Abstract    Social responsibility is a key factor that could result in success and achieving great benefits for supply chains. Responsiveness and reliability are important social responsibility measures for consumers and all stakeholders that strategists and company managers should be concerned about them in long-term planning horizon. Although, presence of uncertainties as an intrinsic part of supply chains could adversely affect the best set plans by field experts. Accordingly, uncertainty of parameters and uncertainties caused by disruptions should be regarded in planning process of networks to prevent unpredictable negative consequences of such uncertainties for all echelons of supply chain. Based on enumerated matters, the aim of this paper is to design a reliable multi-echelon closed loop supply chain network model that maximizes social responsibility while minimizing fixed establishing and variable processing costs of network design. To cope with uncertainty of parameters, stochastic programming is applied and an effective reliable modelling method is employed to appropriately control unpleasant economic impacts of disruptions. Notably, an efficient robust programming method is applied to give the decision makers the capability to control level of risk-averseness of decisions while modelling uncertain parameters. Finally, the proposed model is solved and its outputs are analyzed on the basis of generated test problems which shows correct performance and applicability of extended model in real world problems.

Keywords    supply chain, reliability, social responsibility, robustness, stochastic programming

چکیده    مسئولیت اجتماعی یک فاکتور کلیدی است که منجر به دست­یابی به موفقیت و سود زیاد برای زنجیره­های تامین می­گردد. پاسخ­گویی و پایایی[ah1] ، سنجه­های مهم مسئولیت اجتماعی برای تمامی سهام داران و مشتریان می­باشند که استراتژیست­ها و مدیران سازمانها باید در مورد آن­ها در برنامه­ریزی بلند مدت نگران باشند. گرچه، وجود عدم قطعیت­ها به عنوان یکی از اجزای جداناپذیر زنجیره­های تامین می­تواند به صورت معکوس، بهترین برنامه­های تنظیم شده توسط خبره­های حوزه را تحت تاثیر قرار دهد. بر طبق آنچه گفته شد، عدم قطعیت پارامترها و عدم قطعیت ایجاد شده توسط اختلالات باید در فرایند برنامه­ریزی شبکه­ها مدنظر قرار گیرد تا از نتایج منفی غیرقابل پیش­بینی مربوط به عدم قطعیت­های ذکر شده، برای تمامی سطوح زنجیره­های تامین جلوگیری گردد. بر اساس موارد ذکر شده، هدف این مقاله، طراحی یک مدل شبکه زنجیره تامین حلقه­­بسته پایای چند سطحی می­باشد که مسئولیت اجتماعی را در کنار کمینه سازی هزینه­های ثابت احداث و متغیر عملیاتی طراحی شبکه، بیشینه می­نماید. برای مواجهه با عدم قطعیت پارامترها، برنامه ریزی احتمالی به کار گرفته شده است و از یک رویکرد کارای مدل­سازی پایا استفاده شده است تا بتوان به طور مناسب اثرات نامطلوب اختلالات را کنترل نمود. لازم به ذکر است که از یک رویکرد کارای برنامه­ریزی استوار استفاده شده است تا بتوان قابلیت کنترل سطح ریسک گریزی تصمیمات زمانی که پارامترها به صورت غیرقطعی مدل­سازی می­شوند را به تصمیم گیرندگان داد. در نهایت، مدل توسعه داده شده حل شده و خروجی­های آن بر اساس مسائل نمونه تولید شده آنالیز شده­اند که عملکرد صحیح و قابلیت به کارگیری مدل توسعه داده شده در مسائل واقعی را نشان می­دهد. [ah1]؟؟؟؟

References    1.      Kannan, G., Sasikumar, P. and Devika, K., "A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling", Applied Mathematical Modelling,  Vol. 34, No. 3, (2010), 655-670. 2.      Özceylan, E. and Paksoy, T., "A mixed integer programming model for a closed-loop supply-chain network", International Journal of Production Research,  Vol. 51, No. 3, (2013), 718-734. 3.      Pishvaee, M.S. and Torabi, S.A., "A possibilistic programming approach for closed-loop supply chain network design under uncertainty", Fuzzy Sets and Systems,  Vol. 161, No. 20, (2010), 2668-2683. 4.      Vahdani, B., Tavakkoli-Moghaddam, R. and Jolai, F., "Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model", Applied Mathematical Modelling,  Vol. 37, No. 5, (2013), 3254-3268. 5.      Torabi, S., Namdar, J., Hatefi, S. and Jolai, F., "An enhanced possibilistic programming approach for reliable closed-loop supply chain network design", International Journal of Production Research,  Vol. 54, No. 5, (2016), 1358-1387. 6.      Snyder, L.V. and Daskin, M.S., "Reliability models for facility location: The expected failure cost case", Transportation Science,  Vol. 39, No. 3, (2005), 400-416. 7.      Peng, P., Snyder, L.V., Lim, A. and Liu, Z., "Reliable logistics networks design with facility disruptions", Transportation Research Part B: Methodological,  Vol. 45, No. 8, (2011), 1190-1211. 8.      Vahdani, B., Tavakkoli-Moghaddam, R., Modarres, M. and Baboli, A., "Reliable design of a forward/reverse logistics network under uncertainty: A robust-m/m/c queuing model", Transportation Research Part E: Logistics and Transportation Review,  Vol. 48, No. 6, (2012), 1152-1168. 9.      Hatefi, S., Jolai, F., Torabi, S. and Tavakkoli-Moghaddam, R., "Reliable design of an integrated forward-revere logistics network under uncertainty and facility disruptions: A fuzzy possibilistic programing model", KSCE Journal of Civil Engineering,  Vol. 19, No. 4, (2015), 1117-1128. 10.    Fereiduni, M. and Hamzehee, M., "A p-robust model in humanitarian logistics in a non-neutral political environment", Uncertain Supply Chain Management,  Vol. 4, No. 4, (2016), 249-262. 11.    Drezner, Z., "Heuristic solution methods for two location problems with unreliable facilities", Journal of the Operational Research Society,  (1987), 509-514. 12.    Lim, M., Daskin, M.S., Bassamboo, A. and Chopra, S., "A facility reliability problem: Formulation, properties, and algorithm", Naval Research Logistics (NRL),  Vol. 57, No. 1, (2010), 58-70. 13.    Wang, J. and Shu, Y.-F., "A possibilistic decision model for new product supply chain design", European Journal of Operational Research,  Vol. 177, No. 2, (2007), 1044-1061. 14.    Qin, X.-S., Huang, G.H., Zeng, G.-M., Chakma, A. and Huang, Y., "An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty", European Journal of Operational Research,  Vol. 180, No. 3, (2007), 1331-1357. 15.    Fatrias, D. and Shimizu, Y., "Possibilistic programming model for fuzzy multi-objective periodic review inventory in two-stage supply chain", International Journal of Applied Decision Sciences,  Vol. 7, No. 2, (2014), 168-189. 16.    Vahdani, B., Tavakkoli-Moghaddam, R., Jolai, F. and Baboli, A., "Reliable design of a closed loop supply chain network under uncertainty: An interval fuzzy possibilistic chance-constrained model", Engineering Optimization,  Vol. 45, No. 6, (2013), 745-765. 17.    Hatefi, S.M., Jolai, F., Torabi, S.A. and Tavakkoli-Moghaddam, R., "A credibility-constrained programming for reliable forward–reverse logistics network design under uncertainty and facility disruptions", International Journal of Computer Integrated Manufacturing,  Vol. 28, No. 6, (2015), 664-678. 18.    Lee, D.-H., Dong, M. and Bian, W., "The design of sustainable logistics network under uncertainty", International Journal of Production Economics,  Vol. 128, No. 1, (2010), 159-166. 19.    Pishvaee, M.S., Razmi, J. and Torabi, S.A., "Robust possibilistic programming for socially responsible supply chain network design: A new approach", Fuzzy Sets and Systems,  Vol. 206, (2012), 1-20. 20.    Erol, I., Sencer, S. and Sari, R., "A new fuzzy multi-criteria framework for measuring sustainability performance of a supply chain", Ecological Economics,  Vol. 70, No. 6, (2011), 1088-1100. 21.    Kamali, H., Sadegheih, A., Vahdat-Zad, M. and Khademi-Zare, H., "Deterministic and metaheuristic solutions for closed-loop supply chains with continuous price decrease", International Journal of Engineering-Transactions C: Aspects,  Vol. 27, No. 12, (2014), 1897-1904. 22.    Pishvaee, M.S. and Khalaf, M.F., "Novel robust fuzzy mathematical programming methods", Applied Mathematical Modelling,  Vol. 40, No. 1, (2016), 407-418. 23.    Soyster, A.L., "Convex programming with set-inclusive constraints and applications to inexact linear programming", Operations Research,  Vol. 21, No. 5, (1973), 1154-1157. 24.    Ben-Tal, A. and Nemirovski, A., "Robust convex optimization", Mathematics of Operations Research,  Vol. 23, No. 4, (1998), 769-805. 25.    El Ghaoui, L., Oustry, F. and Lebret, H., "Robust solutions to uncertain semidefinite programs", SIAM Journal on Optimization,  Vol. 9, No. 1, (1998), 33-52. 26.    Inuiguchi, M. and Sakawa, M., "Robust optimization under softness in a fuzzy linear programming problem", International Journal of Approximate Reasoning,  Vol. 18, No. 1-2, (1998), 21-34. 27.    Mulvey, J.M., Vanderbei, R.J. and Zenios, S.A., "Robust optimization of large-scale systems", Operations Research,  Vol. 43, No. 2, (1995), 264-281. 28.    Leung, S.C., Tsang, S.O., Ng, W.L. and Wu, Y., "A robust optimization model for multi-site production planning problem in an uncertain environment", European Journal of Operational Research,  Vol. 181, No. 1, (2007), 224-238. 29.    Pan , F.  and  Nagi,  R.,  "Robust   supply   chain   design   under uncertain demand in agile manufacturing", Computers & Operations Research,  Vol. 37, No. 4, (2010), 668-683. 30.    Pishvaee, M.S., Rabbani, M. and Torabi, S.A., "A robust optimization approach to closed-loop supply chain network design under uncertainty", Applied Mathematical Modelling,  Vol. 35, No. 2, (2011), 637-649. 31.             Ben-Tal, A. and Nemirovski, A., "Robust solutions of uncertain linear programs", Operations Research Letters,  Vol. 25, No. 1, (1999), 1-13.