A Robust Optimization Model Based on The Green Supply Chain Network Design under Uncertainty of Future Economic Conditions

Document Type : Original Article


Industrial Engineering Department, Shiraz University of Technology, Shiraz, Iran.


In this paper, a robust programming model for forward and reverse green (environmental) supply chain network design is established under uncertainty of future economic conditions. Initially, a deterministic mixed integer programming model is provided, and then the robust model based on using a scenario-based approach (two-step) is developed. The network design problem, including assumptions such as: multi-product, multi-echelon and single-period. Considering a situation of instability of the economic situation, the uncertainty has been considered in a different way from previous papers. The unstable economic conditions affect the demand and prices of raw materials and fuel; as a result, demand and total costs of production and transportation parameters in the problem are uncertain. The Proposed model is also considers the release rate of greenhouse gas production and transportation systems in the chain and tries to reduce it by providing an objective function at a time. Besides, Manufacturing and distribution centers work in a dual-purpose manner; its advantages are saving money and reducing pollution resulted from shared transport equipment's and infrastructure.


Atefeh Baghalian, Shabnam Rezapour c, Reza Zanjirani Farahani, (2013), “Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case”, European Journal of Operational Research 227 199–215.
Birge JR, Louveaux F, (1997), “Introduction to stochastic programming”. Springer series in operations research, New York: Springer-Verlag;.
Chen Z-L, Vairaktarakis GL. (2005),” Integrated scheduling of production and distribution operations”. Management Science; 51:614–28.
Chu, C.H., Luh, Y.P., Li, T.C., Chen, H., (2009), “Economical Green Product design based on simplified computer-aided product structure variation”. Computers in Industry 60, 485–500.
Elhedhli S, Goffin J-L, (2005), “Efficient production–distribution system design”, Management Science; 51:1151–64.
 Emmet, S., Sood, V., (2010),” Green Supply Chains: An Action Manifesto”. Willey, UK.
Fleischmann, M., Bloemhof-Ruwaard, J.M., Dekker, R., Van Der Laan, E., Van Nunen, J.A.E.E., Van Wassenhove, L.N., (1997),”Quantitative models for reverse logistics: a review”. European Journal of Operational Research 103, 1–17.
Gutierrez G, Kouvelis P, Kurawala A. (1996),” robustness approach to incapacitated network design problems”. European Journal of Operational Research; 94:362–76.
Hendricks, K.B., Singhal, V.R., (2005),” An empirical analysis of the effect of supply chain disruptions on long-run stock price performance and equity risk of the firm. Production and Operations Management”, 14 (1), 35–52.
Hu, T.L., Sheu, J.B., Huang, K.H., (2002),” A reverse logistics cost minimization model for the treatment of hazardous wastes”. Transportation Research Part E 38, 457– 473.
Iakovou, E., Vlachos, D., Chatzipanagioti, M., Mallidis, I., (2010),” A comprehensive optimization framework for sustainable supply chain networks”, In: Seventh International Conference on Logistics and Sustainable Transport, Slovenia.
Leung S, Tsang S, Ng W, Wu Y. (2007),” A robust optimization model for multi-site production planning problem in an uncertain environment”. European Journal of Operational Research; 181:224–38.
Li, F., Liu, T., Zhang, H., Cao, R., Ding, W., Fasano, J.P., (2008),” Distribution center location for green supply chain”, In: International Conference on Service Operations and Logistics, and informatics, IEEE, pp. 2951–2956.
L. Meade, J. Sarkis, A. Presley, (2007), “The theory and practice of reverse logistics, Int. J. Logistics Syst”, Manage. 3 56–84.
Luh, Y.P., Chu, C.H., Pan, C.C., (2010),” Data management of green product development with generic modularized product architecture”. Computers in Industry 61, 223–234.
M.A. Ilgin, M. Surendra, S.M. Gupta, (2010),” Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art”, J.
Environ. Manage. 91 563–591.
McKinnon, A., Cullinane, S., Browne, M., Whiteing, A., (2010), “Green Logistics: Improving the Environmental Sustainability of Logistics”, Kogan, London.
ministry of  Howusing, (2000),Spatial planning and the environment,the eco-indicator 99,A damage oriented method for life cycle impact assessment: manual for designers, Netherlands.
MirHassani S, Lucas G, Mitra G, Messina E, Poojari C,( 2000),” Computational solution of capacity planning models under uncertainty”, Parallel Computing;94: 511–38.
Neto, J.Q.F., Ruwaard, J.M.B., van Nunen, J.A.E.E., Van Heck, E., (2008),” Designing and evaluating sustainable logistics networks”. International Journal of Production Economics 111, 195–208.
Norrman, A., Jansson, U., (2004),” Ericsson’s proactive supply chain risk management approach after a serious sub-supplier accident”. International Journal of Physical Distribution & Logistics Management 34 (5), 434–456.
O’ Brien, C., (1999),” Sustainable production, new paradigm for a new millennium”. International Journal of Production Economics 60–61, 1–7.
Pishvaee,Jolai,Razmi, (2009),” A stochastic optimization model for integrated forward/reverse logistics network design”, Jornal of Manufacturing systems.(109-111).
Pishvaee, Razmi,(2012),” Environmental supply chain network design using multi-objective fuzzy mathematical programming”,Applied mathematical modeling,(3437-3438).
Ramudhin, A., Chaabane, A., Parquet, A.M., (2009),” On the design of sustainable green supply chains”. In: International Conference on Computers and Industrial Engineering, CIE, pp. 979–984.
 Simchi-Levi, D., Kaminsky, P., (2004).” Managing the Supply Chain: The Definitive Guide for the Business Professional”, Boston, Irwin McGraw-Hill.
Tang, C.S., (2006).” Perspectives in supply chain risk management”, International Journal of Production Economics 103, 451–488.
Tsiakis P, Shah N, Pantelides C. (2001),” Design of multi-echelon supply chain networks under demand uncertainty”, Industrial & Engineering Chemistry Research; 40:3585–604.
Wang, F., Lai, X., Shi, N., (2011),” A multi-objective optimization for green supply chain network design”, Decision Support Systems 51, 262–269.