Set a bi-objectives model for suppliers selection with capacity constraint and reducing lead-time with meta-heuristic algorithms

Document Type : Research Paper


Faculty of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran


Supplier evaluation and selection are some of the essential issues in organizational strategic planning between managers and Entrepreneurs. Nodaway, markets are in a situation where both buyers and suppliers are under the challenge. Supplier selection is a complex problem, and decision-makers need to use mathematical models to solve it. In this paper, we present a bi-objective supplier-selection model. The first objective is minimizing the total annual cost, and the second is minimizing lead times. Since supplier selection belongs to Np. The hard category of problems and the model objectives have conflict, and we used three different multi-objective meta-heuristic algorithms to solve the presented model and compare the results of these algorithms. The solving algorithms are multi-objective invasive weed optimization (MOIWO), Non-dominated Sorting Genetic Algorithm (NSGA-II), and Non-dominated ranked genetic algorithms (NRGA). The algorithm parameters were tuned using the Taguchi method, and for comparing the algorithms, the TOPSIS model has been used.


[1] O. Al Jadaan, C.R. Rao and L. Rajamani, Non-dominated ranked genetic algorithm for solving multi-objective optimization problems: NRGA, J. Theor. Appl. Inf. Technol. (2008), 60–67.
[2] A. Baghalian, S. Rezapour and R.Z. Farahani, Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case, European J. Oper. Res. 227 (2013), no. 1, 199–215.
[3] K. Deb, S. Agrawal, A. Pratap and T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, Proc. Paral. Prob. Solv. From Nature VI (PPSN-VI) Conf., 2000, pp. 849–858.
[4] A. Diabat and M. Al-Salem, An integrated supply chain problem with environmental considerations, Int. J. Prod. Econ. 164 (2015), 330–338.
[5] S.H. Ghodsypour and C. O’Brien, The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraint, Int. J. Prod. Econ. 73 (2001), no. 1, 15–27.
[6] D.R. Goossens, A.J.T. Maas, F.C.R. Spieksma and J.J. Klundert, Exact algorithms for procurement problems under a total quantity discount structure, European J. Oper. Res. 178 (2007), 603–626.
[7] K. Govindan, A. Jafarian and V. Nourbakhsh, Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic, Comput. Oper. Res. 62 (2015), 112–130.
[8] D.K. Kadambala, N. Subramanian, M.K. Tiwari, M. Abdulrahman and C. Liu, Closed-loop supply chain networks: designs for energy and time value efficiency, Int. J. Prod. Econ. 183 (2017), 382–393.
[9] O. Kaya and B. Urek, A mixed integer nonlinear programming model and heuristic solutions for location, inventory, and pricing decisions in a closed-loop supply chain, Comput. Oper. Res. 65 (2016), 93–103.
[10] A.R. Mehrabian and C. Lucas, A novel numerical optimization algorithm inspired by weed colonization, Ecol. Inf. 1 (2006), no. 4, 355–366.
[11] M. Talaei, B.F. Moghaddam, M.S. Pishvaee, A. Bozorgi-Amiri and S. Gholamnejad, A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in the electronics industry, J. Cleaner Prod. 113 (2016), no. 1, 662–673.
[12] W.P. Wang, A fuzzy linguistic computing approach to supplier evaluation, Appl. Math. Model. 34 (2010), no. 10,
[13] C.N. Wang, H.T. Tsai, T.P. Ho, V.T. Nguyen and Y.F. Huang, Multi-criteria decision making (MCDM) model for supplier evaluation and selection for oil production projects in Vietnam, Processes 8 (2020), no. 2, 134.
[14] J. Wei, K. Govindan, Y. Li and J. Zhao, Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Comput. Oper. Res. 54 (2015), 257–265.
[15] M.Q. Wu, C.H. Zhang, X.N. Liu and J.P. Fan, Green supplier selection based on DEA model in interval-valued Pythagorean fuzzy environment, IEEE Access 7 (2019), 108001–108013.
[16] G. Zhang, Research on supplier selection based on fuzzy sets group decision, Comput. Intel. Design 2 (2009), 529–531.
[17] M. Zohal and H. Soleimani, Developing an ant colony approach for green closed-loop supply chain network design:
a case study in the gold industry, J. Cleaner Prod. 133 (2016), no. 1, 314–337.
[18] K.H. Zoroofchi, R.F. Saen, P.B. Lari and M. Azadi, A combination of range-adjusted measure, cross-efficiency and assurance region for assessing sustainability of suppliers in the presence of undesirable factors, Int. J. Indust. Syst. Eng. 29 (2018), no. 2, 163–176.
Volume 13, Issue 2
July 2022
Pages 3291-3305
  • Receive Date: 09 May 2022
  • Revise Date: 28 June 2022
  • Accept Date: 01 July 2022