A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain

Document Type : Article


1 Department of Industrial Management, Faculty of Management and Accounting, University of Shahid Beheshti, Tehran, Iran.

2 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran.


This paperproposes a multi-objective, multi-stage programming model to design a sustainable closed-loop supply chain network considering financial decisions. A multi-product, sustainable closed-loop plastic supply chain network design problem which encompasses economic, environmental and social objectives is modeled in a mathematical manner. The decisions to be made are concerned with location of facilities; the flow of products, loans to take and investments to make. Uncertainty issue is about demand of customers and investment's rate of return. The decision making model is formulated as a multi-objective, multi-stage mixed integer linear programming problem and is solved by implementing path formulation and augmented Ɛ-constraint methods. Computational analysis, is provided based on the subject company to determine the significance of the proposed model and the efficiency regarding integrating financial decisions with supply chain network design decisions.


  1. References:

    1. Devika, K., Jafarian, A., and Nourbakhsh, V. Designing  a sustainable closed-loop supply chain network  based on triple bottom line approach: A comparison  of metaheuristics hybridization techniques", Eur. J.  Oper. Res., 235(3), pp. 594{615 (2014).  
    2. Seuring, S. and Muller, M. From a literature review  to a conceptual framework for sustainable supply chain  management", J. Clean. Prod., 16(15), pp. 1699{1710  (2008). 
    3.  Pishvaee, M.S., Razmi, J., and Torabi, S.A. An accelerated  Benders decomposition algorithm for sustainable  supply chain network design under uncertainty: A  case study of medical needle and syringe supply chain",  Transp. Res. Part E Logist. Transp. Rev., 67, pp. 14{  38 (2014). 
    4.  Eskandarpour, M., Dejax, P., Miemczyk, J., and  Peton, O. Sustainable supply chain network design:  An optimization-oriented review", Omega (United  Kingdom), 54, pp. 11{32 (2015). 
    5. Soleimani, H., Seyyed-Esfahani, M., and Kannan, G.  Incorporating risk measures in closed-loop supply  chain network design", Int. J. Prod. Res., 52(6), pp.  1843{1867 (2014). 
    6. Srivastava, S.K. Green supply-chain management: a  state-of-the-art literature review", Int. J. Manag. Rev.,  9(1), pp. 53{80 (2007).  7. Giarola, S., Shah, N., and Bezzo, F. A comprehensive  approach to the design of ethanol supply chains  including carbon trading e_ects", Bioresour. Technol.,  107, pp. 175{185 (2012).  8. Verma, M., Gendreau, M., and Laporte, G. Optimal  location and capability of oil-spill response facilities for  the south coast of Newfoundland", Omega, 41(5), pp.  856{867 (2013).  9. Pishvaee, M.S., Razmi, J., and Torabi, S.A. Robust  possibilistic programming for socially responsible supply  chain network design: A new approach", Fuzzy sets  Syst., 206, pp. 1{20 (2012).  10. Guill_en-Gos_albez, G. and Grossmann, I. A global optimization  strategy for the environmentally conscious  design of chemical supply chains under uncertainty in  the damage assessment model", Comput. Chem. Eng.,  34(1), pp. 42{58 (2010).  11. Amin, S.H. and Zhang, G. A multi-objective facility  location model for closed-loop supply chain network  under uncertain demand and return", Appl. Math.  Model., 37(6), pp. 4165{4176 (2013).  12. Ruiz-Femenia, R., Guillen-Gosalbez, G., Jimenez, L.,  and Caballero, J.A. Multi-objective optimization of  environmentally conscious chemical supply chains under  demand uncertainty", Chem. Eng. Sci., 95, pp.  1{11 (2013).  13. Shapiro, J.F. Challenges of strategic supply chain  planning and modeling", Comput. J. F. (2004). Challenges  Strateg. Supply Chain Plan. Model. Comput.  Chem. Eng., 28(6), pp. 855{861 (2004).  14. Ramezani, M., Kimiagari, A.M., and Karimi, B.  Closed-loop supply chain network design: A _nancial  approach", Appl. Math. Model., 38(15{16), pp. 4099{  4119 (2014).  15. Nickel, S., Saldanha-da-Gama, F., and Ziegler, H-P. A  multi-stage stochastic supply network design problem  with _nancial decisions and risk management", Omega,  40(5), pp. 511{524 (2012).  16. Wang, B., Huang, D-C., Li, H., and Ding, J-Y.  Optimal decisions and _nancing strategies selection  of supply chain with capital constraint", Math. Probl.  Eng., Article ID: 6597259, 14 pages (2016).  17. Melo, M.T., Nickel, S., and Saldanha da Gama, F.  Dynamic multi-commodity capacitated facility location:  A mathematical modeling framework for strategic  supply chain planning", Comput. Oper. Res., 33(1),  pp. 181{208 (2006).  394 A.S. Mohammadi et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 377{395  18. Birge, J. and Louveaux, F. Introduction to stochastic  programming", Springer Ser. Oper. Res. (1997).  19. Babazadeh, R., Razmi, J., Pishvaee, M.S., and Rabbani,  M. A sustainable second-generation biodiesel  supply chain network design problem under risk",  Omega (United Kingdom), 66, pp. 258{277 (2017).  20. Balaman, S.Y. and Selim, H. Sustainable design of  renewable energy supply chains integrated with district  heating systems: A fuzzy optimization approach", J.  Clean. Prod., 133, pp. 863{885 (2016).  21. Pishvaee, M.S. and Razmi, J. Environmental supply  chain network design using multi-objective fuzzy mathematical  programming", Appl. Math. Model., 36(8),  pp. 3433{3446 (2012).  22. Pishvaee, M.S., Torabi, S.A., and Razmi, J.  Credibility-based fuzzy mathematical programming  model for green logistics design under uncertainty",  Comput. Ind. Eng., 62(2), pp. 624{632 (2012).  23. Sa_ar, M.M. and Razmi, J. A new bi-objective mixed  integer linear programming for designing a supply  chain considering CO2 emission", Uncertain Supply  Chain Manag., 2(4), pp. 275{292 (2014).  24. Sa_ar, M.M. and Razmi, J. A new multi objective  optimization model for designing a green supply chain  network under uncertainty", Int. J. Ind. Eng. Comput.,  6, pp. 15{32 (2015).  25. Guill_en-Gos_albez, G. and Grossmann, I.E. Optimal  design and planning of sustainable chemical supply  chains under uncertainty", AIChE J., 55(1), pp. 99{  121 (2009).  26. Mohammadi, M., Torabi, S.A., and Tavakkoli-  Moghaddam, R. Sustainable hub location under  mixed uncertainty", Transp. Res. Part E: Logist.  Transp. Rev., 62, pp. 89{115 (2014).  27. Zhalechian, M., Tavakkoli-Moghaddam, R., Zahiri, B.,  and Mohammadi, M. Sustainable design of a closedloop  location-routing-inventory supply chain network  under mixed uncertainty", Transp. Res. Part E Logist.  Transp. Rev., 89, pp. 182{214 (2016).  28. Shaw, K., Irfan, M., Shankar, R., and Yadav,  S.S. Computers & industrial engineering low carbon  chance constrained supply chain network design  problem: a Benders decomposition based approach",  Comput. Ind. Eng., 98, pp. 483{497 (2016).  29. Mohseni, S. and Pishvaee, M.S. A robust programming  approach towards design and optimization of  microalgae-based biofuel supply chain", Comput. Ind.  Eng., 100, pp. 58{71 (2016).  30. Mohammed, F., Selim, S.Z., Hassan, A., and Syed,  M.N. Multi-period planning of closed-loop supply  chain with carbon policies under uncertainty", Transp.  Res. Part D Transp. Environ., 51, pp. 146{172 (2017).  31. Ruimin, M.A., Lifei, Y.A.O., Maozhu, J.I.N., Peiyu,  R.E.N., and Zhihan, L.V. Robust environmental  closed-loop supply chain design under uncertainty",  Chaos, Solitons and Fractals, 89, pp. 195{202 (2016).  32. Golp^_ra, H., Zandieh, M., Naja_, E., and Sadi-  Nezhad, S. A multi-objective, multi-echelon green  supply chain network design problem with risk-averse  retailers in an uncertain environment", Sci. Iran. E,  24(1), pp. 413{423 (2017).  33. Plastics Europe, Plastics-The Facts 2013: An Analysis  of European Latest Plastics Production, Demand and  Waste Data, pp. 1{40 (Oct. 2013).  34. Heitsch, H. and Romisch, W. Scenario tree modelling  for multistage stochastic programs", Math. Program.,  118(2), pp. 371{406 (2009).  35. Rebitzer, G., Ekvall, T., Frischknecht, R., Hunkeler,  D., Norris, G., Rydberg, T., Schmidt, W., Suh,  S., Weidema, B., and Pennington, D.W. Life cycle  assessment: Framework, goal and scope de_nition,  inventory analysis, and applications", Environ. Int.,  30(5), pp. 701{720 (2004).  36. Consultants, P., Eco-Indicator 99 Manual for Designers,  Minist. Housing, Spat. Plan. Environ. (2000).  37. Goedkoop, M. and Spriensma, R., The Eco-Indicator  99 - A Damage Oriented Method for Life Cycle Impact  Assessment, Assessment, p. 144 (2001).  38. International Organization for Standardization, Final  Draft International Standard ISO/FDIS 26000, Guidance  on Social Responsibility (2010).  39. CEPAA, G., Guidance Document for Social Accountability  8000, Council on Economiuc Priorities Accreditation  Agency, New York (1999).  40. Institute of Social and Ethical AccountAbility, AccountAbility  1000 (AA1000) Framework: Standard,  Guidelines and Professional Quali_cation, Institute of  Social and Ethical Accountability (1999).  41. Mavrotas, G. E_ective implementation of the constraint  method in multi-objective mathematical programming  problems", Appl. Math. Comput., 213(2),  pp. 455{465 (2009).  42. Nickel, S., Reuter-Oppermann, M., and Saldanha  da Gama, F. Ambulance location under stochastic  demand: A sampling approach", Oper. Res. Heal.  Care, 8, pp. 24{32 (2016).