An Optimization Model for Multi-objective Closed-loop Supply Chain Network under uncertainty: A Hybrid Fuzzy-stochastic Programming Method

Document Type: Research Paper

Author

Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Abstract

In this research, we address the application of uncertainty
programming to design a multi-site, multi-product, multi-period,
closed-loop supply chain (CLSC) network. In order to make the
results of this article more realistic, a CLSC for a case study in
the iron and steel industry has been explored. The presented
supply chain covers three objective functions: maximization of
profit, minimization of new products' delivery time, collection
time and disposal time of used products, and maximizing
flexibility. To solve the proposed model, an interactive hybrid
solution methodology is adopted through combining a hybrid
fuzzy-stochastic programming method and a fuzzy multi-objective
approach. Finally, the numerical experiments are given to
demonstrate the significance of the proposed model and the
solution approach.

Keywords


[1] F. Altiparmak, M. Gen, L. Lin and T. A. Paksoy,genetic algorithm approach for multi-
objective optimization of supply chain networks, Computers and Industrial Engineering, 51
(2006), 197-216.
[2] B. Bilgen,Application of fuzzy mathematical programming approach to the production alloca-
tion and distribution supply chain network problem, Expert Syst Appl, 37 (2010), 4488-4495.
[3] J. R. Birge and F. V. Louveaux,A multi cut algorithm for two-stage stochastic linear pro-
grams, European Journal of Operational Research, 34 (1988), 384-392.

[4] SL. Chung , HM.Wee and PC. Yang ,Optimal policy for a closed-loop sup-ply chain inventory
system with remanufacturing, Math Comput Model, 48 (2008), 867-881.
[5] F. Du and GW. Evans, A bi-objective reverse logistics network analysis for post-sale service,
Computers and Operations Research, 35 (2008), 26-34.
[6] D. Dubois and H. Prade, Possibility Theory - An Approach to the Computerized Processing
of Uncertainty, Plenum Press, New York, (1988), 24-54.
[7] M. El-Sayed, N. A a and A. El-Kharbotly, A stochastic model for forward-reverse logistics
network design under risk, Comput Ind Eng, 58 (2010), 423-431.
[8] M. Fleischmann, P. Beullens, JM. Bloemhof ruwaard and L. Wassenhove, The impact of
product recovery on logistics network design, Production and Operations Management, 10
(1) (2001), 56-73.
[9] R. A.Freeze, J. Massmann, L. Smith, J. Sperling and B. James, Hydrogeological decision
analysis, 1, a framework. Ground Water, 28 (1990), 738-766.
[10] P. Guo, G. H.Huang and Y. P. Li, An inexact fuzzy-chance-constrained two-stage mixed-
integer linear programming approach for
ood diversion planning under multiple uncertain-
ties, Advances in Water Resources, 33 (2010), 81-91.
[11] G. H. Huang and D. P. Loucks, An inexact two stage stochastic programming model for water
resources management under uncertainty, Civil Engineering and Environmental Systems, 17
(2000), 95-118.
[12] G. H. Huang, A hybrid inexact-stochastic water management model, European Journal of
Operational Research, 107 (1998), 137-158.
[13] A. Hasani, SH. Zegordi and E. Nikbakhsh, Robust closed-loop supply chain network design
for perishable goods in agile manufacturing under uncertainty, Int J Prod Res, 50 (2012),
4649-4669.
[14] MA. Ilgin and SM. Gupta, Environmentally conscious manufacturing and product recovery
(ECMPRO): a review of the state of the art, J Environ Manage, 91 (2010), 563-591.
[15] M. Inuiguchi and T. Tanino, Portfolio selection under independent possibilistic information,
Fuzzy Sets and Systems, 115 (2000), 83-92.
[16] M. G. Iskander, A suggested approach for possibility and necessity dominance indices in
stochastic fuzzy linear programming, Applied Mathematics Letters, 18 (2005), 395-399.
[17] S. Kara and S. A. Onut, Stochastic optimization approach for paper recycling reverse logistics
network design under uncertainty, Int J Environ Sci Technol, 4 (2010), 717-730.
[18] D. Lee and M. A. Ong, Heuristic approach to logistics network design for end of lease com-
puter products recovery, Transportation Research Part E, 44 (2008), 455-474.
[19] DH. Lee, M. Dong and W. Bian, The design of sustainable logistics network under uncer-
tainty, Int J Prod Econ, 128 (2010), 159-166.
[20] W. Li, Y. P. Li, C. H. Li and G. H. Huang, An inexact two-stage water management model
for planning agricultural irrigation under uncertainty, Agricultural Water Management, 97
(2010), 1905-1914.
[21] Y. P. Li, J. Liu and G. H. Huang,A hybrid fuzzy-stochastic programming method for water
trading within an agricultural system, Agricultural Systems, 123 (2014), 71-83.
[22] Y. P. Li, G. H. Huang and S. L.Nie, Planning water resources management systems using
a fuzzy-boundary interval stochastic programming method, Advances in Water Resources, 33
(2010), 1105-1117.
[23] Y. P. Li, G. H. Huang, Y. F. Huang and H. D. Zhou, A multistage fuzzy-stochastic program-
ming model for supporting sustainable water resources allocation and management, Environ-
mental Modelling and Software, 7 (2009), 786-797.
[24] Y. J. Lai and C. L. Hwang, Possibilistic linear programming for managing interest rate risk,
Fuzzy Sets and Systems, 54 (1993), 135-146.
[25] E. Melachrinoudis, A. Messac and H. Min, Consolidating a warehouse network: a physical
programming approach, International Journal of Production Economics, 97 (2005), 1-17.
[26] G. A. Mendoza, B. Bruce Bare and Z. H. Zhou, A fuzzy multiple objective linear programming
approach to forest planning under uncertainty, Agricultural Systems, 41 (1993), 257-274.

[27] EU. Olugu and KY. Wong, An expert fuzzy rule-based system for closed-loop supply chain
performance assessment in the automotive industry, Expert Syst Appl, 39 (2012), 375-384.
[28] S. Pokharel and A. Mutha, Perspectives on reverse logistics: a review, Resources, Conserva-
tion and Recycling, 53(4) (2009) 175-82.
[29] MS. Pishvaee and SA. Torabi, A possibilistic programming approach for closed-loop supply
chain network design under uncertainty, Fuzzy Set Syst, 161 (2010), 2668-2683.
[30] MS.Pishvaee and J.Razmi, Environmental supply chain network design using multi objective
fuzzy mathematical programming, Appl Math Model, 36 (2012), 3433-3446.
[31] Q. Qiang, K. Ke and T. Anderson , J.Dong,The closed loop supply chain network with com-
petition, distribution channel investment, and uncertainties, Omega, 41 (2013), 186-194.
[32] S. Rubio, A. Chamorro and FJ. Miranda, Characteristics of the research on reverse logistics,
International Journal of Production Research, 46(4) (2008), 1099-1120.
[33] D. Stindt and R. Sahamie, Review of research on closed loop supply chain management in
the process industry, Flexible Services and Manufacturing Journal, 43(2) (2014), 23-45.
[34] SK. Srivastava, Green supply chain management: a state of the art literature review, Inter-
national Journal of Management Reviews, 9(1) (2007), 53-80.
[35] MIG. Salema, AP.Barbosa-Povoa and AQ.Novais, An optimization model for the design of
a capacitated multi-product reverse logistics network with uncertainty, Eur J Oper Res, 179
(2007), 1063-1077.
[36] K. Subulan, AS. Tasan and A.Baykasoglu, Fuzzy mixed integer programming model for
medium term planning in a closed-loop supply chain with remanufacturing option, J Intel
Fuzzy Syst, 23 (2012), 345-368.
[37] S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple
objective supply chain master planning, Fuzzy Sets and Systems, 159 (2008), 193-214.
[38] S. Verstrepen, F. Cruijssen, M. De Brito and W.Dullaert, An exploratory analysis of reverse
logistics in Flanders., European Journal of Transport and Infrastructure Research, 7(4)
(2007), 301-316.
[39] B. Vahdani, J. Razmi and R. Tavakkoli Moghaddam, Fuzzy possibilistic modeling for closed
loop recycling collection networks, Environ Model Assess, 17 (2012), 623-637.
[40] B. Vahdani, R. Tavakkoli Moghaddam, F. Jolai and A. Baboli, Reliable design of a closed loop
supply chain network under uncertainty: an interval fuzzy possibilistic chance constrained
model, Eng Optim, 45 (2013), 745-765.
[41] B. Vahdani, R. Tavakkoli Moghaddam, M. Modarres and A. Baboli, Reliable design of a
forward/reverse logistics network under uncertainty: a robust-M M c queuing model, Transp
Res Part E, 48 (2012), 1152-1168.
[42] P. Wells and M. Seitz, Business models and closed loop supply chains: a typology, Supply
Chain Management: An International Journal, 10(4) (2005), 249-251.
[43] HF. Wang and HW. Hsu, Resolution of an uncertain closed-loop logistics model: an applica-
tion to fuzzy linear programs with risk analysis, J Environ Manage, 91(21) (2010), 48-62.
[44] L. A. Zadeh, The concept of a linguistic variables and its application to approximate
reasoning-1, Information Sciences, 8 (1975), 199-249.
[45] H. J. Zimmermann, Fuzzy Set Theory and its Applications, third ed, Kluwer Academic Pub-
lishers, (1996), 32-47.
[46] H. J. Zimmermann, Fuzzy programming and linear programming with several objective func-
tions, Fuzzy Sets and Systems, 1 (1978), 45-55.