A fuzzy binary bi objective transportation model: Iranian steel supply network
Abstract
Prominent influence of transportation costs on supply chain overall profit indicates the importance and emergence of transportation optimization models. Regarding this issue and in view of realistic situation consisting of non-deterministic information, in this research optimizing inbound and outbound transportation costs of a multi echelon supply chain has been considered. To deal with uncertain time deliveries and pricing strategies adopted by different members of supply chain, in conjunction with unpredictable demand rate, fuzzy logic and specifically Trapezoidal Fuzzy Numbers (TrFNs) are included. After designing a fuzzy binary multi objective model based upon structural assumptions, the solving approach is proposed and the model is employed on Iranian steel supply network to illustrate the potential and advantages of our scheduled model. The bi-objective mixed integer fuzzy programming model presents and encompasses many realistic circumstances making the model applicable in network transportation cases.
Keyword : fuzzy sets, transportation problem, binary bi objective models, supply network, optimization
How to Cite
Amoozad Mahdiraji, H., Beheshti, M., Razavi Hajiagha, S. H., & Zavadskas, E. K. (2018). A fuzzy binary bi objective transportation model: Iranian steel supply network. Transport, 33(3), 810-820. https://doi.org/10.3846/transport.2018.5800
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Bai, G.; Mao, J.; Lu, G. 2004. Grey transportation problem, Kybernetes 33(2): 219–224. https://doi.org/10.1108/03684920410514148
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Basirzadeh, H. 2011. An approach for solving fuzzy transportation problem, Applied Mathematical Sciences 5(29–32): 1549–1566.
Chanas, S. 2001. On the interval approximation of a fuzzy number, Fuzzy Sets and Systems 122(2): 353–356. https://doi.org/10.1016/S0165-0114(00)00080-4
Chanas, S.; Kołodziejczyk, W.; Machaj, A. 1984. A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13(3): 211–221. https://doi.org/10.1016/0165-0114(84)90057-5
Chanas, S.; Kuchta, D. 1996. A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82(3): 299–305. https://doi.org/10.1016/0165-0114(95)00278-2
Chen, S.-J.; Chen, S.-M. 2007. Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Applied Intelligence 26(1): 1–11. https://doi.org/10.1007/s10489-006-0003-5
Chiang, J. 2005. The optimal solution of the transportation problem with fuzzy demand and fuzzy product, Journal of Information Science and Engineering 21(2): 439–451.
Delgado, M.; Vila, M. A.; Voxman, W. 1998. On a canonical representation of fuzzy numbers, Fuzzy Sets and Systems 93(1): 125–135. https://doi.org/10.1016/S0165-0114(96)00144-3
Deng, J. L. 1989. Introduction to Grey system theory, The Journal of Grey System 1(1): 1–24.
Dubois, D.; Prade, H. 1987. The mean value of a fuzzy number, Fuzzy Sets and Systems 24(3): 279–300. https://doi.org/10.1016/0165-0114(87)90028-5
Ebrahimnejad, A. 2014. A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers, Applied Soft Computing 19: 171–176. https://doi.org/10.1016/j.asoc.2014.01.041
Esmaeili, M.; Aryanezhad, M.-B.; Zeephongsekul, P. 2009. A game theory approach in seller–buyer supply chain, European Journal of Operational Research 195(2): 442–448. https://doi.org/10.1016/j.ejor.2008.02.026
Gani, A. N.; Samuel, A. E.; Anuradha, D. 2011. Simplex type algorithm for solving fuzzy transportation problem, Tamsui Oxford Journal of Information and Mathematical Sciences 27(1): 89–98.
Grzegorzewski, P. 2008. New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval, in Proceedings of IPMU’08, 22–27 June 2008, Torremolinos, Málaga, Spain, 117–123.
Grzegorzewski, P. 1998. Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97(1): 83–94. https://doi.org/10.1016/S0165-0114(96)00322-3
Güzel, N. 2010. Fuzzy transportation problem with the fuzzy amounts and the fuzzy costs, World Applied Sciences Journal 8(5): 543–549.
Heilpern, S. 1992. The expected value of a fuzzy number, Fuzzy Sets and Systems 47(1): 81–86. https://doi.org/10.1016/0165-0114(92)90062-9
Jia, P.; Amoozad Mahdiraji, H.; Govindan, K.; Meidutė, I. 2013. Leadership selection in an unlimited three-echelon supply chain, Journal of Business Economics and Management 14(3): 616–637. https://doi.org/10.3846/16111699.2012.761648
Jiménez, F.; Verdegay, J. L. 1999. Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach, European Journal of Operational Research 117(3): 485–510. https://doi.org/10.1016/S0377-2217(98)00083-6
Jiménez, F.; Verdegay, J. L. 1998. Uncertain solid transportation problems, Fuzzy Sets and Systems 100(1–3): 45–57. https://doi.org/10.1016/S0165-0114(97)00164-4
Jin, S.; Lee, J.; Gen, M. 2011. Multi-product Two-stage Logistics Problem. Waseda University, Japan.
Kaur, A.; Kumar, A. 2012. A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers, Applied Soft Computing 12(3): 1201–1213. https://doi.org/10.1016/j.asoc.2011.10.014
Kocken, H. G.; Sivri, M. 2016. A simple parametric method to generate all optimal solutions of fuzzy solid transportation problem, Applied Mathematical Modelling 40(7–8): 4612–4624. https://doi.org/10.1016/j.apm.2015.10.053
Kumar, A.; Gupta, A. 2011. Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions, Fuzzy Information and Engineering 3(1): 3–21. https://doi.org/10.1007/s12543-011-0062-0
Kumar, A.; Gupta, A.; Sharma, M. K. 2010. Solving fuzzy bi-criteria fixed charge transportation problem using a new fuzzy algorithm International Journal of Applied Science and Engineering 8(1): 77–98.
Kumar, B. R.; Murugesan, S. 2012. On fuzzy transportation problem using triangular fuzzy numbers with modified revised simplex method, International Journal of Engineering Science and Technology 4(1): 285–294.
Kundu, P.; Kar, S.; Maiti, M. 2015. Multi-item solid transportation problem with type-2 fuzzy parameters, Applied Soft Computing 31: 61–80. https://doi.org/10.1016/j.asoc.2015.02.007
Li, Q.-X.; Liu, S.; Wang, N.-A. 2014. Covered solution for a grey linear program based on a general formula for the inverse of a grey matrix, Grey Systems: Theory and Application 4(1): 72–94. https://doi.org/10.1108/GS-10-2013-0023
Lin, F.-T. 2009. Solving the transportation problem with fuzzy coefficients using genetic algorithms, in 2009 IEEE International Conference on Fuzzy Systems, 20–24 August 2009, Jeju Island, South Korea, 1468–1473. https://doi.org/10.1109/FUZZY.2009.5277202
Liu, P.; Yang, L.; Wang, L.; Li, S. 2014. A solid transportation problem with type-2 fuzzy variables, Applied Soft Computing 24: 543–558. https://doi.org/10.1016/j.asoc.2014.08.005
Liu, S.; Lin, Y. 2006. Grey Information: Theory and Practical Applications. Springer. 508 p. https://doi.org/10.1007/1-84628-342-6
Mohanaselvi, S.; Ganesan, K. 2012. Fuzzy optimal solution to fuzzy transportation problem: a new approach, International Journal on Computer Science and Engineering 4(3): 367–386.
Pandian, P.; Natarajan, G. 2010. A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Applied Mathematical Sciences 4(2): 79–90.
Petraška, A.; Čižiūnienė, K.; Jarašūnienė, A.; Maruschak, P.; Prentkovskis, O. 2017. Algorithm for the assessment of heavyweight and oversize cargo transportation routes, Journal of Business Economics and Management 18(6): 1098–1114. https://doi.org/10.3846/16111699.2017.1334229
Poonam, S.; Abbas, S. H.; Gupta, V. K. 2012. Fuzzy transportation problem of triangular numbers with − cut and ranking technique, IOSR Journal of Engineering 2(5): 1162–1164. https://doi.org/10.9790/3021-020511621164
Pramanik, S.; Jana, D. K.; Mondal, S. K.; Maiti, M. 2015. A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments, Information Sciences 325: 190–214. https://doi.org/10.1016/j.ins.2015.07.012
Purusotham, S.; Murthy, S. 2012. An exact algorithm for multi – product bulk transportation problem, International Journal on Computer Science and Engineering 3(9): 3222–3236.
Razavi Hajiagha, S. H.; Mahdiraji, H. A.; Hashemi, S. S. 2014. A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff, The International Journal of Advanced Manufacturing Technology 71(1–4): 117–126. https://doi.org/10.1007/s00170-013-5463-2
Rianthong, N.; Dumrongsiri, A. 2012. A mathematical model for optimal production, inventory and transportation planning with direct shipment, International Proceedings of Economics Development and Research 36: 23–27.
Ritha, W.; Vinotha, J. M. 2009. Multi-objective two stage fuzzy transportation problem, Journal of Physical Sciences 13: 107–120.
Samuel, A. E.; Venkatachalapathy, M. 2014. Improving IZPM for unbalanced fuzzy transportation problems, International Journal of Pure and Applied Mathematics 94(3): 419–424. https://doi.org/10.12732/ijpam.v94i3.9
Sharma, G.; Abbas, S. H.; Gupta, V. K. 2012. Solving transportation problem with the help of integer programming problem, IOSR Journal of Engineering 2(6): 1274–1277. https://doi.org/10.9790/3021-026112741277
Stević, Ž; Pamučar, D.; Zavadskas, E. K.; Ćirović, G.; Prentkovskis, O. 2017. The selection of wagons for the internal transport of a logistics company: a novel approach based on rough BWM and rough SAW methods, Symmetry 9(11): 1–25. https://doi.org/10.3390/sym9110264
Wang, Y.-J. 2015. Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation, Applied Mathematical Modelling 39(2): 586–599. https://doi.org/10.1016/j.apm.2014.06.011
Yeh, C.-T. 2008. Trapezoidal and triangular approximations preserving the expected interval, Fuzzy Sets and Systems 159(11): 1345–1353. https://doi.org/10.1016/j.fss.2007.09.010
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zimmermann, H.-J. 1978. Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1(1): 45–55. https://doi.org/10.1016/0165-0114(78)90031-3
Allahviranloo, T.; Firozja, M. A. 2007. Note on “Trapezoidal approximation of fuzzy numbers”, Fuzzy Sets and Systems 158(7): 755–756. https://doi.org/10.1016/j.fss.2006.10.017
Amoozad Mahdiraji, H.; Razavi Hajiagha, S. H.; Hashemi, S. S.; Zavadskas, E. K. 2016. A grey multi-objective linear model to find critical path of a project by using time, cost, quality and risk parameters, E+M Ekonomie a Management 19(1): 49–61. https://doi.org/10.15240/tul/001/2016-1-004
Amoozad Mahdiraji, H.; Razavi Hajiagha, S. H.; Pourjam, R. 2011. A grey mathematical programming model to time-cost trade-offs in project management under uncertainty, in Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services, 15–18 September 2011, Nanjing, China, 698–704. https://doi.org/10.1109/GSIS.2011.6044123
Amoozad Mahdiraji, H.; Zavadskas, E.; Razavi Hajiagha, S. H. 2015. Game theoretic approach for coordinating unlimited multi echelon supply chains, Transformations in Business & Economics 14(2): 133–151.
Bai, G.; Mao, J.; Lu, G. 2004. Grey transportation problem, Kybernetes 33(2): 219–224. https://doi.org/10.1108/03684920410514148
Ban, A. I.; Coroianu, L. 2014. Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition, Fuzzy Sets and Systems 257: 3–22. https://doi.org/10.1016/j.fss.2013.07.004
Basirzadeh, H. 2011. An approach for solving fuzzy transportation problem, Applied Mathematical Sciences 5(29–32): 1549–1566.
Chanas, S. 2001. On the interval approximation of a fuzzy number, Fuzzy Sets and Systems 122(2): 353–356. https://doi.org/10.1016/S0165-0114(00)00080-4
Chanas, S.; Kołodziejczyk, W.; Machaj, A. 1984. A fuzzy approach to the transportation problem, Fuzzy Sets and Systems 13(3): 211–221. https://doi.org/10.1016/0165-0114(84)90057-5
Chanas, S.; Kuchta, D. 1996. A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82(3): 299–305. https://doi.org/10.1016/0165-0114(95)00278-2
Chen, S.-J.; Chen, S.-M. 2007. Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Applied Intelligence 26(1): 1–11. https://doi.org/10.1007/s10489-006-0003-5
Chiang, J. 2005. The optimal solution of the transportation problem with fuzzy demand and fuzzy product, Journal of Information Science and Engineering 21(2): 439–451.
Delgado, M.; Vila, M. A.; Voxman, W. 1998. On a canonical representation of fuzzy numbers, Fuzzy Sets and Systems 93(1): 125–135. https://doi.org/10.1016/S0165-0114(96)00144-3
Deng, J. L. 1989. Introduction to Grey system theory, The Journal of Grey System 1(1): 1–24.
Dubois, D.; Prade, H. 1987. The mean value of a fuzzy number, Fuzzy Sets and Systems 24(3): 279–300. https://doi.org/10.1016/0165-0114(87)90028-5
Ebrahimnejad, A. 2014. A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers, Applied Soft Computing 19: 171–176. https://doi.org/10.1016/j.asoc.2014.01.041
Esmaeili, M.; Aryanezhad, M.-B.; Zeephongsekul, P. 2009. A game theory approach in seller–buyer supply chain, European Journal of Operational Research 195(2): 442–448. https://doi.org/10.1016/j.ejor.2008.02.026
Gani, A. N.; Samuel, A. E.; Anuradha, D. 2011. Simplex type algorithm for solving fuzzy transportation problem, Tamsui Oxford Journal of Information and Mathematical Sciences 27(1): 89–98.
Grzegorzewski, P. 2008. New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval, in Proceedings of IPMU’08, 22–27 June 2008, Torremolinos, Málaga, Spain, 117–123.
Grzegorzewski, P. 1998. Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97(1): 83–94. https://doi.org/10.1016/S0165-0114(96)00322-3
Güzel, N. 2010. Fuzzy transportation problem with the fuzzy amounts and the fuzzy costs, World Applied Sciences Journal 8(5): 543–549.
Heilpern, S. 1992. The expected value of a fuzzy number, Fuzzy Sets and Systems 47(1): 81–86. https://doi.org/10.1016/0165-0114(92)90062-9
Jia, P.; Amoozad Mahdiraji, H.; Govindan, K.; Meidutė, I. 2013. Leadership selection in an unlimited three-echelon supply chain, Journal of Business Economics and Management 14(3): 616–637. https://doi.org/10.3846/16111699.2012.761648
Jiménez, F.; Verdegay, J. L. 1999. Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach, European Journal of Operational Research 117(3): 485–510. https://doi.org/10.1016/S0377-2217(98)00083-6
Jiménez, F.; Verdegay, J. L. 1998. Uncertain solid transportation problems, Fuzzy Sets and Systems 100(1–3): 45–57. https://doi.org/10.1016/S0165-0114(97)00164-4
Jin, S.; Lee, J.; Gen, M. 2011. Multi-product Two-stage Logistics Problem. Waseda University, Japan.
Kaur, A.; Kumar, A. 2012. A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers, Applied Soft Computing 12(3): 1201–1213. https://doi.org/10.1016/j.asoc.2011.10.014
Kocken, H. G.; Sivri, M. 2016. A simple parametric method to generate all optimal solutions of fuzzy solid transportation problem, Applied Mathematical Modelling 40(7–8): 4612–4624. https://doi.org/10.1016/j.apm.2015.10.053
Kumar, A.; Gupta, A. 2011. Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions, Fuzzy Information and Engineering 3(1): 3–21. https://doi.org/10.1007/s12543-011-0062-0
Kumar, A.; Gupta, A.; Sharma, M. K. 2010. Solving fuzzy bi-criteria fixed charge transportation problem using a new fuzzy algorithm International Journal of Applied Science and Engineering 8(1): 77–98.
Kumar, B. R.; Murugesan, S. 2012. On fuzzy transportation problem using triangular fuzzy numbers with modified revised simplex method, International Journal of Engineering Science and Technology 4(1): 285–294.
Kundu, P.; Kar, S.; Maiti, M. 2015. Multi-item solid transportation problem with type-2 fuzzy parameters, Applied Soft Computing 31: 61–80. https://doi.org/10.1016/j.asoc.2015.02.007
Li, Q.-X.; Liu, S.; Wang, N.-A. 2014. Covered solution for a grey linear program based on a general formula for the inverse of a grey matrix, Grey Systems: Theory and Application 4(1): 72–94. https://doi.org/10.1108/GS-10-2013-0023
Lin, F.-T. 2009. Solving the transportation problem with fuzzy coefficients using genetic algorithms, in 2009 IEEE International Conference on Fuzzy Systems, 20–24 August 2009, Jeju Island, South Korea, 1468–1473. https://doi.org/10.1109/FUZZY.2009.5277202
Liu, P.; Yang, L.; Wang, L.; Li, S. 2014. A solid transportation problem with type-2 fuzzy variables, Applied Soft Computing 24: 543–558. https://doi.org/10.1016/j.asoc.2014.08.005
Liu, S.; Lin, Y. 2006. Grey Information: Theory and Practical Applications. Springer. 508 p. https://doi.org/10.1007/1-84628-342-6
Mohanaselvi, S.; Ganesan, K. 2012. Fuzzy optimal solution to fuzzy transportation problem: a new approach, International Journal on Computer Science and Engineering 4(3): 367–386.
Pandian, P.; Natarajan, G. 2010. A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Applied Mathematical Sciences 4(2): 79–90.
Petraška, A.; Čižiūnienė, K.; Jarašūnienė, A.; Maruschak, P.; Prentkovskis, O. 2017. Algorithm for the assessment of heavyweight and oversize cargo transportation routes, Journal of Business Economics and Management 18(6): 1098–1114. https://doi.org/10.3846/16111699.2017.1334229
Poonam, S.; Abbas, S. H.; Gupta, V. K. 2012. Fuzzy transportation problem of triangular numbers with − cut and ranking technique, IOSR Journal of Engineering 2(5): 1162–1164. https://doi.org/10.9790/3021-020511621164
Pramanik, S.; Jana, D. K.; Mondal, S. K.; Maiti, M. 2015. A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments, Information Sciences 325: 190–214. https://doi.org/10.1016/j.ins.2015.07.012
Purusotham, S.; Murthy, S. 2012. An exact algorithm for multi – product bulk transportation problem, International Journal on Computer Science and Engineering 3(9): 3222–3236.
Razavi Hajiagha, S. H.; Mahdiraji, H. A.; Hashemi, S. S. 2014. A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff, The International Journal of Advanced Manufacturing Technology 71(1–4): 117–126. https://doi.org/10.1007/s00170-013-5463-2
Rianthong, N.; Dumrongsiri, A. 2012. A mathematical model for optimal production, inventory and transportation planning with direct shipment, International Proceedings of Economics Development and Research 36: 23–27.
Ritha, W.; Vinotha, J. M. 2009. Multi-objective two stage fuzzy transportation problem, Journal of Physical Sciences 13: 107–120.
Samuel, A. E.; Venkatachalapathy, M. 2014. Improving IZPM for unbalanced fuzzy transportation problems, International Journal of Pure and Applied Mathematics 94(3): 419–424. https://doi.org/10.12732/ijpam.v94i3.9
Sharma, G.; Abbas, S. H.; Gupta, V. K. 2012. Solving transportation problem with the help of integer programming problem, IOSR Journal of Engineering 2(6): 1274–1277. https://doi.org/10.9790/3021-026112741277
Stević, Ž; Pamučar, D.; Zavadskas, E. K.; Ćirović, G.; Prentkovskis, O. 2017. The selection of wagons for the internal transport of a logistics company: a novel approach based on rough BWM and rough SAW methods, Symmetry 9(11): 1–25. https://doi.org/10.3390/sym9110264
Wang, Y.-J. 2015. Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation, Applied Mathematical Modelling 39(2): 586–599. https://doi.org/10.1016/j.apm.2014.06.011
Yeh, C.-T. 2008. Trapezoidal and triangular approximations preserving the expected interval, Fuzzy Sets and Systems 159(11): 1345–1353. https://doi.org/10.1016/j.fss.2007.09.010
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zimmermann, H.-J. 1978. Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1(1): 45–55. https://doi.org/10.1016/0165-0114(78)90031-3