عنوان مقاله [English]
Facility location problem is one of the most important and useful topics in the field of decision-making. Cost reduction is always one of the main criteria in these problems. Since environmental concerns increment in recent years, harmful gas emissions and environmental pollution is regarded as other affective criteria in locating of facilities and also allocating them to customers. In this paper, a capacitated bi-objective facility location problem with multi-source and multi-product is studied. In this problem, financial costs and gas emissions are considered simultaneously. First the mathematical model is presented, and then a robustness analysis using Mont Carlo simulation method is applied for solving it. Through using this method it is possible to determine stability level of Pareto optimal solutions to make better decisions for establishing facilities and allocating customers to them. Finally, the computational results are presented.
 A. Klose and A. Drexl, "Facility location models for distribution system design," European Journal of Operational Research, vol. 162(1), pp. 4-29, 2005.
 R. Tavakkoli-Moghaddam, M. Omidi-Rekavandi, and A. Ghodratnam, "Mathematical Modeling for the Forward and Reverse Logistics Network Design," Management Researches in Iran, vol. 17(4), pp. 43-63, 2014.
 M.S. Daskin, "Network and discrete location: models, algorithms and applications," Journal of the Operational Research, Wiley- Interscience Publication, New York. Society, 1995.
 Z. Drezner and H.W. Hamacher, Facility location: applications and theory, Berlin, Springer, 2002.
 S.H. Owen and M.S. Daskin, "Strategic facility location: a review," European Journal of Operational Research, vol. 111, pp. 423–447, 1998.
 S. Liao, C. Hsieh, and Y. Lin, "A multi-objective evolutionary optimization approach for an integrated location-inventory distribution network problem under vendor-managed inventory systems," Annals of Operations Research, vol. 186 (1), pp. 213–229, 2011.
 H. Javanshir, S. Ebrahimnejad, and S. Nouri, "Bi-objective supply chain problem using MOPSO an NSGA-II," International Journal of Industrial Engineering Computations, vol. 3(4), pp. 681–694, 2012.
 B. Latha Shankar, S. Basavarajappa, J.C.H. Chen, and R.S. Kadadevaramath, "Location and allocation decisions for multi-echelon supply chain network – a multi-objective evolutionary approach," Expert Systems with Applications, vol. 40 (2), pp. 551–562, 2013.
 D. Ozgen and B. Gulsun, "Combining possibilistic linear programming and fuzzy AHP for solving the multi-objective capacitated multi-facility location problem," Information Sciences, vol. 268, pp. 185–201, 2014.
 B.M. Beamon, "Designing the green supply chain," Logistics Information Management, vol. 12(4), pp. 332-342, 1999.
 R.Z. Farahani, M. Steadiesei, and N. Asgari, "Multiple criteria facility location problems: a survey," Applied Mathematical Modelling, vol. 34(7), pp. 1689-1709, 2010.
 D. Lee and M. Dong, "A heuristic approach to logistics network design for end-of-lease computer products recovery," Transportation Research Part E: Logistics and Transportation Review, vol. 44(3), pp. 455-474, 2008.
 N. Kumar, R.P. Agrahari, and D. Roy, "Review of green supply chain processes," IFAC-Paper OnLine, vol. 48(3), pp. 374-381, 2015.
 H.H. Khoo, I. Bainbridge, T.A. Spedding, and D.M. Taplin, "Creating a green supply chain," Greener Management International, vol. 35, pp. 71–88, 2001.
 R.K. Pati, P. Vrat, and P. Kumar, "A goal programming model for paper recycling system," Omega, vol. 36, pp. 405-417, 2008.
 J. Quariguasi Frota Neto, J.M. Bloemhof-Ruwaard, J.A.E.E. Van Nunen, and E. Van Heck, "Designing and evaluating sustainable logistics networks,"International Journal of Production Economics, vol. 111(2), pp. 195–208, 2008.
 A.D. Bojarski, J.M. Lainez, A. Espuna, and L. Puigjaner, "Incorporating environmental impacts and regulations in a holistic supply chains modeling: an LCA approach," Computers & Chemical Engineering, vol. 33(10), pp. 1747–1759, 2009.
 F. Wang, X. Lai, and N. Shi, "A multi-objective optimization for green supply chain network design," Decision Support Systems, vol. 51(2), pp. 262–269, 2011.
 I. Harris, M. Naim, A. Palmer, A. Potter, and C. Mumford, "Assessing the impact of cost optimization based on infrastructure modelling on CO2 emissions," International Journal of Production Economics, vol. 131(1), pp. 313–321, 2011.
 I. Harris, C. Mumford, and M. Naim, "An evolutionary bi-objective approach to the capacitated facility location problem with cost and CO2 emissions," Genetic and Evolutionary Computation, GECCO 2011, ACM.
 M.S. Pishvaee and J. Razmi, "Environmental supply chain network design using multi-objective fuzzy mathematical programming," Applied Mathematical Modelling, vol. 36(8), pp. 3433–3446, 2012.
 I. Harris, C. Mumford, and M. Naim, "A hybrid multi-objective approach to capacitated facility location with flexible store allocation for green logistics modeling," Transportation Research Part E, vol. 66, pp. 1–22, 2014.
 H. Afshari, M. Sharafi, T. ElMekkawy, and Q. Peng, "Optimizing multi-objective dynamic facility location decisions within green distribution network design," Procedia CIRP, vol. 17, pp. 675 – 679, 2014.
 A. Zakeri, F. Dehghanian, B. Fahimnia, and J. Sarkis, "Carbon pricing versus emissions trading: A supply chain planning perspective," International Journal of Production Economics, vol. 164, pp. 197–205, 2015.
 B. Fahimnia, J. Sarkis, A. Choudhary, and A. Eshragh, "Tactical supply chain planning under a carbon tax policy scheme: A case study," International Journal of Production Economics, vol. 164, pp. 206–215, 2015.
 M. Soltani Tehrani, H.A. Hassanpour, and S.Ramezani, "Two-objective optimization model of costs and carbon dioxide in closed loop supply chain," Management Researches in Iran, vol. 19(1), pp. 169-189, 2015 (In Persian).
 L. Babaee, M. Rabieh, E. Nikbakhsh, and M.Esmaeili, " Multi- Objective Mathematical Model for Green Supplier Selection (Case Study: Supply Chain of IRAN KHODRO Company)," Modern Researches in Decision Making, vol. 2 (2), pp. 1-261, 2017 (In Persian).
 E.M. Toro, J.F. Franco, M.G. Echeverri, and F.G. Guimarães, "A multi-objective model for the green capacitated location-routing problem considering environmental impact," Computers & Industrial Engineering, vol. 110, pp. 114–125, 2017.
 G. Mavrotas, O. Pechak, E. Siskos, H. Doukas, and J. Psarras, "Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation," European Journal of Operational Research, vol. 240, pp. 193–201, 2015.
 J.M. Mulvey, R.J. Vanderbei, and S.A. Zenios, "Robust optimization of large scale systems," Operations Research, vol. 43(2), pp. 264–281, 1995.