Multi-item multi-objective fixed charged solid transportation problem with type-2 fuzzy variables
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-03-0038Keywords:
Solid transportation problem, Fixed charge transportation problem, Multi-item multi-objective transportation problem, Chance constrained programming, Type-2 fuzzy set, Type-2 triangular fuzzy variableAbstract
A multi-item multi-objective fixed charged solid transportation problema with guidelines e.g. unit transportation penalty, amounts, requirements, and conveyances as type-2 triangular fuzzy variables with conditions on few items and conveyances is formulated here. A chance constrained programming model applying generalized credibility measure for the objective function as well as the constraints is formed with the critical value based reductions of corresponding type-2 fuzzy guidelines for this particular problem. The model is then converted into the equivalent crisp deterministic form. The optimal compromise solutions are obtained by fuzzy programming technique. An example is contributed to highlight the model and is then solved by applying Generalized Reduced Gradient (GRG) technique (applying LINGO 16). The sensitivity analysis of the model is also given to illustrate the model.
References
S.-M. Chen and C.-Y. Wang, “Fuzzy decision making systems based on interval type-2 fuzzy sets”, Information sciences, vol. 242, pp. 1–21, Sep. 2013, doi: 10.1016/j.ins.2013.04.005
A. Das, U. K. Bera, and M. Maiti, “A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters”, Applied intelligence, vol. 45, no. 3, pp. 923–951, Jun. 2016, doi: 10.1007/s10489-016-0794-y
A. Dutta and D. K. Jana, “Expectations of the reductions for type-2 trapezoidal fuzzy variables and its application to a multi-objective solid transportation problem via goal programming technique”, Journal of uncertainty analysis and applications, vol. 5, no. 1, pp. Art ID. 5, Mar. 2017, doi: 10.1186/s40467-017-0057-4
D. Dutta and M. Sen, “A new method for solving multi-item multi-objective solid fixed charged shipment model with type-2 fuzzy variables”, Global and stochastic analysis, vol. 4, no. 1, pp. 35-47, Jan. 2017. [On line]. Available: https://bit.ly/3gzPAUv
D. Dutta and M. Sen, “Multi-item Fixed Charged Solid Shipment Problem with Type-2 Fuzzy Variables”, in Soft computing: theories and applications, vol. 1, M. Pant, K. Ray, T. Sharma, S. Rawat, and A. Bandyopadhyay, Eds. Singapore: Springer, 2018, pp. 689–702, doi: 10.1007/978-981-10-5687-1_61
D. Dutta and M. Sen, “Fixed charged solid transportation problem with budget constraints in type-2 fuzzy variables: multi-objective solid transportation problem”, in Soft computing techniques and applications in mechanical engineering, M. Ram and J. P. Davim, Eds. Hershey, PA: IGI Global Publisher, 2018, pp. 35–71, doi: 10.4018/978-1-5225-3035-0.ch002
P. Kundu, S. Kar, and M. Maiti, “Multi-objective multi-item solid transportation problem in fuzzy environment”, Applied mathematical modelling, vol. 37, no. 4, pp. 2028–2038, Feb. 2013, doi: 10.1016/j.apm.2012.04.026
P. Kundu, S. Kar, and M. Maiti, “Fixed charge transportation problem with type-2 fuzzy variables”, Information sciences, vol. 255, pp. 170–186, 2014, doi: 10.1016/j.ins.2013.08.005
P. Kundu, S. Kar, and M. Maiti, “Multi-item solid transportation problem with type-2 fuzzy parameters”, Applied soft computing, vol. 31, pp. 61–80, Jun. 2015, doi: 10.1016/j.asoc.2015.02.007
Y. Li, K. Ida, M. Gen, and R. Kobuchi, “Neural network approach for multicriteria solid transportation problem”, Computers & industrial engineering, vol. 33, no. 3-4, pp. 465–468, Dec. 1997, doi: 10.1016/S0360-8352(97)00169-1
Y. Li, K. Ida, and M. Gen, “Improved genetic algorithm for solving multiobjective solid transportation problem with fuzzy numbers”, Computers & industrial engineering, vol. 33, no. 3-4, pp. 589–592, Dec. 1997, doi: 10.1016/S0360-8352(97)00199-X
B. Liu and Y.-K. Liu, “Expected value of fuzzy variable and fuzzy expected value models”, IEEE transactions on fuzzy systems, vol. 10, no. 4, pp. 445–450, Aug. 2002, doi: 10.1109/TFUZZ.2002.800692
Z.-Q. Liu and Y.-K. Liu, “Type-2 fuzzy variables and their arithmetic”, Soft computing, vol. 14, no. 7, pp. 729–747, Jun. 2009, doi: 10.1007/s00500-009-0461-x
B. Liu and K. Iwamura, “Chance constrained programming with fuzzy parameters”, Fuzzy sets and systems, vol. 94, no. 2, pp. 227–237, Mar. 1998, doi: 10.1016/S0165-0114(96)00236-9
S. Nahmias, “Fuzzy variables”, Fuzzy sets and systems, vol. 1, no. 2, pp. 97–110, Apr. 1978, doi: 10.1016/0165-0114(78)90011-8
P. Pandian and D. Anuradha, “A new approach for solving solid transportation problems”, Applied mathematical sciences, vol. 4, no. 69-72, pp. 3603-3610, 2010. [On line]. Available: https://bit.ly/2ZJFYAg
R. Qin, Y.-K. Liu, and Z.-Q. Liu, “Methods of critical value reduction for type-2 fuzzy variables and their applications”, Journal of computational and applied mathematics, vol. 235, no. 5, pp. 1454–1481, Jan. 2011, doi: 10.1016/j.cam.2010.08.031
L. Yang and L. Liu, “Fuzzy fixed charge solid transportation problem and algorithm”, Applied soft computing, vol. 7, no. 3, pp. 879–889, Jun. 2007, doi: 10.1016/j.asoc.2005.11.011
L. Zadeh, “Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338–353, Jun. 1965, doi: 10.1016/S0019-9958(65)90241-X
L. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning—I”, Information sciences, vol. 8, no. 3, pp. 199–249, 1975, doi: 10.1016/0020-0255(75)90036-5
H.-J. Zimmermann, “Fuzzy programming and linear programming with several objective functions”, Fuzzy sets and systems, vol. 1, no. 1, pp. 45–55, Jan. 1978, doi: 10.1016/0165-0114(78)90031-3
Published
How to Cite
Issue
Section
Copyright (c) 2020 Dhiman Dutta, Mausumi Sen, Biplab Singha
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
