K. Rosentrater, data Envelopment Analysis Approach to compare the Environmental Efficiency of Energy utilization. International Journal of Green Computing (IJGC), 2010. 1(2): p. 1-17.
[12]    Salari Boron, M. and M. Zandieh, Measuring the efficiency of internet shops using a multi stages Data Envelopment Analysis (DEA) model. Management Research in Iran, 2016. 20(3): p. 127-152.
[13]    Sueyoshi, T. and K. Sekitani, Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach. European Journal of Operational Research, 2007. 176(3): p. 1918-1946.
[14]    Krivonozhko, V.E., F.R. Førsund, and A.V. Lychev, Measurement of returns to scale using non-radial DEA models. European Journal of Operational Research, 2014. 232(3): p. 664-670.
[15]    Krivonozhko, V.E., A.V. Lychev, and F. Førsund, Measurement of returns to scale in radial DEA models. Computational mathematics and mathematical physics, 2017. 57(1): p. 83-93.
[16]    h.    Fakhr Mousavi, S.M., et al., Non-radial two-stage network DEA model to estimate returns to scale. Journal of Modelling in Management, 2021. ahead-of-print(ahead-of-print).
[17]    Yuan, G., Two-stage fuzzy production planning expected value model and its approximation method. Applied Mathematical Modelling, 2012. 36(6): p. 2429-2445.
[18]    Khaledian, F. and M. Momeni, Leveling of Project Resources under Fuzzy-Stochastic Conditions. Modern Research in Decision Making, 2021. 6(3): p. 129-154.
[19]    Shakouri Gangavi, H. and A. Kazemi, Reduction of Energy Intensity in a Hospital after Implementation of an Energy Management System Considering Consumer Fuzzy Preferences. Modern Research in Decision Making, 2018. 2(4): p. 105-128.
[20]    Soltanzadeh, E. and H. Omrani, Dynamic network data envelopment analysis model with fuzzy inputs and outputs: An application for Iranian Airlines. Applied Soft Computing, 2018. 63: p. 268-288.
[21]    Heydari, C., H. Omrani, and R. Taghizadeh, A fully fuzzy network DEA-Range Adjusted Measure model for evaluating airlines efficiency: A case of Iran. Journal of Air Transport Management, 2020. 89: p. 101923.
[22]    Aida, K., et al., Evaluating water supply services in Japan with RAM: a range-adjusted measure of inefficiency. Omega, 1998. 26(2): p. 207-232.
[23]    Cooper, W.W., K.S. Park, and J.T. Pastor, RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. Journal of Productivity analysis, 1999. 11(1): p. 5-42.
[24]    Banker, R.D., et al., Returns to scale in different DEA models. European Journal of Operational Research, 2004. 154(2): p. 345-362.
[25]    Sueyoshi, T. and M. Goto, Measurement of returns to scale and damages to scale for DEA-based operational and environmental assessment: how to manage desirable (good) and undesirable (bad) outputs? European journal of operational research, 2011. 211(1): p. 76-89.
[26]    Thrall, R.M., Duality, classification and slacks in DEA. Annals of Operations Research, 1996. 66(2): p. 109-138.
[27]    Bhadra, D., Race to the bottom or swimming upstream: performance analysis of US airlines. Journal of Air Transport Management, 2009. 15(5): p. 227-235.
[28]    Hong, S. and A. Zhang, An efficiency study of airlines and air cargo/passenger divisions: a DEA approach. World Review of Intermodal Transportation Research, 2010. 3(1-2): p. 137-149.
[29]    Tavassoli, M., G.R. Faramarzi, and R.F. Saen, Efficiency and effectiveness in airline performance using a SBM-NDEA model in the presence of shared input. Journal of Air Transport Management, 2014. 34: p. 146-153.
[30]    Li, Y. and Q. Cui, Airline efficiency with optimal employee allocation: an input-shared network range adjusted measure. Journal of Air Transport Manage