A belief-degree based multi-objective transportation problem with multi-choice demand and supply
DOI:
https://doi.org/10.11121/ijocta.2022.1166Keywords:
Multi-objective transportation problem, Multi-choice, Uncertain programming, Fuzzy programming techniqueAbstract
This paper focusses on the development of a Multi-choice Multi-objective Transportation Problem (MCMOTP) in the uncertain environment. The parameters associated with the objective functions in MCMOTP are regarded as uncertain variables and the other parameters associated with supply capacity and demand requirements are considered under the multi-choice environment. In this paper, two ranking criteria have been utilized to convert the uncertain objectives into their crisp form. Using these two ranking criteria for the uncertain MCMOTP model, two deterministic models have been developed namely, Expected Value Model (EV Model) and Optimistic Value Model (OV Model). The multi-choice parameters in the constraints are converted to a single choice parameters with the help of binary variable approach. The EV and OV models are solved directly in the LINGO 18.0 software using minimizing distance method and fuzzy programming technique. At last, a numerical illustration is provided to demonstrate the application and algorithm of the models. The sensitivity of the objective functions in OV Model is also examined with respect to the confidence levels to investigate variation in the objective functions.
Downloads
References
Hitchcock, F. L. (1941). The distribution of a product from several sources to numerous localities. Journal of mathematics and physics, 20(1-4), 224-230.
Ozmen, A. (2022). Multi-objective regression modeling for natural gas prediction with ridge regression and CMARS. An International Journal of Optimization and Control: Theories & Applications, 12(1), 56–65.
Shahraki, Z., Allahdadi, M., & Mishmast Nehi, H. (2015). Fuzzy multi objective linear programming problem with imprecise aspiration Level and parameters. An International Journal of Optimization and Control: Theories & Applications, 5(2), 81–86.
Rudy, J., & ?Zelazny, D. (2014). Solving multi-objective job shop problem using nature-based algorithms: new Pareto approximation features. An International Journal of Optimization and Control: Theories & Applications, 5(1), 1–11.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.
Eghbali, H., Eghbali, M. A., & Vahidian Kamyad, A. (2012). Optimizing human diet problem based on price and taste using multi-objective fuzzy linear programming approach. An International Journal of Optimization and Control: Theories & Applications, 2(2), 139–151.
Bit, A. K., Biswal, M. P., Alam, S. S. (1993). Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57(2), 183-94.
Kumar, M., Vrat, P., Shankar, R. (2006). A fuzzy programming approach for vendor selection problem in a supply chain. International Journal of Production Economics, 101(2), 273-85.
Zadeh, L.A. (1965). Fuzzy sets. Information and control 8(3), 338–353.
Kolmogorov, A. N., Bharucha-Reid, A. T. (2018). Foundations of the theory of probability: Second English Edition, Courier Dover Publications, New York.
Moore, R.E. (1966). Interval Analysis 4. Englewood Cliffs: Prentice-Hall.
Bhargava, A. K., Singh, S. R., & Bansal, D. (2014). Multi-objective fuzzy chance constrained fuzzy goal programming for capacitated transportation problem. International Journal of Computer Applications, 107(3).
Giri, P. K., Maiti, M. K., & Maiti, M. (2014). Fuzzy stochastic solid transportation problem using fuzzy goal programming approach. Computers & Industrial Engineering, 72, 160-168.
Ebrahimnejad, A. (2015). An improved approach for solving fuzzy transportation problem with triangular fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 29(2), 963-974.
Maity, G., & Roy, S. K. (2016). Solving multi-objective transportation problem with interval goal using utility function approach. International Journal of Operational Research, 27(4), 513-529.
Roy, S. K., Ebrahimnejad, A., Verdegay, J. L., & Das, S. (2018). New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana, 43(1), 1-12.
Gupta, S., Ali, I., & Ahmed, A. (2018). Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment. Opsearch, 55(2), 447-477.
Singh, S., Pradhan, A., & Biswal, M. P. (2019). Multi-objective solid transportation problem under stochastic environment. Sadhana, 44(5), 1-12.
Gupta, S., Ali, I., & Ahmed, A. (2020). An extended multi-objective capacitated transportation problem with mixed constraints in fuzzy environment. International Journal of Operational Research, 37(3), 345-376.
Liu, B. (2007). Uncertainty Theory. In Uncertainty Theory Springer, Berlin, Heidelberg.
Mou, D., Zhao, W., & Chang, X. (2013). A transportation problem with uncertain truck times and unit costs. Industrial Engineering and Management Systems, 12(1), 30-35.
Chen, L., Peng, J., & Zhang, B. (2017). Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, 51, 49-59.
Liu, L., Zhang, B., & Ma, W. (2018). Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Computing, 22(17), 5825-5833.
Dalman, H. (2018). Uncertain programming model for multi-item solid transportation problem. International Journal of Machine Learning and Cybernetics, 9(4), 559-567.
Mahmoodirad, A., Dehghan, R., & Niroomand, S. (2019). Modelling linear fractional transportation problem in belief degree-based uncertain environment. Journal of Experimental & Theoretical Artificial Intelligence, 31(3), 393-408.
Chen, B., Liu, Y., & Zhou, T. (2019). An entropy based solid transportation problem in uncertain environment. Journal of Ambient Intelligence and Humanized Computing, 10(1), 357-363.
Dalman, H. (2019). Entropy-based multi-item solid transportation problems with uncertain variables. Soft Computing, 23(14), 5931-5943.
Zhao, G., & Pan, D. (2020). A transportation planning problem with transfer costs in uncertain environment. Soft Computing, 24(4), 2647-2653.
Chang, C. T. (2007). Multi-choice goal programming. Omega, 35(4), 389-396.
Biswal, M. P., & Acharya, S. (2009). Multi-choice multi-objective linear programming problem. Journal of Interdisciplinary Mathematics, 12(5), 606-637.
Acharya, S., & Acharya, M. M. (2012). Generalized Transformation Techniques for Multi- Choice Linear Programming Problems. An International Journal of Optimization and Control: Theories & Applications, 3(1), 45–54.
Acharya, S., & Biswal, M. P. (2016). Solving multi-choice multi-objective transportation problem. International Journal of Mathematics in Operational Research, 8(4), 509-527.
Roy, S. K., Mahapatra, D. R., & Biswal, M. P. (2012). Multi-choice stochastic transportation problem with exponential distribution. Journal of uncertain systems, 6(3), 200-213.
Mahapatra, D. R. (2013). Multi-choice stochastic transportation problem involving weibull distribution. An International Journal of Optimization and Control: Theories & Applications, 4(1), 45–55.
Roy, S. K. (2014). Multi-choice stochastic transportation problem involving Weibull distribution. International Journal of Operational Research, 21(1), 38-58.
Maity, G., & Kumar Roy, S. (2016). Solving a multiobjective transportation problem with nonlinear cost and multi-choice demand. International Journal of Management Science and Engineering Management, 11(1), 62-70.
Gupta, S., Ali, I., & Ahmed, A. (2018). Multi-choice multi-objective capacitated transportation problem-a case study of uncertain demand and supply. Journal of Statistics and Management Systems, 21(3), 467-491.
Roy, S. K., Maity, G., Weber, G. W., & Gok, S. Z. A. (2017). Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Annals of Operations Research, 253(1), 599-620.
Nasseri, S. H., & Bavandi, S. (2020). Solving multi-objective multi-choice stochastic transportation problem with fuzzy programming approach. In 2020 8th Iranian Joint Congress on Fuzzy and intelligent Systems (CFIS), IEEE, 207-210.
Nayak, J., & Acharya, S. (2020). Dealing with a transportation problem with multi choice cost coefficients and fuzzy supplies and demands. Global Journal of Pure and Applied Mathematics, 16(6), 783-788.
Agrawal, P., & Ganesh, T. (2020). Solving Multi-choice fractional stochastic transportation problem involving Newton’s divided difference. Numerical Optimization in Engineering and Sciences, Springer, Singapore, 289-298.
Vijayalakshmi, P., & Vinotha, J. M. (2020). Multi choice ecological intuitionistic fuzzy multi objective transportation problem with non linear cost. Solid State Technology, 63(2), 2675-2689.
Agrawal, P., & Ganesh, T. (2021). Solution of stochastic transportation problem involving multi-choice random parameter using Newton’s divided difference interpolation. Journal of Information and Optimization Sciences, 42(1), 77-91.
Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Vandana Kakran, Jayesh Dhodiya
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- 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.
This work is licensed under a Creative Commons Attribution 4.0 International License.
