Economical Heuristics for Fully Interval Integer Multi-Objective Fuzzy and Non-Fuzzy Transportation Problems
DOI:
https://doi.org/10.2298/YJOR240115035BKeywords:
Fuzzy integer multi-objective transportation problem, solution approach, integer interval multi-objective transportation problem, decision makingAbstract
The single-objective fuzzy or non-fuzzy transportation problem (TP) is not capable of dealing with real-life decision-making problems due to our current competitive market state. In this article, we investigate a fully integer interval multiobjective transportation problem (FIIMOTP) and a fully fuzzy integer multi-objective transportation problem (FFIMOTP). We also provide two solution approaches for solving the FIIMOTP and FFIMOTP. Numerical examples are provided to validate these two approaches. Our results show that the proposed algorithm hugely outperforms the best solution approaches.References
A. Akilbasha, P. Pandian and G. Natarajan, “Finding an optimal solution of the interval integer transportation problems with rough nature by split and separation method,” International Journal of Pure and Applied Mathematics, vol. 106, pp. 1-8, 2016.
A. Akilbasha, P. Pandian and G. Natarajan, “An innovation exact method for solving fully interval integer transportation problems,” Informatics in Medicine Unlocked, vol. 11, pp. 95-99, 2018. https://doi.org/10.1016/j.imu.2018.04.007.
M. S. Annie Christi and I. Kalpana, “Solutions of multi objective fuzzy transportation problems with non-linear membership functions,” International Journal of Engineering Research and Application, vol. 6, no. 11, pp. 52-57, 2016.
R. E. Bellman and L. A. Zadeh, “Decision making in a fuzzy environment,” Management Science, vol. 17, no. 4, pp. 141-164, 1970. https://doi.org/10.1287/mnsc.17.4.B141.
S. Chanas and D. Kuchta, “A concept of the optimal solution of the transportation problem with fuzzy cost coefficients,” Fuzzy Sets and Systems, vol. 82, no. 3, pp. 299-305, 1996. https://doi.org/10.1016/0165-0114(95)00278-2.
H. Dalman, “A fuzzy programming approach for interval multi objective solid transportation problem,” New Trends in Mathematical Sciences, vol. 4, pp. 114-127, 2016. https://doi.org/10.20852/ntmsci.2016422557.
A. Ebrahimnejad, “A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers,” Applied Soft Computing, vol. 19, pp. 171-176, 2014. https://doi.org/10.1016/j.asoc.2014.01.041.
F. L. Hitchcock, “The distribution of a product from several sources to numerous localities,” Journal of Mathematical Physics, vol. 20, pp. 224-230, 1941. http://dx.doi.org/10.1002/sapm1941201224.
E. Hosseinzade and H. Hassanpour, “The karush-kuhn-tucker optimality conditions in interval-valued multi objective programming problems,” Journal of Applied Mathematics & Informatics, vol. 29, pp. 1157-1165, 2011.
H. Ishibuchi and H. Tanaka, “Multi objective programming in optimization of the interval objective function,” European Journal of Operational Research, vol. 48, no. 2, pp. 219-225, 1990. https://doi.org/10.1016/0377-2217(90)90375-L.
T. C. Koopman, “Optimum utilization of the transportation system,” Proceeding of the International Statistical Conference, Washington, D.C, 1947.
G. Maity and S. K. Roy, “Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand,” International Journal of Management Science and Engineering Management, vol. 11, no. 1, pp. 62-70, 2016. https://doi.org/10.1080/17509653.2014.988768.
R. E. Moore, Method and applications of interval analysis, Philadelphia, PA: SLAM, 1979.
C. Oliveira and C. H. Antunes, “Multiple objective linear programming models with interval coefficients-an illustrated overview,” European Journal of Operational Research, vol. 181, no. 3, pp. 1434-1463, 2007. https://doi.org/10.1016/j.ejor.2005.12.042.
A. Panda and C. B. Das, “Cost varying interval transportation problem under two vehicle,” Journal of New Results in Science, vol. 3, pp. 19-37, 2013.
P. Pandian and G. Natarajan, “A new method for finding an optimal solution of fully interval integer transportation problems,” Applied Mathematical Sciences, vol. 4, no. 37, pp. 1819-1830, 2010.
P. Pandian and G. Natarajan, “A new method for finding an optimal solution for transportation problems,” International Journal of Mathematical Sciences and Engineering Applications, vol. 4, pp. 59-65, 2010.
P. Pandian and G. Natarajan, “A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems,” Applied Mathematical Sciences, vol. 4, no. 2, pp. 79-90, 2010.
P. Pandian and G. Natarajan, “A fully rough integer interval transportation problems,” International Journal of Pharmacy & Technology, vol. 8, no. 2, pp. 13866-13876, 2016.
J. G. Patel and J. M. Dhodiya, “Solving multi-objective interval transportation problem using gray situation decision-making theory based on grey numbers,” International Journal of Pure and Applied Mathematics, vol. 2, pp. 219-233, 2017. https://doi.org/10.12732/ijpam.v113i2.3.
D. Rani, “Fuzzy programming technique for solving different types of multi-objective transportation problem,” Thesis, Thapar University, Punjab, 2010.
S. K. Roy and D. R. Mahapatra, “Multi-objective interval-valued transportation probabilistic problem involving log-normal,” International Journal of Mathematics and Scientific Computing, vol. 1, no. 2, pp. 14-21, 2011.
A. Sengupta and T. K. Pal, “Interval-valued transportation problem with multiple penalty factors,” VU Journal of Physical Sciences, vol. 9, pp. 71-81, 2003. https://doi.org/10.1007/978-3-540-89915-0_7.
S. K. Singh and M. Goh, “Multi objective mixed integer programming and an application in a pharmaceutical supply chain,” International Journal of Production Research, vol. 57, no. 4, pp. 1214-1237, 2019. https://doi.org/10.1080/00207543.2018.1504172.
S. Tong, “Interval number and fuzzy number linear programming,” Fuzzy Sets and Systems, vol. 66, no. 3, pp. 301-306, 1994. https://doi.org/10.1016/0165-0114(94)90097-3.
F. Vincent Yu, Kuo-Jen Hu and An-Yuan Chang, “An interactive approach for the multi-objective transportation problem with interval parameters,” International Journal of Production Research, vol. 53, no. 4, pp. 1051-1064, 2014. https://doi.org/10.1080/00207543.2014.939236.
M. C. Yeola and V. A. Jahav, “Solving multi-objective transportation problem using fuzzy programming technique-parallel method,” International Journal of Recent Scientific Research, vol. 7, no. 1, pp. 8455-8457, 2016.
H. J. Zimmermann, “Fuzzy programming and linear programming with several objective functions,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 45-55, 1978. https://doi.org/10.1016/0165-0114(78)90031-3.
Z. A. M. S. Juman and M. A. Hoque, “An efficient heuristic to obtain a better initial feasible solution to the transportation problem,” Applied Soft Computing, vol. 34, pp. 813-826, 2015.
S. S. Ali, H. Barman, R. Kaur, H. Tomaskova and S. K. Roy, “Multi-product multi echelon measurements of perishable supply chain: fuzzy nonlinear programming approach,” Mathematics, vol. 9, pp. 2093, 2021. https://doi.org/10.3390/math9172093
A. Das and G. M. Lee, “A multi-objective stochastic solid transportation problem with the supply, demand, and conveyance capacity following the weibull distribution,” Mathematics, vol. 9, pp. 1757, 2021. https://doi.org/10.3390/math9151757
K. Palanivel and A. Das, “A mathematical model for nonlinear optimization which attempts membership functions to address the uncertainties,” Mathematics, vol. 10, pp. 1743, 2022. https://doi.org/10.3390/math10101743
J. Pratihar, R. Kumar, S. A. Edalatpanah and A. Dey, “Modified Vogel’s approximation method for transportation problem under uncertain environment,” Complex and Intelligent Systems, vol. 7, no. 1, pp. 29-40, 2021. doi:10.1007/s40747-020-00153-4
C. Veeramani, S. A. Edalatpanah and S. Sharanya, “Solving the multiobjective fractional transportation problem through the neutrosophic goal programming approach,” Discrete Dynamics in Nature and Society, 2021. doi:10.1155/2021/7308042
R. Kumar, S. A. Edalatpanah, S. Jha and R. Singh, “A Pythagorean fuzzy approach to the transportation problem,” Complex and Intelligent Systems, vol. 5, no. 2, pp. 255-263, 2019. doi:10.1007/s40747-019-0108-1
M. Akram, S. M. U. Shah, M. M. Ali Al-Shamiri and S. A. Edalatpanah, “Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets,” AIMS Mathematics, vol. 8, no. 1, pp. 924-961, 2023. doi:10.3934/math.2023045
C. Wang, “Big Data and Computing Visions Avoidance Traffic Congestion through Smart Transportation Approach,” Big. Data. Comp. Vis, vol. 2, no. 4, pp. 159-162, 2022, doi: 10.22105/bdcv.2022.332460.1064.
S. A. Edalatpanah, “Multidimensional solution of fuzzy linear programming,” PeerJ Computer Science, vol. 9, 2023, doi: 10.7717/peerj-cs.1646.
H. A. E.-W. Khalifa, S. A. Edalatpanah, and D. Bozanic, “On Min-Max Goal Programming Approach for Solving Piecewise Quadratic Fuzzy Multi- Objective De Novo Programming Problems,” Systemic Analytics, vol. 2, no. 1, pp. 36-48, Feb. 2024, doi: 10.31181/sa21202411.
P. Ghasemi, H. Hemmaty, A. Pourghader Chobar, M. R. Heidar, and M. Keramati, “A Multi-Objective and Multi-Level Model for Location-Routing Problem in the Supply Chain Based on the Customer’s Time Window,” Journal of Applied Research on Industrial Engineering, vol. 10, no. 3, pp. 412-426, Jul. 2023, doi: 10.22105/jarie.2022.321454.1414.
S. Abdou El-Morsy, “Optimization of fuzzy zero-base budgeting,” Computational Algorithms and Numerical Dimensions, vol. 1, no. 4, pp. 147-154, 2022, doi: 10.22105/cand.2022.155548.
L. Kané, M. Diakité, S. Kané, H. Bado, M. Konaté, and K. Traoré, “The New Algorithm for Fully Fuzzy Transportation Problem by Trapezoidal Fuzzy Number (A Generalization of Triangular Fuzzy Number),” Journal of Fuzzy Extension and Applications, vol. 2, no. 3, pp. 204-225, Sep. 2021, doi: 10.22105/jfea.2021.287198.1148.
L. Kané et al., “A Simplified Method for Solving Transportation Problem with Triangular Fuzzy Numbers under Fuzzy Circumstances,” Journal of Fuzzy Extension and Applications www.journal-fea.com J. Fuzzy. Ext. Appl, vol. 2, no. 1, pp. 89-105, 2021, doi: 10.22105/jfea.2021.275280.1084aaihe.ac.
A. Alburaikan, S. A. Edalatpanah, R. Alharbi, and H. A. El-Wahed Khalifa, “Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems,” International Journal of Neutrosophic Science, vol. 23, no. 1, pp. 350-365, 2024, doi: 10.54216/IJNS.230130.
A. Sheikhi and M. J. Ebadi, “On Solving Linear Fractional Programming Transportation Problems with Fuzzy Numbers,” Journal of Fuzzy Extension and Applications, vol. 4, no. 4, pp. 327-339, Oct. 2023, doi: 10.22105/jfea.2024.402392.1294.
M. Akram, S. M. U. Shah, M. M. Ali Al-Shamiri, and S. A. Edalatpanah, “Fractional transportation problem under interval-valued Fermatean fuzzy sets,” AIMS Mathematics, vol. 7, no. 9, pp. 17327-17348, 2022, doi: 10.3934/math.2022954.
R. Komijan, “Development of a multi-objective model for the routing problem of vehicles carrying valuable commodity under route risk conditions (Case study of Shahr Bank),” J. Appl. Res. Ind. Eng, vol. x, No. x (xx) x-x, doi: 10.22105/jarie.2023.391399.1540.
H. A. El-Wahed Khalifa and B. A. Ali Yousif, “Addressing Cost-Efficiency Problems Based on Linear Ordering of Piecewise Quadratic Fuzzy Quotients,” Journal of Operational and Strategic Analytics, vol. 1, no. 3, pp. 124-130, Sep. 2023, doi: 10.56578/josa010303.
M. Akram, S. M. U. Shah, M. M. Ali Al-Shamiri, and S. A. Edalatpanah, “Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets,” AIMS Mathematics, vol. 8, no. 1, pp. 924-961, 2023, doi: 10.3934/math.2023045.
M. Akram, I. Ullah, T. Allahviranloo, and S. A. Edalatpanah, “LR-type fully Pythagorean fuzzy linear programming problems with equality constraints,” Journal of Intelligent and Fuzzy Systems, vol. 41, no. 1, pp. 1975-1992, 2021, doi: 10.3233/JIFS-210655.
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