An effective solution approach to multi-objective fractional fixed charge problem with fuzzy parameters

Document Type : Article

Authors

1 Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran

2 Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran.

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Abstract

A multi-objective fixed charge problem in existence of several fractional objective functions with triangular fuzzy parameters is considered in this study. The problem previously has been tackled only by Upmanyu and Saxena (2016) with a method containing wrong mathematical concepts (see the commentary of Kaur and Kumar (2017)). To overcome the shortcomings of the literature, an effective solution approach based on a typical goal programming approach is proposed to solve the problem for obtaining a Pareto-optimal solution. The proposed approach considers the shortcomings of the method of Upmanyu and Saxena (2016) and applies no ranking function of fuzzy numbers. In addition, the goal programming stage considers no preference from decision maker. The computational experiments provided by an example of the literature, prove the effectiveness of the proposed approach.

Keywords


References:
1. Upmanyu, M. and Saxena, R.R. "On solving a multiobjective fixed 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 fixed charge problem with imprecise fractional objectives"", Applied Soft Computing, 61, pp. 681-682 (2017).
3. Hirsch, W. and Dantzig, G.B. "The fixed charge problem", Navel Research Logistics, 15, pp. 413-424 (1968).
4. Steinberg, D.I. "The fixed charge problem", Navel Research Logistics Quarterly, 172, pp. 17-36 (1970).
5. Cooper, L. and Drebes, C. "An approximate solution method for the fixed charge problem", Navel Research Logistics, 14, pp. 101-113 (1967).
6. Murty, K.G. "Solving the fixed 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 fixed charge problem", Management Science, 22, pp. 587-596 (1976).
8. Adlakha, V. and Kowalski, K. "A heuristic algorithm for the fixed 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 fixedcharge network design", EURO Journal on Computational Optimization, 2(1-2), pp. 55-75 (2014).
10. Fernandez, E. and Landete, M. "Fixed-charge facility location problems", Location Science, Springer, pp. 47-77 (2015).
11. Shishebori, D., Yousefi 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 fixed 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 fixed costs: An ant colony optimization approach", International Journal of Production Economics, 204, pp. 214-226 (2018).
15. Calvete, H.I., Gale, C., Iranzo, J.A., and Toth, P. "A metaheuristic for the two-stage fixed-charge transportation problem", Computers & Operations Research, 95, pp. 113-122 (2018).
16. Bertazzi, L. and Maggioni, F. "A stochastic multistage fixed 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 fixed 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 fixed 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 fixed-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 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 Rosario, 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.