تخمین کشش مقیاس جهتی فرایندهای دومرحله‌ای در حضور خروجی‌های نامطلوب

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، گروه مهندسی صنایع، دانشکده فنی و مهندسی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

2 استاد، گروه ریاضی، دانشکده علوم پایه، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

3 استاد، گروه ریاضی، دانشکده علوم پایه، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران

4 استادیار، گروه مهندسی صنایع، دانشکده فنی و مهندسی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

چکیده

با توجه به پیچیدگی فرایندها، تحلیل عملکرد سیستم‌ها و بررسی تغییر مقیاس عملیات به منظور بهبود بهره‌وری از اهمیت به‌سزایی برخوردار است. بنابراین در این تحقیق یک روش تحلیل پوششی داده‌های شبکه‌ای دو مرحله‌ای جهت‌دار به منظور تخمین کارایی کلی و کارایی هر مرحله از فرایندهای دو مرحله‌ای پیشنهاد می‌شود در حالی که خروجی‌های نامطلوب علاوه بر خروجی‌های مطلوب تولید می‌شوند. تکنولوژی مطرح شده بر مبنای اصل دسترسی‌پذیری ضعیف خروجی‌های نامطلوب و بازده به مقیاس متغیر می‌باشد. به علاوه پس از ارایه تابع پاسخ، روش‌هایی به منظور تخمین کشش مقیاس راست و چپ فرایندهای دومرحله‌ای کارای کلی مطرح می‌شوند. به منظور بررسی اعتبار روش پیشنهادی، مجموعه داده‌ای از 78 شعبه یکی از بانک‌های ایران به‌کار می‌رود و کارایی و کشش مقیاس آن‌ها مورد بررسی قرار می‌گیرند. نتایج نشان می‌دهد روش پیشنهادی به منظور تحلیل عملکرد و تخمین کشش مقیاس سیستم‌های شبکه‌ای دومرحله‌ای در حضور خروجی‌های نامطلوب مفید و پرکاربرد خواهد بود.

کلیدواژه‌ها


عنوان مقاله [English]

Estimating the directional scale elasticity of two-stage processes in the presence of undesirable outputs

نویسندگان [English]

  • Roghayeh Azizi Usefvand 1
  • Sohrab Kordrostami 2
  • Alireza Amirteimoori 3
  • Maryam Daneshmand-Mehr 4
1 PhD student, Department of Industrial Engineering, Faculty of Technology and Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2 Professor, Department of Mathematics, Faculty of Basic Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran
3 Professor, Department of Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran
4 Assistant Professor, Department of Industrial Engineering, Technical and Engineering Faculty, Lahijan Branch, Islamic Azad University, Lahijan, Iran
چکیده [English]

Due to the complexity of the processes, analyzing the performance of the systems and examining the change in the scale of operations to improve productivity is a significant aspect. Therefore, in this research, a two-stage directional network data envelopment analysis approach is proposed to estimate the overall efficiency and the performance of each stage of two-stage processes, while undesirable outputs are produced in addition to desirable outputs. The proposed technology is based on the properties of the weak disposability of undesirable outputs and variable returns to scale. In addition, after presenting the response function, methods are proposed to calculate the right and left scale elasticities of overall efficient two-stage processes. In order to investigate the validity of the proposed method, a data set from 78 branches of the Iranian bank is used and their efficiency and scale elasticity are examined. The results show that the introduced method is useful and widely applicable to analyze the performance and scale of two-stage network systems in the presence of undesirable outputs.

کلیدواژه‌ها [English]

  • Data envelopment analysis
  • Scale Elasticity
  • Undesirable Output
  • Two-stage Process
[1].Seyhani,F.,2020. “Undesirable factors in nonparametric production processes”, ”,PH.D Thesis in applied mathematic,faculty of science , Lahijan  Islamic Azad University , Autumn.
[2].Azizi Usefvand, R., Nahavandi , N., Farzandi,GH.,2017 “The Role of Supply Chain Risk Management on the Efficiency of the Pharmaceutical Distribution Companies” International Journal of Industrial Engineering & Production Management, Volume 28, Number 1 , pp 119- 137.
[3].Mehdizadeh, S.,2019. “ Efficiency analysis in network process with stochastic data”,PH.D Thesis in applied mathematic,faculty of science ,Rasht  Islamic Azad University , Autumn. 
[4].Charles,V., Cornillier , F.,2017. “Value of the stochastic efficiency in data envelopment analysis”. Expert Systems with Applications. Volume 81, 15 September 2017, Pages 349-357.
[5]. Färe, R., & Grosskopf, S. (2000). “Network DEA”, Socio-Economic Planning Sciences, 34, 35-49. 
[6]. Chen,Y., Liang, L.,Yang,F.,  “A DEA game model approach to supply chain efficiency,” Annals of Operations Research, vol. 145, pp. 5–13, 2006. View at Publisher • View at Google Scholar • View at Zentralblatt MATH
[7]. Liang, L.,Yang, F. Cook,W. D and Zhu, J. “DEA models for supply chain efficiency evaluation,” Annals of Operations Research, vol. 145, pp. 35–49, 2006. View at Publisher • View at Google Scholar • View at Zentralblatt MATH
[8]. Talluri, S., R. Narasimhan, A. Nair, 2006.”Vendor performance with supply risk:a chance-constrained DEA approach”, International Journal of Production Economics, 100(2), 212–222.
[9]. Farzipoor Saen, R.,2010.”Restricting weights in supplier selection decisions in the presence of dual-role factors”, Applied Mathematical Modeling, 34,PP 2820–2830.
[10]. Tajbakhsh, A .,Hassini,E., 2015.” A data envelopment analysis approach to evaluate   sustainability in supply chain networks”, Journal of Cleaner Production 105, 74-85 
 [11]. Motevali Haghighi, S., Torabi, S.A.,Ghasemi, R., 2016.”An integrated approach for performance evaluation in sustainable supply chain networks(with a case study)”, Journal of Cleaner Production, Volume 137, 20, Pages 579-597.
[12]. Jahani Sayyad Noveiri, M., Kordrostami, S., Wu, J., Amirteimoori ,A., 2019.”Supply chains performance with undesirable factors and reverse flows: A DEA-based approach”. Journal of the Operational Research Society 70 (1), 125-135.
[13]. Jahani Sayyad Noveiri, M., Kordrostami, S., Amirteimoori, A., 2020. “Efficiency evaluation of closed-loop supply chains with proportional dual-role measures”.Kybernetika 56 (4), 695-721.
[14]. Amirteimoori, A., Khoshandam, L., Kordrostami, S., Jahani Sayyad Noveiri, M.,2021. “Performance analysis in a stochastic supply chain with reverse flows: a DEA-based approach”. IMA Journal of Management Mathematics.
[15]. Jahani Seyyed Noveiri, M., Kordrostami, S., Amirteimoori,A.,2017.“Cost Efficiency Of Closed–Loop Supply Chain In The Presence Of Dual-Role And Undesirable Factors”. Journal of new researches in mathematics. Volume 3 , Number 9; Page(s) 5 To 16.
[16]. Färe, R., & Grosskopf, S. (1994). “Estimation of returns to scale using data envelopment analysis”: A comment. Journal of Operational Research, 79, 379–382.
[17]. Chen, Y., Chen, W. D., Cook x, N., & Zhu, J. 2009. "Additive efficiency decomposition in twostage DEA". European Journal of Operational Research, 196(3), 1170–1176.
[18]. Khodabakhshi, M., Gholami, Y., & Kheirollahi, H.2010. "An additive model approach for estimating returns to scale in imprecise data envelopment analysis". Applied Mathematical Modelling, 34, 1247–1257.
[19]. Sahoo, B. K., Zhu, J., & Tone, K.2014.”Decomposing efficiency and returns to scale in two-stage network systems”. In Data Envelopment Analysis (pp. 137-164). Springer, Boston, MA.
[20]. Zhang, Q., & Yang, Z. 2015. "Returns to scale of two-stage production process". Computers & Industrial Engineering. 90, 259–268.
[21]. Zhou, X., Zhang, Zh., Pedrycz, W., & Kuang, Y. 2016. "Type-2 Fuzzy Multi-Objective DEA Model: An Application to Sustainable Supplier Evaluation". Applied Soft Computing, 1-27.
[22]. Tavana, M., Kalili_Damghani, K., Arteaga, F., Mahmoudi, R., & Kafezal Kotob, A. 2018. "Efficiency Decomposition and Measurement in Two-Stage Fuzzy DEA Models Using a Bargaining Game Approach". Computers & Industrial Engineering, 1-36.
[23]. Hosseinzadeh Saljooghi, F., &  Rahimi, A.,2019. “Evaluation Of Efficiency And Returns To Scale Of Resin Chemical Industry Supply Chain Using Crisp And Fuzzy Data Envelopment”. Production and operations managment.Volume 10 , Number 1 (18) ; Page(s) 47 To 63.
[24]. Amirmohammadi, H., Amirteimoori, A. A., Kordrostami, S., & Vaez-Ghasemi, M. (2021). “Scale elasticity in the presence of integer data: An application to electricity distribution companies”. Studies of Applied Economics, 39(2).
[25].Jahani Sayyad Noveiri, M., Kordrostami, S.,Amirteimoor,A,.2021.“Sustainability Assessment and Most Productive Scale Size: a Stochastic DEA Approach with Dual Frontiers”.Environmental Modeling & Assessment 26 (5), 723-735.
[26]. 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(3), 605-616.
[27].Matin R.K.,2011. “A Review On Using Weak Disposability Axiom In Modeling Undesirable Outputs In Non-Parametric Activity Analysis ”. Journal of operational research and ITS applications (JOURNAL OF APPLIED MATHEMATICS), Volume 8 , Number 3 (30); Page(s) 53 To 69.
[28].Färe, R., & Grosskopf, S. (2003).”Nonparametric productivity analysis with undesirable outputs”. American Journal of Agricultural Economics, 85(4),1070-1074.
[29]. Kuosmanen, T. 2005. Weak Disposability in Nonparametric Productivity Analysis with Undesirable Outputs. American Journal of Agricultural Economics ,87 , 1077-1082.
[30].Nasirian,H.,2015. “Return to sacle and losses scale in data envelopment analysis”.M.S Thesis in applied mathematic,faculty of science,Sistan University.
[31]. Darvish Motevally, M.H., Hosseinzadeh Lotfi, F., Shoja, N., Abri, AGh.,2019. Calculating The Sustainable Supply Chain Performance In The Cement Industry (Application Of Network Data Envelopment Analysis Model).Economic Modeling. Volume 13 , Number 2 (46) ; Page(s) 73 To 99.