Fixed cost allocation in two-stage system in the presence of undesirable outputs
الموضوعات : International Journal of Data Envelopment AnalysisLeila Emami 1 , Farhad Hosseinzadeh Lotfi 2 , Mohsen Rostamy 3
1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.
3 - Department of Mathematics, science and research Branch, Islamic Azad University, Tehran, Iran
الکلمات المفتاحية: Network Data Envelopment Analysis, Fixed Cost Allocation, Undesirable Outputs.,
ملخص المقالة :
Data Envelopment Analysis (DEA) is a mathematical programming-based technique used to determine the efficiency of a set of homogeneous decision-making units (DMUs). In certain cases, these units operate as a multi-stage process, where the outputs of one stage serve as inputs for the next. Such a structure is particularly common in production lines of industrial and manufacturing systems, where raw materials are used as inputs in the first stage, and the desired product is progressively completed through various stages, with the final product being the main output in the last stage. In most production activities and daily operations, besides desirable outputs, undesirable outputs such as harmful emissions, production waste, etc., are also generated. As a result, numerous studies in economics, management, and production emphasize reducing energy consumption to protect the environment and control pollution. In this paper, a new model is proposed that includes undesirable outputs and allocates fixed costs within networks. The focus of these models is to design approaches for allocating fixed costs where the reduction ratio of undesirable outputs is higher than that of desirable outputs.
[1] Amirteimoori, A., Fouladvand, M., & Kordrostami, S. (2017). Efficiency measurement using nonparametric production analysis in the presence of undesirable outputs. Application to power plants. Operations research and decisions, 27(3), 5-20.
[2] Amirteimoori, A., Kordrostami, S., & Sarparast, M. (2006). Modeling undesirable factors in data envelopment analysis. Applied Mathematics and Computation, 180(2), 444-452.
[3] Amirteimoori, A., & Masrouri, S. (2021). DEA-based competition strategy in the presence of undesirable products: an application to paper mills. Operations Research and Decisions, 31(2).
[4] Bian, Y., Liang, N., & Xu, H. (2015). Efficiency evaluation of Chinese regional industrial systems with undesirable factors using a two-stage slacks-based measure approach. Journal of Cleaner Production, 87, 348-356.
[5] Charnes A, Cooper WW, Rhodes E . Measuring the efficiency of decision-making units. European Journal of Operational Research 1978;2(6):429–44.
[6] Chen, C. M., Du, J., Huo, J., & Zhu, J. (2012). Undesirable factors in integer-valued DEA: Evaluating the operational efficiencies of city bus systems considering safety records. Decision Support Systems, 54(1), 330-335.
[7] Chen, S., Li, A., Hu, L., & N’Drin, M. G. R. (2024). Understanding the efficiency in generating human development in sub-Saharan Africa: A two-stage network DEA approach. Social Indicators Research, 171(1), 295-324.
[8] Chen, Y. C., Chiu, Y. H., & Chiu, C. J. (2020). The performance evaluation of banks considering risk: an application of undesirable relation network DEA. International transactions in operational research, 27(2), 1101-1120.
[9] Färe, R., & Grosskopf, S. (2003). Nonparametric productivity analysis with undesirable outputs: comment. American journal of agricultural economics, 85(4), 1070-1074.
[10] Färe, R., & Grosskopf, S. (2009). A comment on weak disposability in nonparametric production analysis. American Journal of Agricultural Economics, 91(2), 535-538.
[11] Fare, R., Grosskopf, S., & pasurka, C. (2013). Joint production of Good and Bad Outputs with a Network Application. Encyclopedia of Energy, Natural Resource, and Environmental Economics, 2, 109-118.
[12] Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society: series A (General), 120(3), 253-281.
[13] Feng, Q., & Wu, Z. (2023). Allocating a fixed cost as a reduction of outputs in a non-cooperative decision-making environment: A data envelopment analysis approach. Journal of the Operational Research Society, 74(6), 1507-1519.
[14] Fouladvand, m. (2017). Undesirable Outputs in production process with weak disposability assumption in data envelopment analysis, Ph.D. thesis in Mathematics, Faculty of Science, Islamic Azad University, Science and Research Branch of Tehran (Giulan).
[15] Hailu, A., & Veeman, T.S. (2001). Non-parametric productivity analysis with undesirable outputs: an application to the Canadian pulp and paper industry, American Journal of Agricultural Economics, 83, 605-616.
[16] Izadikhah, M., & Farzipoor Saen, R. (2018). Assessing sustainability of supply chains by chance– constrained two– stage DEA model in the presence of undesirable factors, Camputers&operations Research, 100, 343-367.
[17] Jahanshahloo, G.R., Hadi Vencheh, A., Foroughi, A.A., & Kazemi Matin, R. (2004). Inputs/outputs estimation in DEA when some factors are undesirable, Applied Mathematics and Computation, 156, 19-32.
[18] Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2005). Undesirable inputs and outputs in DEA models, Applied Mathematics and Computation, 169, 917-925.
[19] Kalhor, A., & KazemiMatin, R. (2018). Study the effects of abatement factors of weakdisposability in network data envelopment analysis with undesirable outputs, Journal of operational reearch and its applications, 15, 103-121.
[20] Khoshandam, L., & Nematizadeh, M. (2024). An inverse network DEA model for two-stage processes in the presence of undesirable factors. Journal of Applied Research on Industrial Engineering, 11(2), 179-194.
[21] Kordrostami, S., & Amirteimoori, A. (2005). Un-desirable factors in multi-component performance measurement. Applied Mathematics and Computation, 171(2), 721-729.
[22] Kuosmanen, T. (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American journal of agricultural economics, 87(4), 1077-1082.
[23] Kuosmanen, T., & Podinovski, V. (2009). Weak disposability in nonparametric production analysis: reply to Färe and Grosskopf. American journal of agricultural economics, 91(2), 539-545.
[24] Liu, W., Zhou, Z., Ma, C., Liu, D., & Shen, W. (2015). Two-stage DEA models with undesirable input-intermediate-outputs. Omega, 56, 74-87.
[25] Lozano, S., Gutiérrez, E., & Moreno, P. (2013). Network DEA approach to airports performance assessment considering undesirable outputs. Applied Mathematical Modelling, 37(4), 1665-1676.
[26] Ma, H., Geng, B., Fu, Y., Sun, Y., & Sun, Z. (2022). Efficiency analysis of industrial water treatment in China based on two-stage undesirable fixed-sum output DEA model. Journal of Systems Science and Information, 9(6), 660-680.
[27] Maghbouli, M., Amirteimoori, A., & Kordrostami, S. (2014). Two-stage network structures with undesirable outputs: A DEA based approach. Measurement, 48, 109-118.
[28] Monzeli, A., Daneshian, B., Tohidi, G., Sanei, M., & Razavian, S. (2020). Efficiency study with undesirable inputs and outputs in DEA. Journal of fuzzy extension and applications, 1(1), 73-80.
[29] Najari Alamuti, M., Kazemi Matin, R., Khounsiavash, M., & Moghadas, Z. (2021). Evaluation of the Performance in Dynamic Network Data Envelopment Analysis with Undesirable Outputs. Iranian Journal of Optimization, 13(3), 169-179.
[30] Omrani, H., Oveysi, Z., Emrouznejad, A., & Teplova, T. (2023). A mixed-integer network DEA with shared inputs and undesirable outputs for performance evaluation: Efficiency measurement of bank branches. Journal of the Operational Research Society, 74(4), 1150-1165.
[31] Omrani, H., Yang, Z., Karbasian, A., & Teplova, T. (2023). Combination of top-down and bottom-up DEA models using PCA: A two-stage network DEA with shared input and undesirable output for evaluation of the road transport sector. Socio-Economic Planning Sciences, 89, 101706.
[32] Rostamy-Malkhalifeh, M., Sanei, M., & Saleh, H. (2009). A New Method for Solving Fuzzy DEA Models by Trapeziodal Approximation. Journal of Mathematical Extension.
[33] Saleh, H. I. L. D. A., Hosseinzadeh Lotfi, F., Rostmay-Malkhalifeh, M., & Shafiee, M. (2021). Provide a mathematical model for selecting suppliers in the supply chain based on profit efficiency calculations. Journal of New Researches in Mathematics, 7(32), 177-186.
[34] Saleh, H., Hosseinzadeh, F., Rostamy, M., & Shafiee, M. (2020). Performance evaluation and specifying of return to scale in network DEA. Journal of advanced mathematical modeling, 10(2), 309-340.
[35] Sarkhosh-Sara, A., Tavassoli, M., & Heshmati, A. (2020). Assessing the sustainability of high-, middle-, and low-income countries: A network DEA model in the presence of both zero data and undesirable outputs. Sustainable Production and Consumption, 21, 252-268.
[36] Scheel, H. (2001). Undesirable outputs in efficiency valuations. European journal of operational research, 132(2), 400-410.
[37] Shafiee, M., Hosseinzade Lotfi, F., & Saleh, H. (2021). Benchmark forecasting in data envelopment analysis for decision making units. International Journal of Industrial Mathematics, 13(1), 29-42.
[38] Shafiee, M., Saleh, H., & Ziyari, R. (2022). Projects efficiency evaluation by data envelopment analysis and balanced scorecard. Journal of decisions and operations research, 6(Special Issue), 1-19.
[39] Sharafi, H., Lotfi, F. H., Jahanshahloo, G. R., & Razipour-GhalehJough, S. (2020). Fair allocation fixed cost using cross-efficiency based on Pareto concept. Asia-Pacific Journal of Operational Research, 37(01), 1950036.
[40] Shi, X., Emrouznejad, A., & Yu, W. (2021). Overall efficiency of operational process with undesirable outputs containing both series and parallel processes: A SBM network DEA model. Expert Systems with Applications, 178, 115062.
[41] Soofizadeh, S., & Fallahnejad, R. (2022). A bargaining game model for performance evaluation in network DEA considering shared inputs in the presence of undesirable outputs. Journal of Mathematical Modeling, 10(2), 227-245.
[42] Streimikis, J., & Saraji, M. K. (2022). Green productivity and undesirable outputs in agriculture: A systematic review of DEA approach and policy recommendations. Economic research-Ekonomska istraživanja, 35(1), 819-853.
[43] Toloo, M., & Hančlová, J. (2020). Multi-valued measures in DEA in the presence of undesirable outputs. Omega, 94, 102041.
[44] Wu, J., Zhu, Q., Chu, J., & Liang, L. (2015). Two-stage network structures with undesirable intermediate outputs reused: a DEA based approach. Computational Economics, 46, 455-477..
[46] Wu, J., Zhu, Q., Ji, X., Chu, J., & Liang, L. (2016). Two-stage network processes with shared resources and resources recovered from undesirable outputs. European journal of operational research, 251(1), 182-197.
[46] Yu, S., Liu, J., & Li, L. (2020). Evaluating provincial eco-efficiency in China: an improved network data envelopment analysis model with undesirable output. Environmental Science and Pollution Research, 27, 6886-6903.
[47] Zhou, S., & Zhiwei, Xu. (2022). Energy efficiency assessment of RCEP member states: A three-stage slack based measurement DEA with undesirable outputs, Energy, 253, 124170.
