1. Upmanyu, M. and Saxena, R.R. On solving a multiobjective _xed charge problem with imprecise fractional objectives", Applied Soft Computing, 40, pp. 64{69 (2016). 2. Kaur, J. and Kumar, A. Commentary on On solving a multiobjective _xed charge problem with imprecise fractional objectives"", Applied Soft Computing, 61, pp. 681{682 (2017). 3. Hirsch, W. and Dantzig, G.B. The _xed charge problem", Navel Research Logistics, 15, pp. 413{424 (1968). 4. Steinberg, D.I. The _xed charge problem", Navel Research Logistics Quarterly, 172, pp. 17{36 (1970). 5. Cooper, L. and Drebes, C. An approximate solution method for the _xed charge problem", Navel Research Logistics, 14, pp. 101{113 (1967). 6. Murty, K.G. Solving the _xed charge transportation problem by extreme point ranking", Operations Research Quarterly, 16, pp. 268{279 (1968). 7. Walker, W.E. A heuristic adjacent extreme point algorithm for the _xed charge problem", Management Science, 22, pp. 587{596 (1976). 8. Adlakha, V. and Kowalski, K. A heuristic algorithm for the _xed charge problem", Opsearch, 47(2) pp. 166{175 (2010). 9. Gendron, B. and Larose, M. Branch-and-price-andcut for large-scale multicom-modity capacitated _xedcharge network design", EURO Journal on Computational Optimization, 2(1{2), pp. 55{75 (2014). 10. Fern_andez, E. and Landete, M. Fixed-charge facility location problems", Location Science, Springer, pp. 47{77 (2015). 11. Shishebori, D., Youse_ Babadi, A., and Noormohammadzadeh, Z. A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem", Scientia Iranica, 25(3), pp. 1750{ 1767 (2018). 12. Rabieh, M., Modarres, M., and Azar, A. Robustfuzzy model for supplier selection under uncertainty: An application to the automobile industry", Scientia Iranica, 25(4), pp. 2297{2311 (2018). 13. Arora, S.R. A note on fractional _xed charge problem", NZOR, 5(2), pp. 66{71 (1977). 14. Hong, J., Diabat, A., Panicker, V.V., and Rajagopalan, S. A two-stage supply chain problem with _xed costs: An ant colony optimization approach", International Journal of Production Economics, 204, pp. 214{226 (2018). 15. Calvete, H.I., Gal_e, C., Iranzo, J.A., and Toth, P. A metaheuristic for the two-stage _xed-charge transportation problem", Computers & Operations Research, 95, pp. 113{122 (2018). 16. Bertazzi, L. and Maggioni, F. A stochastic multistage _xed charge transportation problem: Worst-case analysis of the rolling horizon approach", European Journal of Operational Research, 267(2), pp. 555{569 (2018). 17. Bazaraa, M.S., Sherali, H.D., and Shetty C.M., Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, New York (2013). 18. Stancu Minasian, I.M. A eighth bibliography of fractional programming", Optimization, 66(3), pp. 439{ 470 (2017). 19. Almogy, Y. and Levin, O. The fractional _xed charge problem", Navel Research Logistics, 18(3), pp. 307{ 315 (1971). 20. Arya, R., Singh, P., and Bhati, D. A fuzzy based branch and bound approach for multi-objective linear fractional (MOLF) optimization problems", Journal of Computational Science, 24, pp. 54{64 (2018). 21. Osman, M.S., Emam, O.E., and Elsayed, M.A. Interactive approach for multi-level multi-objective fractional programming problems with fuzzy parameters", Beni-Suef University Journal of Basic and Applied Sciences, 7(1), pp. 139{149 (2018). 22. Kaufmann, A. and Gupta, M.M., Introduction to Fuzzy Arithmetics: Theory and Applications, Van Nostrand Reinhold, New York (1985). 23. Gupta, P. and Mehlawat, M.K. A new possibilistic programming approach for solving fuzzy multiobjective assignment problem", IEEE Transactions on Fuzzy Systems, 22(1), pp. 16{34 (2014). 24. Mahmoodirad, A., Hassasi, H., Tohidi, Gh., and Sanei, M. On approximation of the fully fuzzy _xed charge transportation problem", International Journal of Industrial Mathematics, 6(4), pp. 307{314 (2014). 25. Mahmoodirad, A. and Sanei, M. Solving a multistage multi-product solid supply chain network design problem by meta-heuristics", Scientia Iranica, 23(3), pp. 1428{1440 (2016). 26. Sanei, M., Mahmoodirad, A., Niroomand, S., Jamalian, A., and Gelareh, S. Step _xed-charge solid transportation problem: a Lagrangian relaxation heuristic approach", Computational and Applied Mathematics, 36(3), pp. 1217{1237 (2017). 27. Charnes, A. and Cooper, W.W. Programming with linear fractional functionals", Naval Research Logistics Quarterly, 9, pp. 181{186 (1962). 28. Bal, A. and Satoglu, S.I. A goal programming model for sustainable reverse logistics operations planning and an application", Journal of Cleaner Production, 201, pp. 1081{1091 (2018). 29. Wang, Z.J. A goal programming approach to deriving interval weights in analytic form from interval fuzzy preference relations based on multiplicative 2068 A. Mahmoodirad et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 2057{2068 consistency", Information Sciences, 462, pp. 160{181 (2018). 30. Komsiyah, S. and Centika, H.E. A fuzzy goal programming model for production planning in furniture company", Procedia Computer Science, 135, pp. 544{ 552 (2018). 31. Xavier, A., Costa-Freitas, M.D.B., Fragoso, R., and Ros_ario, M.D.S. A regional composite indicator for analysing agricultural sustainability in Portugal: A goal programming approach", Ecological Indicators, 89, pp. 84{100 (2018). 32. Alikhani-Kooshkak, R., Tavakkoli-Moghaddam, R., Jamili, A., and Ebrahimnejad, S. Multi-objective mathematical modeling of an integrated train makeup and routing problem in an Iranian railway company", Scientia Iranica, 26(6), pp. 3765{3779 (2019). DOI: 10.24200/SCI.2018.20782