Abstract
The real life transportation problems (TP) face a lot of problems due to uncertainties and lack of precise data. The present paper focuses on the two methods for solving intuitionistic fuzzy TP. One of the methods uses intuitionistic fuzzy programming technique together with the three different membership functions—linear, exponential and hyperbolic and the other method uses crisp linear programming taking intuitionistic fuzzy data in both the methods for the cost objective functions in the TP. The first method uses the membership and non-membership degrees separately to find the crisp solution using the fuzzy programming technique and then the optimal solution is calculated in terms of intuitionistic fuzzy data with the help of defined cost membership functions using the different membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find crisp solution considering a single objective function. The cost objective function is taken as intuitionistic fuzzy data and the methods have been used as such for the first time. A large scale real life intuitionistic TP has been solved using the two methods. The results obtained for different membership functions have been compared.
Similar content being viewed by others
References
Aggarwal S, Gupta C (2014) Algorithm for solving intuitionistic fuzzy transportation problem with generalized trapezoidal intuitionistic fuzzy number via new ranking method. export.arxiv.org, 01/2014, Source: arXiv
Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306
Antony RJP, Savarimuthu SJ, Pathinathan T (2014) Method for solving the transportation problem using triangular intuitionistic fuzzy number. Int J Comput Algorithm 03:590–605
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bit AK, Biswal MP, Alam SS (1992) Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets Syst 50:135–141
Bit AK, Biswal MP, Alam SS (1993) An additive fuzzy programming model for multi-objective transportation problem. Fuzzy Sets Syst 57:313–319
Cao B (1992) Transportation problem with nonlinear side constraints: a branch and bound approach. ZOR Methods Models Oper Res 36(2):185–197. doi:10.1007/BF01417216
Chanas S, Kuchta D (1996) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst 82:299–305
Chanas S, Kuchta D (1998) Fuzzy integer transportation problem. Fuzzy Sets Syst 98:291–298
Chanas S, Kolodziejczyk W, Machaj A (1984) A fuzzy approach to the transportation problem. Sets Syst 13:211–221
Kaur D, Mukherjee S, Basu K (2011) Multi-objective multi-index real life transportation problem with crisp objective function and interval valued supply and destination parameters. In: Proceedings of international conference on mathematical and computational models, (ICMCM’ 2011), Dec 19–21 2011, computational and mathematical modeling, pp 284–291, PSG College of Technology, Coimbatore, ISBN: 978-81-8487-1647
Kaur D, Mukherjee S, Basu K (2012a) Multi-objective multi-index real life transportation problem with interval valued parameters. In: Proceedings of the national seminar on recent advances in mathematics and its applications in engineering sciences (RAMAES 2012), March 16–17 2012, Bengal College of Engineering and Technology, Durgapur, pp 29–36, ISBN: 978-93-5067-395-9
Kaur D, Mukherjee S, Basu K (2012b) Goal programming approach to multi-index real life transportation problem with crisp objective function and interval valued supply and destination parameters. In: Proceedings of international conference on optimization, computing and business analytics (ICOCBA 2012), December 20–22 2012, pp 30–36, ISBN: 978-81-8424-8142
Kaur D, Mukherjee S, Basu K (2013) Solution of a multi-index real life transportation problem by fuzzy non-linear goal programming. In: Proceedings to RAMA-2013, Feb 14–16 2013, ISM, Dhanbad, pp 148–158, ISBN: 978-81-8424-821-0
Kaur D, Mukherjee S, Basu K (2015) Solution of a multi-objective and multi-index real life transportation problem using different fuzzy membership functions. J Optim Theory Appl 164(2):666–678
Dangalchev CA (1996) Partially-linear transportation problems. Eur J Oper Res 91(3):623–633. doi:10.1016/0377-2217(94)00367-X
Dangalchev CA (2000) Optimization of the transportation expense of a firm with contractual supplies. Transp Res Part B Methodol 34(3):203–217. doi:10.1016/S0191-2615(99)00021-1
Das SK, Goswami A, Alam SS (1997) Multiobjective transportation problem with interval cost, source and destination parameters. Eur J Oper Res 117(1):100–112
Dorigo M, Maniezzo V, Colorni A (1996) The ant system optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybernet Part B Cybernet 26(1):29–41. doi:10.1109/3477.484436
Gani AN, Abbas S (2013) A new method for solving intuitionistic fuzzy transportation problem. Appl Math Sci 7(28):1357–1365
Gao C, Yan C, Zhang Z, Hu Y, Mahadevan S, Deng Y (2014) An amoeboid algorithm for solving linear transportation problem. Phys A Stat Mech Appl 398:179–186
Glover F (1977) Heuristic for integer programming using surrogate constraints. Decis Sci 8(1):156–166. doi:10.1111/j.1540-5915.1977.tb01074.x
Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230
Holland JH (1975) Adaptation in natural and artificial systems: monograph. University of Michigan Press, Ann Arbor, p 183
Hussain RJ, Kumar PS (2012) Algorithmic approach for solving intuitionistic fuzzy transportation problem. Appl Math Sci 6(80):3981–3989
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: 1995 IEEE international conference on neural networks proceedings, 1942–1948
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimiza-optimization by simulated annealing. Science 220(4598):671–680. doi:10.1126/science.220.4598.671
Kuno T, Utsunomiya T (2000) A Lagrangian based branch-and-bound algorithm for production-transportation problems. J Global Optim 18(1):59–73. doi:10.1023/A:1008373329033
Li L, Lai KK (2000) A fuzzy approach to the multiobjective transportation problem. Comput Oper Res 27(1):43–57
Nagai H, Kuno T (2005) A simplicial branch-and-bound algorithm for production-transportation problems with inseparable concave production cost. J Oper Res Soc Jpn 48(2):97–100
Zadeh LA (1965) Fuzzy sets, Inform. Control 8:338–353
Zhang Y et al (2013) A biologically inspired solution for fuzzy shortest path problems. Appl Soft Comput 13(5):2356–2363
Zhang X et al (2014) A biologically inspired optimization algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths. J Optim Theory Appl 163(3):1049–1056
Zhang X et al (2016) A physarum-inspired approach to supply chain network design. Sci China Inf Sci 59:1–14
Zimmermann HJ (1978) Fuzzy linear programming with several objective functions. Fuzzy Sets Syst 1:46–55
Zmmermann HJ (1976) Description and optimization of fuzzy systems. Int J General Syst 2:209–215
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kour, D., Mukherjee, S. & Basu, K. Solving intuitionistic fuzzy transportation problem using linear programming. Int J Syst Assur Eng Manag 8 (Suppl 2), 1090–1101 (2017). https://doi.org/10.1007/s13198-017-0575-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-017-0575-y
Keywords
- Transportation problem
- Fuzzy linear programming
- Crisp linear programming
- Intuitionistic fuzzy data
- Membership and non-membership degree