Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station
RAIRO. Operations Research, Tome 55 (2021), pp. S2923-S2952

In this contribution, for the first time, an efficient model of multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station is formulated. Transfer station inserts transfer cost and type-I fixed-charge. Our aim is to analyze an extra cost that treats as type-II fixed-charge and truck load constraints in the designed model that required when the amount of items exceeds the capacity of vehicle for fulfilling the shipment by more than one trip. Type-II fixed-charge is added with transportation cost and other cost from transfer station. We consider here an important issue of the multi-objective transportation problem as product blending constraints for transporting raw materials with different purity levels for customers’ satisfaction. In realistic point of view, the parameters of the model are imprecise in nature due to existing several unpredictable factors. These factors are apprehended by incorporating the fuzzy-rough environment on the parameters. Expected-value operator is utilized to derive the deterministic form of fuzzy-rough data, and the model is experienced with help of fuzzy programming, neutrosophic linear programming and global criteria method. Two numerical examples are illustrated to determine the applicability of the proposed model.

DOI : 10.1051/ro/2020129
Classification : 90B06, 90C08, 90C29, 90C70
Keywords: Transportation problem, fixed-charge and transfer cost, truck load constraints and product blending, multi-objective optimization, fuzzy-rough uncertainty, fuzzy programming and neutrosophic linear programming, global criteria method 
@article{RO_2021__55_S1_S2923_0,
     author = {Ghosh, Shyamali and Roy, Sankar Kumar},
     title = {Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station},
     journal = {RAIRO. Operations Research},
     pages = {S2923--S2952},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     doi = {10.1051/ro/2020129},
     mrnumber = {4223196},
     zbl = {1469.90038},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2020129/}
}
TY  - JOUR
AU  - Ghosh, Shyamali
AU  - Roy, Sankar Kumar
TI  - Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station
JO  - RAIRO. Operations Research
PY  - 2021
SP  - S2923
EP  - S2952
VL  - 55
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2020129/
DO  - 10.1051/ro/2020129
LA  - en
ID  - RO_2021__55_S1_S2923_0
ER  - 
%0 Journal Article
%A Ghosh, Shyamali
%A Roy, Sankar Kumar
%T Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station
%J RAIRO. Operations Research
%D 2021
%P S2923-S2952
%V 55
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2020129/
%R 10.1051/ro/2020129
%G en
%F RO_2021__55_S1_S2923_0
Ghosh, Shyamali; Roy, Sankar Kumar. Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station. RAIRO. Operations Research, Tome 55 (2021), pp. S2923-S2952. doi: 10.1051/ro/2020129

[1] R. M. Rizk-Allah, A. E. Hassanien and M. Elhoseny, A multi-objective transportation model under neutrosophic environment. Comput. Electr. Eng. 69 (2018) 705–719. | DOI

[2] P. Anukokila, B. Radhakrishnan and A. Anju, Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters. RAIRO:OR 53 (2019) 157–178. | MR | Zbl | Numdam | DOI

[3] A. N. Balaji, J. M. Nilakantan, I. Nielsen, N. Jawahar and S. G. Ponnambalam, Solving fixed-charge transportation problem with truck load constraint using metaheuristics. Ann. Oper. Res. 273 (2019) 207–236. | MR | Zbl | DOI

[4] S. K. Das and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment. Comput. Ind. Eng. 132 (2019) 311–324. | DOI

[5] S. K. Das, S. K. Roy and G. W. Weber, Application of type-2 fuzzy logic to a multi-objective green solid transportation-location problem with dwell time under carbon emission tax, cap and offset policy: Fuzzy vs. Non-fuzzy techniques, IEEE Trans. Fuzzy Syst. 28 (2020) 2711–2725. | DOI

[6] A. Ebrahimnejad, A simplified new approach for solving fuzzy transportation problem with generalized trapezoidal fuzzy numbers. Appl. Soft Comput. 19 (2014) 171–176. | DOI

[7] A. Ebrahimnejad, New method for solving fuzzy transportation problems with LR flat fuzzy numbers. Inf. Sci. 357 (2016) 108–124. | Zbl | DOI

[8] A. Ebrahimnejad, A method for solving linear programming with interval-valued trapezoidal fuzzy variables. RAIRO:OR 52 (2018) 955–979. | MR | Zbl | Numdam | DOI

[9] Y. Gao and S. Kar, Uncertain solid transportation problem with product blending. Int. J. Fuzzy Syst. 19 (2017) 1916–1926. | MR | DOI

[10] M. Ghaznavi, N. Hoseinpoor and F. Soleimani, A Newton method for capturing Pareto optimal solutions of fuzzy multi-objective optimization problems. RAIRO:OR 53 (2019) 867–886. | MR | Zbl | Numdam | DOI

[11] N. Hashmi, S. A. Jalil and S. Javaid, A model for two-stage fixed-charge transportation problem with multiple objectives and fuzzy linguistic preferences. Soft Comput. 23 (2019) 12401–12415. | Zbl | DOI

[12] W. M. Hirsch and G. B. Dantzig, The fixed-charge problem. Nav. Res. Logistics Q. 15 (1968) 413–424. | MR | Zbl | DOI

[13] F. L. Hitchcock, The distribution of a product from several sources to numerous localities. J. Math. Phys. 20 (1941) 224–230. | MR | JFM | DOI

[14] P. Kaur, V. Verma and K. Dahiya, Capacitated two-stage time minimization transportation problem with restricted flow. RAIRO:OR 51 (2017) 447–467. | MR | Zbl | Numdam | DOI

[15] L. Li and K. K. Lai, A fuzzy approach to the multi-objective transportation problem. Comput. Oper. Res. 27 (2000) 43–57. | MR | Zbl | DOI

[16] B. Liu, Theory and Practice of Uncertain Programming. Springer, Berlin-Heidelberg (2009). | Zbl

[17] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Vol. 300 of Studies in Computational Intelligence Springer, Berlin-Heidelberg (2010).

[18] B. Liu and Y. K. Liu, Expected value of the fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10 (2002) 445–450. | DOI

[19] G. Maity, S. K. Roy and J.-L. Verdegay, Multi-objective transportation problem with cost reliability under uncertain environment. Int. J. Comput. Intell. Syst. 9 (2016) 839–849. | DOI

[20] G. Maity, S. K. Roy and J.-L. Verdegay, Time variant multi-objective interval valued transportation problem in sustainable development. Sustainability 11 (2019) 6161. | DOI

[21] A. Hatami-Marbini, P. J. Agrell, M. Tavana and A. Emrouznejad, A stepwise fuzzy linear programming model with possibility and necessity relations. J. Intell. Fuzzy Syst. 25 (2013) 81–93. | MR | Zbl | DOI

[22] A. Menni and D. Chaabane, A possibilistic optimization over an integer efficient set within a fuzzy environment. RAIRO:OR 54 (2020) 1437–1452. | MR | Zbl | Numdam | DOI

[23] S. Midya and S. K. Roy, Solving single-sink, fixed-charge, multi-objective, multi-index stochastic transportation problem. Am. J. Math. Manage. Sci. 33 (2014) 300–314.

[24] S. Midya and S. K. Roy, Analysis of interval programming in different environments and its application to fixed-charge transportation problem. Dis. Math. Algorithms App. 9 (2017) 1750040. | MR | Zbl | DOI

[25] S. Midya and S. K. Roy, Multi-objective fixed-charge transportation problem using rough programming. Int. J. Oper. Res. 37 (2020) 377–395. | MR | DOI

[26] S. Midya, S. K. Roy and V. F. Yu, Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain. To appear in: Int. J. Mach. Learn. Cybern. (2020) DOI: . | DOI

[27] D. J. Papageorgiou, A. Toriello, G. L. Nemhauser and M. W. P. Savelsbergh, Fixed-charge transportation with product blending. Transp. Sci. 46 (2012) 281–295. | DOI

[28] Z. Pawlak, Rough sets. Int. J. Comput. Inf. Sci. 11 (1982) 341–356. | MR | Zbl | DOI

[29] S. K. Roy and S. Midya, Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment. Appl. Intell. 49 (2019) 3524–3538. | DOI

[30] S. K. Roy, A. Ebrahimnejad, J.-L. Verdegay and S. Das, New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana 43 (2018) 3. | MR | Zbl | DOI

[31] S. K. Roy, S. Midya and V. F. Yu, Multi-objective fixed-charge transportation problem with random rough variables. Int. J. Univ. Fuzziness Knowl.-Based Syst. 26 (2018) 971–996. | MR | Zbl | DOI

[32] S. K. Roy, S. Midya and G. W. Weber, Multi-objective multi-item fixed-charge solid transportation problem under two-fold uncertainty. Neural Comput. App. 31 (2019) 8593–8613. | DOI

[33] F. Smarandache, A unifying field in logics. Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1999).

[34] D. Sengupta, A. Das and U. K. Bera, A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission. Appl. Intell. 48 (2018) 3995–4022. | DOI

[35] J. Xu and Z. Tao, Rough Multiple Objective Decision Making. Taylor and Francis Group CRC Press (2012). | MR

[36] J. Xu and L. Yao, A class of multi-objective linear programming models with random rough coefficients. Math. Comput. Modell. 49 (2009) 189–206. | MR | Zbl | DOI

[37] J. Xu and X. Zhou, Fuzzy-like Multiple Objective Decision Making. Vol. 263 of Studies in Fuzziness and Soft Computing Springer, Berlin (2011). | MR | Zbl

[38] L. A. Zadeh, Fuzzy sets. Inf. Control 8 (1965) 338–353. | MR | Zbl | DOI

[39] G. Zhao and D. Pan, A transportation planning problem with transfer cost in uncertain environment. Soft Comput. 24 (2019) 2647–2653. | Zbl | DOI

[40] T. Zhimiao and J. Xu, A class of rough multiple objective programming and its application to solid transportation problem. Inf. Sci. 188 (2012) 215–235. | MR | Zbl | DOI

[41] H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1 (1978) 45–55. | MR | Zbl | DOI

Cité par Sources :