Evaluating the Effectiveness of Integrated Benders Decomposition Algorithm and Epsilon Constraint Method for Multi-Objective Facility Location Problem under Demand Uncertainty

Abdolmohammadi, H. R., & Kazemi, A. (2013). A benders decomposition approach for a combined heat and power economic dispatch. Energy Conversion and Management, 71, 21-31.
Aghaei, J., Amjady, N., & Shayanfar, H. A. (2011). Multi-objective electricity market clearing considering dynamic security by lexicographic optimization and augmented epsilon constraint method. Applied Soft Computing, 11(4), 3846-3858.
Aghezzaf, E. (2005). Capacity planning and warehouse location in supply chains with uncertain demands. Journal of the Operational Research Society, 56(4), 453-462.
Al-Agtash, S., & Yamin, H. (2004). Optimal supply curve bidding using Benders decomposition in competitive electricity markets. Electric Power Systems Research, 71(3), 245-255.
Arjmand, M., & Najafi, A. A. (2015). Solving a multi-mode bi-objective resource investment problem using meta-heuristic algorithms. Advanced Computational Techniques in Electromagnetics, 2015(1), 41-58.
Baghalian, A., Rezapour, S., & Farahani, R. Z. (2013). Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. European Journal of Operational Research, 227(1), 199-215.
Behmanesh, R., & Rahimi, I. (2012). Using combination of optimized recurrent neural network with design of experiments and regression for control chart forecasting. Business Engineering and Industrial Applications Colloquium, 435-439.
Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.
Boschetti, M., & Maniezzo, V. (2009). Benders decomposition, lagrangean relaxation and metaheuristic design. Journal of Heuristics, 15(3), 283-312.
Çakır, O. (2009). Benders decomposition applied to multi-commodity, multi-mode distribution planning. Expert Systems with Applications, 36(4), 8212-8217.
Chan, Y., Carter, W. B., & Burnes, M. D. (2001). A multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands. Computers & Operations Research, 28(8), 803-826.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.

Charwand, M., Ahmadi, A., Heidari, A. R., & Esmaeel Nezhad, A. (2014). Benders decomposition and normal boundary intersection method for multiobjective decision making framework for an electricity retailer in energy markets. IEEE Systems Journal, 9(4), 1475-1484.
Chu, Y., & You, F. (2013). Integration of production scheduling and dynamic optimization for multi-product CSTRs: Generalized Benders decomposition coupled with global mixed-integer fractional programming. Computers & Chemical Engineering, 58, 315-333.
Coello, C. A. C., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems. New York, NY: Springer.
Dabia, S., Talbi, E. G., Van Woensel, T., & De Kok, T. (2013). Approximating multi-objective scheduling problems. Computers & Operations Research, 40(5), 1165-1175.
Danesh Asgari, S., & Haeri, A. (2017). Selection of appropriate measures by integrating the balanced scorecard and three-stage data envelopment analysis approaches. Iranian Journal of Management Studies, 10(2), 527-550.
Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8(3), 631-657.
Daskin, M. S., Snyder, L. V., & Berger, R. T. (2005). Logistics systems: Design and optimization. In Facility location in Supply chain design (pp. 39-65). Heidelberg, Berlin: Springer.
de Camargo, R. S., Miranda, G. D., & Luna, H. (2008). Benders decomposition for the uncapacitated multiple allocation hub location problem. Computers & Operations Research, 35(4), 1047-1064.
de Sá, E. M., de Camargo, R. S., & de Miranda, G. (2013). An improved Benders decomposition algorithm for the tree of hubs location problem. European Journal of Operational Research, 226(2), 185-202.
Esmaili, M., Ebadi, F., Shayanfar, H. A., & Jadid, S. (2013). Congestion management in hybrid power markets using modified Benders decomposition. Applied Energy, 102, 1004-1012.
Fortz, B., & Poss, M. (2009). An improved benders decomposition applied to a multi-layer network design problem. Operations Research Letters, 37(5), 359-364.
Fowler, R. J., Paterson, M. S., & Tanimoto, S. L. (1981). Optimal packing and covering in the plane are NP-complete. Information Processing Letters, 12(3), 133-137.

Ghane-Kanafi, A., & Khorram, E. (2015). A new scalarization method for finding the efficient frontier in non-convex multi-objective problems. Applied Mathematical Modelling, 1-16. DOI: 10.1016/j.apm.2015.03.022.
Gonzalez, T. F. (1985). Clustering to minimize the maximum intercluster distance. Theoretical Computer Science, 38, 293-306.
Ismail-Yahaya, A., & Messac, A. (2002). Effective generation of the Pareto frontier using the normal constraint method. AIAA 40th Aerospace Sciences Meeting and Exhibit, 1-12.
Kagan, N., & Adams, R. (1993). A Benders' decomposition approach to the multi-objective distribution planning problem. International Journal of Electrical Power & Energy Systems, 15(5), 259-271.
Khalili-Damghani, K., & Amiri, M. (2012). Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA. Reliability Engineering & System Safety, 103, 35-44.
Klimberg, R. K., & Ratick, S. J. (2008). Modeling data envelopment analysis (DEA) efficient location/allocation decisions. Computers & Operations Research, 35(2), 457-474.
Laumanns, M., Thiele, L., & Zitzler, E. (2006). An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research, 169(3), 932-942.
Longinidis, P., & Georgiadis, M. C. (2011). Integration of financial statement analysis in the optimal design of supply chain networks under demand uncertainty. International Journal of Production Economics, 129(2), 262-276.
Megiddo, N., & Tamir, A. (1982). On the complexity of locating linear facilities in the plane. Operations Research Letters, 1(5), 194-197.
Melo, M. T., Nickel, S., & Saldanha-Da-Gama, F. (2009). Facility location and supply chain management–A review. European Journal of Operational Research, 196(2), 401-412.
Messac, A., Ismail-Yahaya, A., & Mattson, C. A. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25(2), 86-98.
Mirghafoori, S. H., Ardakani, F. A., & Azizi, F. (2014). Developing a method for risk analysis in tile and ceramic industry using failure mode and effects analysis by data envelopment analysis. Iranian Journal of Management Studies, 7(2), 229.

 

Moheb-Alizadeh, H., Rasouli, S., & Tavakkoli-Moghaddam, R. (2011). The use of multi-criteria data envelopment analysis (MCDEA) for location–allocation problems in a fuzzy environment. Expert Systems with Applications, 38(5), 5687-5695.
Montemanni, R. (2006). A Benders decomposition approach for the robust spanning tree problem with interval data. European Journal of Operational Research, 174(3), 1479-1490.
Oliveira, F., Grossmann, I. E., & Hamacher, S. (2014). Accelerating Benders stochastic decomposition for the optimization under uncertainty of the petroleum product supply chain. Computers & Operations Research, 49, 47-58.
Osman, H., & Demirli, K. (2010). A bilinear goal programming model and a modified Benders decomposition algorithm for supply chain reconfiguration and supplier selection. International Journal of Production Economics, 124(1), 97-105.
Pishvaee, M., Razmi, J., & Torabi, S. (2014). An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain. Transportation Research Part E: Logistics and Transportation Review, 67, 14-38.
Rahimi, I., Askari, M., Tang, S., Lee, L., Azfanizam Binti Ahmad, S., & Sharaf, A. M. (2016). Development model for supply chain network design by demand uncertainty and mode selection. International Journal of Applied Operational Research-An Open Access Journal, 6(1), 51-64.
Taguchi, G. (1986). Introduction to quality engineering: Designing quality into products and processes. Quality and Reliability Engineering International, 4, 198-199.
Tang, S. H., Rahimi, I., & Karimi, H. (2016). Objectives, products and demand requirements in integrated supply chain network design: A review. International Journal of Industrial and Systems Engineering, 23(2), 181-203.
Torabi, M., & Mahlooji, H. (2017). An integrated simulation-DEA approach to multi-criteria ranking of scenarios for execution of operations in a construction project. Iranian Journal of Management Studies, 9(4), 801-827.
Üster, H., & Agrahari, H. (2011). A Benders decomposition approach for a 

distribution network design problem with consolidation and capacity considerations. Operations Research Letters, 39(2), 138-143.
Wang, F., Lai, X., & Shi, N. (2011). A multi-objective optimization for green supply chain network design. Decision Support Systems, 51(2), 262-269.
Yang, Y., & Lee, J. M. (2012). A tighter cut generation strategy for acceleration of Benders decomposition. Computers & Chemical Engineering, 44, 84-93.
Zitzler, E. (1999). Evolutionary algorithms for multiobjective optimization: Methods and applications (Doctoral dissertaion). ETH Zurich, Switzerland.