Abstract
In this paper, an improved algorithm has been proposed for solving fully fuzzy transportation problems. The proposed algorithm deals with finding a starting basic feasible solution to the transportation problem with parameters in fuzzy form. The proposed algorithm is an amalgamation of two existing approaches that can be applied to a balanced fuzzy transportation problem where uncertainties are represented by trapezoidal fuzzy numbers. Instead of transforming these uncertainties into crisp values, the proposed algorithm directly handles the fuzzy nature of the problem. To illustrate its effectiveness, the article presents several numerical examples in which parameter uncertainties are characterized using trapezoidal fuzzy numbers. A comparative analysis is performed between the algorithm’s outcomes and the existing results. The existing results are compared with the obtained results. A case study has also been discussed to enhance the significance of the algorithm.
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References
Ahuja RK (1986) Algorithms for minmax transportation problem. Naval Res Logist Quat 33:725–739. https://doi.org/10.1002/nav.3800330415
Babu MdA, Hoque MA, Uddin MdS (2020) A heuristic for obtaining better initial feasible solution to the transportation problem. Opsearch 57:221–245. https://doi.org/10.1007/s12597-019-00429-5
Ban AI, Coroianu L (2014) Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition. Fuzzy Sets Syst 257:3–22. https://doi.org/10.1016/j.fss.2013.07.004
Basirzadeh H (2011) An approach for solving fuzzy transportation problem. Appl Math Sci 5(32):1549–1566
Chandrasekaran K, Ghafar AFA, Roslee AA, Yaacob SNK, Omar Sl, Dahalan WM (2023) Port Kelang development moving toward adopting industrial revolution 40 in the seaport system: a review. Adv Technol Transf through IoT IT Solut 73–79 https://doi.org/10.1007/978-3-031-25178-8_8
Charnes A, Cooper WW (1954) The stepping stone method for explaining linear programming calculation in transportation problem. Manage Sci 1:49–69. https://doi.org/10.1287/mnsc.1.1.49
Choudhary A, Yadav SP (2022) An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2. Int J Syst Assur Eng Manag 13:2992–3001. https://doi.org/10.1007/s13198-022-01771-6
Clifton KJ, Handy SL (2003) Qualitative methods in travel behaviour research, Transport survey quality and innovation. Emerald Group Publishing Limited, Bingley, pp 283–302. https://doi.org/10.1108/9781786359551-016
Dantzig GB (1963) Linear Programming and Extensions. Princeton University Press, Princeton. https://doi.org/10.7249/r366
Dash S, Mohanty SP (2018) Uncertain transportation model with rough unit cost, demand and supply. Opsearch 55:1–13. https://doi.org/10.1007/s12597-017-0317-6
De D (2016) A method for solving fuzzy transportation problem of trapezoidal number. In: Proceedings of "The 7th SEAMS-UGC Conference 2015", pp 46–54
Deshmukh A, Mhaske A, Chopade PU, Bondar KL (2018) Fuzzy transportation problem by using trapezoidal fuzzy numbers. Int J Res Analy Rev 5(3):261–265
Ebrahimnejad A (2014) A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers. Appl Soft Comput 19:171–176. https://doi.org/10.1016/j.asoc.2014.01.041
Ebrahimnejad A (2016) New method for solving fuzzy transportation problems with LR flat fuzzy numbers. Inf Sci 357:108–124. https://doi.org/10.1016/j.ins.2016.04.008
Gani AN, Samuel AE, Anuradha D (2011) Simplex type algorithm for solving fuzzy transportation problem. Tamsui Oxford J Inf Math Sci 27(1):89–98
George G, Maheswari PU, Ganesan K (2020) A modified method to solve fuzzy transportation problem involving trapezoidal fuzzy numbers. In AIP conference proceedings, vol 2277, no 1. https://doi.org/10.1063/5.0025266
Ghadle KP, Pathade PA (2017) Solving transportation problem with generalized hexagonal and generalized octagonal fuzzy numbers by ranking method. Global J Pure Appl Math 13(9):6367–6376
Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230. https://doi.org/10.1002/sapm1941201224
Kaur A, Kumar A (2011a) A new method for solving fuzzy transportation problems using ranking function. Appl Math Model 35(12):5652–5661. https://doi.org/10.1016/j.apm.2011.05.012
Kaur A, Kumar A (2012) A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl Soft Comput 12(3):1201–1213. https://doi.org/10.1016/j.asoc.2011.10.014
Kirca O, Stair A (1990) A heuristic for obtaining an initial solution for the transportation problem. J Oper Res Soc 41:865–867. https://doi.org/10.1038/sj/jors/0410909
Kishore N, Jayswal A (2002) Prioritized goal programming formulation of an unbalanced transportation problem with budgetary constraints: a fuzzy approach. Opsearch 39:151–160. https://doi.org/10.1007/bf03398676
Koc E (2022) What are the barriers to the adoption of industry 40 in container terminals? A qualitative study on Turkish Ports. J Transp Logist 7(2):367–386. https://doi.org/10.26650/jtl.2022.1035565
Koopmans TC (1947) Optimum utilization of the transportation system. In: Proceeding of the international statistical conference, Washington DC. https://doi.org/10.2307/1907301
Kumar PS (2016) PSK method for solving type-1 and type-3 fuzzy transportation problems. Int J Fuzzy Syst Appl (IJFSA) 5(4):121–146. https://doi.org/10.4018/ijfsa.2016100106
Kumar PS (2020a) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11:189–222. https://doi.org/10.1007/s13198-019-00941-3
Kumar PS (2020b) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1):189–222. https://doi.org/10.1007/s13198-019-00941-3
Kumar PS, Hussain RJ (2015) Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. Int J Syst Assur Eng Manag 7(S1):90–101. https://doi.org/10.1007/s13198-014-0334-2
Kumar A, Kaur A (2011b) Application of linear programming for solving fuzzy transportation problems. J Appl Math Inf 29(3–4):831–846
Kumar A, Kaur A (2011c) Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems. Fuzzy Inf Eng 3(1):81–99. https://doi.org/10.1007/s12543-011-0068-7
Littlewood DC, Kiyumbu WL (2018) “Hub” organisations in Kenya: What are they? What do they do? And what is their potential? Technol Forecast Soc Chang 131:276–285. https://doi.org/10.1016/j.techfore.2017.09.031
Malini P (2019) A new ranking technique on heptagonal fuzzy numbers to solve fuzzy transportation problem. Int J Math Oper Res 15(3):364–371. https://doi.org/10.1504/ijmor.2019.102078
Mathew ER, Kalayathankal SJ (2019) A New ranking method using dodecagonal fuzzy number to solve fuzzy transportation problem. Int J Appl Eng Res 14(4):948–951
Mathur N, Srivastava PK, Paul A (2016) Trapezoidal fuzzy model to optimize transportation problem. Int J Model Simul Sci Comput 7(3):1650028-1–1650038. https://doi.org/10.1142/s1793962316500288
Mohideen SI, Kumar PS (2010) A comparative study on transportation problem in fuzzy environment. Int J Math Res 2(1):151–158
Muthuperumal S, Titus P, Venkatachalapathy M (2020) An algorithmic approach to solve unbalanced triangular fuzzy transportation problems. Soft Comput 24(24):18689–18698. https://doi.org/10.35625/cm960127u
Nagar P, Srivastava PK, Srivastava A (2022) A new dynamic score function approach to optimize a special class of Pythagorean fuzzy transportation problem. Int J Syst Assur Eng Manag 13(2):904–913. https://doi.org/10.1007/s13198-021-01339-w
Narayanamoorthy S, Saranya S, Maheswari S (2013) A method for solving fuzzy transportation problem using fuzzy Russell’s method. Int J Intell Syst Appl 5(2):71–75. https://doi.org/10.5815/ijisa.2013.02.08
Ngastiti PTB, Surarso B, Sutimin T (2018) Zero point and zero suffix methods with robust ranking for solving fully fuzzy transportation problems. J Phys Conf Ser. https://doi.org/10.1088/1742-6596/1022/1/012005
Pandian P, Natarajan G (2010a) A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Appl Math Sci 4(2):79–90
Pandian P, Natrajan G (2010b) An optimal more-for-less solution to fuzzy transportation problems with mixed constraints. Appl Math Sci 4(29):1405–1415
Saad OM (2005) On the integer solutions of the generalized transportation problem under fuzzy environment. Opsearch 42:238–251. https://doi.org/10.1007/bf03398733
Salleh NHM, Selvaduray M, Jeevan J, Ngah AH, Zailani S (2021) Adaptation of industrial revolution 4.0 in a seaport system. Sustainability 13(9):10667. https://doi.org/10.3390/su131910667
Sam'an M, Farikhin, Surarso B, Zaki S (2018) A modified algorithm for full fuzzy transportation problem with simple additive weighting. In: International conference on information and communications technology (ICOIACT). IEEE, pp 684–688. https://doi.org/10.1109/icoiact.2018.8350745
Savitha MT, Mary G (2017) New methods for ranking of trapezoidal fuzzy numbers. Adv Fuzzy Math 12(5):1159–1170
Shanmugasundari M, Ganesan K (2013) A novel approach for the fuzzy optimal solution of fuzzy transportation problem. Int J Eng Res Appl 3(1):1416–1424
Singh SK, Yadav SP (2016) Intuitionistic fuzzy transportation problem with various kinds of uncertainties in parameters and variables. Int J Syst Assur Eng Manag 7:262–272. https://doi.org/10.1007/s13198-016-0456-9
Thamaraiselvi A, Santhi R (2015) Solving fuzzy transportation problem with generalized hexagonal fuzzy numbers. IOSR J Math 11(5):8–13
Vimala S, Prabha SK (2016) Fuzzy transportation problem through Monalisha’s approximation method. Br J Math Comput Sci 17(2):1–11. https://doi.org/10.9734/bjmcs/2016/26097
Vinoliah EM, Ganesan K (2017) Solution of fuzzy transportation problem- a new approach. Int J Pure Appl Math 113(13):20–29
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Agrawal, A., Singhal, N. An efficient computational approach for basic feasible solution of fuzzy transportation problems. Int J Syst Assur Eng Manag 15, 3337–3349 (2024). https://doi.org/10.1007/s13198-024-02340-9
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DOI: https://doi.org/10.1007/s13198-024-02340-9