Document Type : Original Article

Authors

1 Department of Management, Yazd Branch, Islamic Azad University, Yazd, Iran.

2 Department of Management, Meybod University, Meybod, Iran.

Abstract

This paper presents a common set of weights (CSWs) method for multi-stage or network structured decision-making units (DMUs). The decision-making approaches proposed here consist of three stages. In the first step, a hybrid dynamic network data envelopment analysis (DNDEA) model is used to determine the efficiency values of the supply chain. Next, a CSW model is developed using the range-adjusted measure (RAM). In the third step, the extracted CSWs are used to compute a separate weight for each component of each DMU.  the extracted CSWs are then used in the third step to calculate DMUs weights separately for each component. Then the overall efficiency is obtained by weighted averaging of the efficiency of individual components. Thus, this model evaluates the overall efficiency of a network process as well as the contribution of individual network components. The results of this study demonstrate the model’s capability to evaluate the efficiency of dynamic network structures with very high discriminatory power. In an implementation of the model in a case study, only one supplier (KARAN) earned the maximum efficiency value, and the efficiency scores of other suppliers were in the range of 0.6409-0.9983. After applying the CSWs, KARAN remained the most efficient supplier, and the efficiency scores of other suppliers moved to the range of 0.5002-0.9349. The range shifted to 0.4823-0.9921 after applying the stages weights. This weighting method should be considered an integral part of such modeling procedures, Given the enhancement observed in the results of CSW after incorporating the component weights.

Keywords

Amiri, M., Hashemi-Tabatabaei, M., Ghahremanloo, M., Keshavarz-Ghorabaee, M., Zavadskas, E. K., & Banaitis, A. (2021). A new fuzzy BWM approach for evaluating and selecting a sustainable supplier in supply chain management. International Journal of Sustainable Development & World Ecology, 28(2), 125-142.
Anisimov, V., Anisimov, E., Saurenko, T., Yavorsky, V., & Marchenko, R. (2022). Assessment of the Effectiveness of Sustainable Management in Supply Chains. In XIV International Scientific Conference “INTERAGROMASH 2021" (pp. 703-710). Springer, Cham.
Arman, H., & Hadi‐Vencheh, A. (2021). Restricting the relative weights in data envelopment analysis. International Journal of Finance & Economics, 26(3), 4127-4136.
Avkiran, N. K., & McCrystal, A. (2014). Dynamic network range-adjusted measure vs. dynamic network slacks-based measure. Journal of the Operations Research Society of japan, 57(1), 1-14.
Banker, R. D., A. Charnes, and W. W. Cooper. )1984(.Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science 30(9):1078–92.
Bansal, P., & Mehra, A. (2022). Integrated dynamic interval data envelopment analysis in the presence of integer and negative data. Journal of Industrial & Management Optimization, 18(2), 1339.
Caggiani, L., Camporeale, R., Hamidi, Z., & Zhao, C. (2021). Evaluating the efficiency of bike-sharing stations with data envelopment analysis. Sustainability, 13(2), 881.
Charnes, A., W. W. Cooper, and E. Rhodes. 1978. Measuring the Efficiency of Decision Making Units. European Journal of Operational Research 2(6):429–44.
Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two-stage DEA. European journal of operational research, 196(3), 1170-1176.
Chiang, C. I., Hwang, M. J., & Liu, Y. H. (2011). Determining a common set of weights in a DEA problem using a separation vector. Mathematical and Computer Modelling, 54(9-10), 2464-2470.
Cook, Wade D., and Joe Zhu. 2007. “Within-Group Common Weights in DEA: An Analysis of Power Plant Efficiency.” European Journal of Operational Research 178(1):207–16.
Cook, W. D., Zhu, J., Bi, G., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European journal of operational research, 207(2), 1122-1129.
Elmsalmi, M., Hachicha, W., & Aljuaid, A. M. (2021). Modeling Sustainable Risks Mitigation Strategies Using a Morphological Analysis-Based Approach: A Real Case Study. Sustainability, 13(21), 12210.
Färe, R. (1991). Measuring Farrell efficiency for a firm with intermediate inputs. Academia Economic Papers, 19(2), 329-340.
Färe, R., & Grosskopf, S. (1996). Productivity and intermediate products: A frontier approach. Economics letters, 50(1), 65-70.
Fare, Rolf, Gerald Whittaker, and Following Fare. 1995. AN INTERMEDIATE INPUT MODEL 46(2):201–13.
Fathi, A., Karimi, B., & Saen, R. F. (2022). Sustainability assessment of supply chains by a novel robust two-stage network DEA model: a case study in the transport industry. Soft Computing, 1-18.
Fukuyama, H., & Weber, W. L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega, 38(5), 398-409.
Gasser, P., Cinelli, M., Labijak, A., Spada, M., Burgherr, P., Kadziński, M., & Stojadinović, B. (2020). Quantifying electricity supply resilience of countries with robust efficiency analysis. Energies, 13(7), 1535.
Gavião, L. O., Meza, L. A., Lima, G. B. A., de Almada Garcia, P. A., & Kostin, S. (2019). Avaliação de investimentos em modernização dos portos por Análise Envoltória de Dados. SIMPÓSIO DE PESQUISA OPERACIONAL E LOGÍSTICA DA MARINHA–SPOLM, 1-16.
Ge, H. (2022). DEA Algorithm for Performance Evaluation of Public Sector with Benchmarking Management. In 2021 International Conference on Big Data Analytics for Cyber-Physical System in Smart City (pp. 571-577). Springer, Singapore.
Gharakhani, D., Eshlaghy, A. T., Hafshejani, K. F., Mavi, R. K., & Lotfi, F. H. (2018). Common weights in dynamic network DEA with goal programming approach for performance assessment of insurance companies in Iran. Management Research Review.
Ghasemi, M., Mozaffari, M. R., Rostamy Malkhalifeh, M., & Behzadi, M. H. (2022). Stochastic Efficiency Based on a Common Set of Weights in Data Envelopment‎ Analysis. International Journal of Industrial Mathematics, 14(2), 139-152.
Hajiagha, S. H. R., Mahdiraji, H. A., Tavana, M., & Hashemi, S. S. (2018). A novel common set of weights method for multi-period efficiency measurement using mean-variance criteria. Measurement, 129, 569-581..
Hashimoto, A., Fukuyama, H., & Tone, K. (2013). Dynamic network DEA and an application to Japanese Prefectures. In Workshop on Dynamic and Network DEA 2013 (pp. 39-46).
Lotfi, F. H., Hatami-Marbini, A., Agrell, P. J., Aghayi, N., & Gholami, K. (2013). Allocating fixed resources and setting targets using a common-weights DEA approach. Computers & Industrial Engineering, 64(2), 631-640.
Jahanshahloo, G. R., Lotfi, F. H., Khanmohammadi, M., Kazemimanesh, M., & Rezaie, V. (2010). Ranking of units by positive ideal DMU with common weights. Expert Systems with applications, 37(12), 7483-7488.
Vickers, N. J. (2017). Animal communication: when i’m calling you, will you answer too?. Current biology, 27(14), R713-R715.
Johnson, A. L., Pope, B., & Tone, K. (2013). US hospital performance: a dynamic network analysis. In Proceedings of the workshop on DNDEA 2013.
Kalantary, M., Farzipoor Saen, R., & Toloie Eshlaghy, A. (2018). Sustainability assessment of supply chains by inverse network dynamic data envelopment analysis. Scientia Iranica, 25(6), 3723-3743.
Kalantary, M., & Saen, R. F. (2019). Assessing sustainability of supply chains: An inverse network dynamic DEA model. Computers & Industrial Engineering, 135, 1224-1238.
Kao, C., & Hung, H. (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the operational research society, 56(10), 1196-1203.
Kao, C., & Liu, S. T. (2022). Group decision making in data envelopment analysis: A robot selection application. European Journal of Operational Research, 297(2), 592-599.
Kiaei, H., & Kazemi Matin, R. (2022). New common set of weights method in black-box and two-stage data envelopment analysis. Annals of Operations Research, 309(1), 143-162.
Krysiak, F. C. (2009). Risk management as a tool for sustainability. Journal of business ethics, 85(3), 483-492.
Li, X. B., & Reeves, G. R. (1999). A multiple criteria approach to data envelopment analysis. European journal of operational research, 115(3), 507-517.
Liang, L., Cook, W. D., & Zhu, J. (2008). DEA models for two‐stage processes: Game approach and efficiency decomposition. Naval Research Logistics (NRL), 55(7), 643-653.
Liu, F. H. F., & Peng, H. H. (2008). Ranking of units on the DEA frontier with common weights. Computers & operations research, 35(5), 1624-1637.
Liu, M., Zhang, C., Liu, Y., Ni, A., Xiao, G., & Luo, Q. Evaluating the Benefits of Public Transport Service: The Cross-Efficiency of Dynamic Network Data Envelopment Analysis. Available at SSRN 4070835.
Longoni, A., & Cagliano, R. (2015). Environmental and social sustainability priorities: Their integration in operations strategies. International Journal of Operations & Production Management.
Guillot, A., & Collet, C. (2008). Construction of the motor imagery integrative model in sport: a review and theoretical investigation of motor imagery use. International Review of Sport and Exercise Psychology, 1(1), 31-44..
Makuei, A., A. Alinezhad, MAVI R. KIANI, and M. Zohrehbandian. 2008. “A Goal Programming Method for Finding Common Weights in DEA with an Improved Discriminating Power for Efficiency.” Journal of Industrial and Systems Engineering 1(4):293-303 [ in persian].
Mavi, R. K., & Mavi, N. K. (2021). National eco-innovation analysis with big data: A common-weights model for dynamic DEA. Technological Forecasting and Social Change, 162, 120369.
Moradi, H., M. Rabbani, H. babaei meybodi, and M. Honari. )2022(.Development of a Hybrid Model for Sustainable Supply Chain Evaluation with Dynamic Network Data Envelopment Analysis Approach. Iranian Journal of Operations Research in press(x).
Motevalli, M. H. D., & Motamedi, M. (2020). Dynamic modeling to evaluate the efficiency of a sequential multilevel supply network. Journal of Decisions & Operations Research, 5(3).
Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The computer journal, 7(4), 308-313.
Nemoto, J., & Goto, M. (2003). Measurement of dynamic efficiency in production: an application of data envelopment analysis to Japanese electric utilities. Journal of Productivity analysis, 19(2), 191-210.
Omrani, H., Valipour, M., & Mamakani, S. J. (2019). Construct a composite indicator based on integrating Common Weight Data Envelopment Analysis and principal component analysis models: An application for finding development degree of provinces in Iran. Socio-Economic Planning Sciences, 68, 100618.
Paul, S., Ali, S. M., Hasan, M. A., Paul, S. K., & Kabir, G. (2022). Critical success factors for supply chain sustainability in the wood industry: an integrated PCA-ISM model. Sustainability, 14(3), 1863.
Pourmahmoud, J., & Sharak, N. B. (2020). Evaluating Cost Efficiency Using Fuzzy Data Envelopment Analysis method. Iranian Journal of Operations Research, 11(1), 25-42.
Ramezani-Tarkhorani, S., Khodabakhshi, M., Mehrabian, S., & Nuri-Bahmani, F. (2014). Ranking decision-making units using common weights in DEA. Applied Mathematical Modelling, 38(15-16), 3890-3896.
Ramezankhani, M. J., Torabi, S. A., & Vahidi, F. (2018). Supply chain performance measurement and evaluation: A mixed sustainability and resilience approach. Computers & Industrial Engineering, 126, 531-548.
Rezaie, V., Ahmad, T., Awang, S. R., Khanmohammadi, M., & Maan, N. (2014). Ranking DMUs by calculating the interval efficiency with a common set of weights in DEA. Journal of Applied Mathematics, 2014.
Roll, Y., Cook, W. D., & Golany, B. (1991). Controlling factor weights in data envelopment analysis. IIE transactions, 23(1), 2-9.
Saati, S., Hatami-Marbini, A., Agrell, P. J., & Tavana, M. (2012). A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial & Management Optimization, 8(3), 623.
Salimian, S., Mousavi, S. M., & Antucheviciene, J. (2022). An Interval-Valued Intuitionistic Fuzzy Model Based on Extended VIKOR and MARCOS for Sustainable Supplier Selection in Organ Transplantation Networks for Healthcare Devices. Sustainability, 14(7), 3795.
Sarkis, J. (2007). Preparing your data for DEA. In Modeling data irregularities and structural complexities in data envelopment analysis (pp. 305-320). Springer, Boston, MA.
Shieh, H. S., Li, Y., Hu, J. L., & Ang, Y. Z. (2022). A Comparison of Efficiency of Life Insurance Companies in Mainland China and Taiwan Using Bootstrapped Truncated Regression Approach. Cogent Economics & Finance, 10(1), 2043571.
Soltanifar, M., Hosseinzadeh Lotfi, F., Sharafi, H., & Lozano, S. (2022). Resource allocation and target setting: a CSW–DEA based approach. Annals of Operations Research, 1-33.
Sugiyama, Manabu, and Toshiyuki Sueyoshi. )2014(. Finding a Common Weight Vector of Data Envelopment Analysis Based upon Bargaining Game. Studies in Engineering and Technology 1(1):13–21.
Sun, Jiasen, Jie Wu, and Dong Guo.)2013(.Performance Ranking of Units Considering Ideal and Anti-Ideal DMU with Common Weights. Applied Mathematical Modelling 37(9):6301–10.
Tabatabaei, Somayeh, Mohammad Reza Mozaffari, Mohsen Rostamy-Malkhalifeh, and Farhad Hosseinzadeh Lotfi. )2022(.Fuzzy Efficiency Evaluation in Relational Network Data Envelopment Analysis: Application in Gas Refineries. Complex & Intelligent Systems 1–29.
Toloo, M. (2013). The most efficient unit without explicit inputs: An extended MILP-DEA model. Measurement, 46(9), 3628-3634.
Toloo, M. (2014). An epsilon-free approach for finding the most efficient unit in DEA. Applied Mathematical Modelling, 38(13), 3182-3192.
Tone, K., Kweh, Q. L., Lu, W. M., & Ting, I. W. K. (2019). Modeling investments in the dynamic network performance of insurance companies. Omega, 88, 237-247.
Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European journal of operational research, 197(1), 243-252.
Tone, K., & Tsutsui, M. (2010). Dynamic DEA: A slacks-based measure approach. Omega, 38(3-4), 145-156.
Tecchio, P., McAlister, C., Mathieux, F., & Ardente, F. (2017). In search of standards to support circularity in product policies: A systematic approach. Journal of cleaner production, 168, 1533-1546.
You, Y. Q., & Jie, T. (2016). A study of the operation efficiency and cost performance indices of power-supply companies in China based on a dynamic network slacks-based measure model. Omega, 60, 85-97.
Zhang, D., Wang, H., & Wang, W. (2022). The Influence of Relational Capital on the Sustainability Risk: Findings from Chinese Non-State-Owned Manufacturing Enterprises. Sustainability, 14(11), 6904.