Research Article
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Year 2022, Volume: 12 Issue: 3, 1776 - 1789, 01.09.2022
https://doi.org/10.21597/jist.1107648

Abstract

References

  • Ahlatçıoğlu M, Sivri M, 1988. A Solution Proposal for Solving Three-Dimension Transportation Problem. İ.T.Ü, Istanbul-Turkey, 22: 9-12.
  • Anuradha D, Jayalakshmi M, Deepa G, Sujatha V, 2019. Solution of Multiobjective Solid Transportation Problem in Fuzzy Approach. AIP Conference Proceedings, No.1, P020009-1- 020009-5.5.
  • Arslan O, Archetti C, Jabali O, Laporte G, Speranza MG, 2020. Minimum cost network design in strategic alliances. Omega, Vol. 96, 102079.
  • Bit AK, Biswal MP, Alam SS, 1993. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57:183-194.
  • Bodkhe, SG, Bajaj VH, Dhaigude DB, 2010. Fuzzy programming technique to solve multi-objective solid transportation problem with some non-linear membership functions. Advances in Computational Research, 2(1):15-20.
  • Chen Lin, Jin P, Zhang B, 2017. Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, 51: 49–59.
  • Chen B, Liu Y, Zhou T, 2017. An entropy based solid transportation problem in uncertain environment”. Journal of Ambient Intelligence and Humanized Computing, 10(1): 357 –363.
  • Cui Q, Sheng Y, 2012. Uncertain programming model for solid transportation problem. Information, 15: 342–348.
  • Dalman H, Sivri M, 2017. Multi-objective Solid Transportation Problem in Uncertain Environment. Iranian Journal of Science and Technology, Transactions A: Science, 41:505-514.
  • Guu SM, Wu Y, 1997. Weighted coefficients in two-phase approach for solving the multiple objective programming problems. Fuzzy Sets and Systems, 85: 45-48.
  • Hu Y, Zhao X, Liu J, Liang B, Ma C, 2020. An efficient algorithm for solving minimum cost flow problem with complementarity slack conditions. Mathematical Problems in Engineering, 2020:1-5.
  • Kaur, D, Mukherjee S, Basu K, 2015. Solution of a multi-objective and multi-index real-life transportation problem using different fuzzy membership functions. Journal of Optimization Theory and Applications, 164:666-678.
  • Khan IU, Rafique F, 2021. Minimum-cost capacitated fuzzy network, fuzzy linear programming formulation, and perspective data analytics to minimize the operations cost of American airlines. Soft Computing, 25(2):1411-1429.
  • Khurana A, Adlakha V, 2015. On multi-index fixed charge bi-criterion transportation problem. Opsearch, 52(4):733-745.
  • Khurana A, Adlakha V, Lev B, 2018. Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities. Operations Research Perspectives, 5:319-333.
  • Kundu P, Kar S, Maiti M, 2014. Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci, 45(8):1668–1682.
  • Leberling H, 1981. On finding compromise solutions in multicriteria problems using the fuzzy min-operator. Fuzzy sets and systems, 6(2):105-118.
  • Lee ES, Li RJ, 1993. Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets and Systems, 53:275-288.
  • Li RJ, Lee ES, 1991. An exponential membership function for fuzzy multiple objective linear programming. Computers Math Applic, 22(12):55-60.
  • Mahmood T, Ali Z, (2022). Prioritized Muirhead Mean Aggregation Operators under the Complex Single-Valued Neutrosophic Settings and Their Application in Multi-Attribute Decision-Making. Journal of Computational and Cognitive Engineering, 1(2): 56–73.
  • Memiş S, Enginoğlu S, Erkan U, (2022). A new classification method using soft decision-making based on an aggregation operator of fuzzy parameterized fuzzy soft matrices. Turkish Journal of Electrical Engineering & Computer Sciences, 30(3): 871-890.
  • Mollanoori H, Moghaddam RT, Triki C, Kestheli MH, Sabohi F, 2019. Extending the solid step fixed-charge transportation problem to consider two-stage networks and multi-item shipments. Computers & Industrial Engineering, 137:106008.
  • Ojha A, Das B, Mondal S, Maiti M, 2010. A stochastic discounted multi-objective solid transportation problem for breakable items using analytical hierarchy process. Appl. Math. Model, 34(8):2256–2271.
  • Peidroa D, Vasant P, 2011. Transportation planning with modified S-curve membership functions using an interactive fuzzy multi-objective approach. Applied Soft Computing, 11:2656-2663.
  • Pramanik S, Jana D, Maiti M, 2013. Multi-objective solid transportation problem in imprecise environments. Journal of Transportation Security, 6:131–150.
  • Qiyas M, Naeem M, Abdullah S, Khan F, Khan N, Garg H, 2022. Fractional orthotriple fuzzy rough Hamacher aggregation operators and-their application on service quality of wireless network selection. Alexandria Engineering Journal, 61(12), 10433:10452.
  • Rath P, Dash RB, 2017. Solution of Fuzzy Multi-Objective Linear Programming Problems using Fuzzy Programming Techniques based on Exponential Membership Functions. International Journal of Mathematics Trends and Technology, 41(3).
  • Sadore DS, Tuli R, 2019. Optimal Solution of the Planar Four Index Transportation Problem. Amity International Conference on Artificial Intelligence (AICAI), doi: 10.1109/AICAI.2019.8701265,pp: 548-553.
  • Singh S, Pradhan A, Biswal MP, 2019. Multi-objective solid transportation problem under stochastic environment. Sadhana, 44:105.
  • Tiryaki F, 2006. Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems. Fuzzy Sets and Systems, 157:3072-3090.
  • Verma R, Biswal M, Biswas A, 1997. Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Sets and Systems, 91:37-43.
  • Werners BM,1988. Aggregation models in mathematical programming. in (G. Mitra, Ed.), Mathematical Models for Decision Support, Springer, Berlin, 295-305.
  • Wu YK, Guu SM, 2001. A compromise model for solving fuzzy multiple objective problems. Journal of the Chinese Institute of Industrial Engineers, 18(5):87-93.
  • Zadeh LA, 1965. Fuzzy Sets. Information and Control, 8:338-353.

New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators

Year 2022, Volume: 12 Issue: 3, 1776 - 1789, 01.09.2022
https://doi.org/10.21597/jist.1107648

Abstract

A solid transportation problem emerges when the decision variables are represented by three items: the source, the destination, and the mode of transport. In applications, the STP generally requires considering multiple objectives such as cost minimization, time minimization, security level maximization, etc. In this way, a multi-objective solid transportation problem arises. This paper deals with the solution of the problem and analyzes the effect of several important fuzzy aggregation operators on the solution of the problem. In this context, the most commonly used aggregation operators are investigated for this problem. To explain the solution approach, a numerical example from the literature is given and a Pareto-optimal solution set is provided to offer the decision-maker. Furthermore, graphical comparisons and sensitivity analysis are presented with the solution obtained.

References

  • Ahlatçıoğlu M, Sivri M, 1988. A Solution Proposal for Solving Three-Dimension Transportation Problem. İ.T.Ü, Istanbul-Turkey, 22: 9-12.
  • Anuradha D, Jayalakshmi M, Deepa G, Sujatha V, 2019. Solution of Multiobjective Solid Transportation Problem in Fuzzy Approach. AIP Conference Proceedings, No.1, P020009-1- 020009-5.5.
  • Arslan O, Archetti C, Jabali O, Laporte G, Speranza MG, 2020. Minimum cost network design in strategic alliances. Omega, Vol. 96, 102079.
  • Bit AK, Biswal MP, Alam SS, 1993. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57:183-194.
  • Bodkhe, SG, Bajaj VH, Dhaigude DB, 2010. Fuzzy programming technique to solve multi-objective solid transportation problem with some non-linear membership functions. Advances in Computational Research, 2(1):15-20.
  • Chen Lin, Jin P, Zhang B, 2017. Uncertain goal programming models for bicriteria solid transportation problem. Applied Soft Computing, 51: 49–59.
  • Chen B, Liu Y, Zhou T, 2017. An entropy based solid transportation problem in uncertain environment”. Journal of Ambient Intelligence and Humanized Computing, 10(1): 357 –363.
  • Cui Q, Sheng Y, 2012. Uncertain programming model for solid transportation problem. Information, 15: 342–348.
  • Dalman H, Sivri M, 2017. Multi-objective Solid Transportation Problem in Uncertain Environment. Iranian Journal of Science and Technology, Transactions A: Science, 41:505-514.
  • Guu SM, Wu Y, 1997. Weighted coefficients in two-phase approach for solving the multiple objective programming problems. Fuzzy Sets and Systems, 85: 45-48.
  • Hu Y, Zhao X, Liu J, Liang B, Ma C, 2020. An efficient algorithm for solving minimum cost flow problem with complementarity slack conditions. Mathematical Problems in Engineering, 2020:1-5.
  • Kaur, D, Mukherjee S, Basu K, 2015. Solution of a multi-objective and multi-index real-life transportation problem using different fuzzy membership functions. Journal of Optimization Theory and Applications, 164:666-678.
  • Khan IU, Rafique F, 2021. Minimum-cost capacitated fuzzy network, fuzzy linear programming formulation, and perspective data analytics to minimize the operations cost of American airlines. Soft Computing, 25(2):1411-1429.
  • Khurana A, Adlakha V, 2015. On multi-index fixed charge bi-criterion transportation problem. Opsearch, 52(4):733-745.
  • Khurana A, Adlakha V, Lev B, 2018. Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities. Operations Research Perspectives, 5:319-333.
  • Kundu P, Kar S, Maiti M, 2014. Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci, 45(8):1668–1682.
  • Leberling H, 1981. On finding compromise solutions in multicriteria problems using the fuzzy min-operator. Fuzzy sets and systems, 6(2):105-118.
  • Lee ES, Li RJ, 1993. Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets and Systems, 53:275-288.
  • Li RJ, Lee ES, 1991. An exponential membership function for fuzzy multiple objective linear programming. Computers Math Applic, 22(12):55-60.
  • Mahmood T, Ali Z, (2022). Prioritized Muirhead Mean Aggregation Operators under the Complex Single-Valued Neutrosophic Settings and Their Application in Multi-Attribute Decision-Making. Journal of Computational and Cognitive Engineering, 1(2): 56–73.
  • Memiş S, Enginoğlu S, Erkan U, (2022). A new classification method using soft decision-making based on an aggregation operator of fuzzy parameterized fuzzy soft matrices. Turkish Journal of Electrical Engineering & Computer Sciences, 30(3): 871-890.
  • Mollanoori H, Moghaddam RT, Triki C, Kestheli MH, Sabohi F, 2019. Extending the solid step fixed-charge transportation problem to consider two-stage networks and multi-item shipments. Computers & Industrial Engineering, 137:106008.
  • Ojha A, Das B, Mondal S, Maiti M, 2010. A stochastic discounted multi-objective solid transportation problem for breakable items using analytical hierarchy process. Appl. Math. Model, 34(8):2256–2271.
  • Peidroa D, Vasant P, 2011. Transportation planning with modified S-curve membership functions using an interactive fuzzy multi-objective approach. Applied Soft Computing, 11:2656-2663.
  • Pramanik S, Jana D, Maiti M, 2013. Multi-objective solid transportation problem in imprecise environments. Journal of Transportation Security, 6:131–150.
  • Qiyas M, Naeem M, Abdullah S, Khan F, Khan N, Garg H, 2022. Fractional orthotriple fuzzy rough Hamacher aggregation operators and-their application on service quality of wireless network selection. Alexandria Engineering Journal, 61(12), 10433:10452.
  • Rath P, Dash RB, 2017. Solution of Fuzzy Multi-Objective Linear Programming Problems using Fuzzy Programming Techniques based on Exponential Membership Functions. International Journal of Mathematics Trends and Technology, 41(3).
  • Sadore DS, Tuli R, 2019. Optimal Solution of the Planar Four Index Transportation Problem. Amity International Conference on Artificial Intelligence (AICAI), doi: 10.1109/AICAI.2019.8701265,pp: 548-553.
  • Singh S, Pradhan A, Biswal MP, 2019. Multi-objective solid transportation problem under stochastic environment. Sadhana, 44:105.
  • Tiryaki F, 2006. Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems. Fuzzy Sets and Systems, 157:3072-3090.
  • Verma R, Biswal M, Biswas A, 1997. Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Sets and Systems, 91:37-43.
  • Werners BM,1988. Aggregation models in mathematical programming. in (G. Mitra, Ed.), Mathematical Models for Decision Support, Springer, Berlin, 295-305.
  • Wu YK, Guu SM, 2001. A compromise model for solving fuzzy multiple objective problems. Journal of the Chinese Institute of Industrial Engineers, 18(5):87-93.
  • Zadeh LA, 1965. Fuzzy Sets. Information and Control, 8:338-353.
There are 34 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Nurdan Kara 0000-0001-6195-288X

Hale Köçken 0000-0003-1121-7099

Early Pub Date August 26, 2022
Publication Date September 1, 2022
Submission Date April 22, 2022
Acceptance Date May 30, 2022
Published in Issue Year 2022 Volume: 12 Issue: 3

Cite

APA Kara, N., & Köçken, H. (2022). New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators. Journal of the Institute of Science and Technology, 12(3), 1776-1789. https://doi.org/10.21597/jist.1107648
AMA Kara N, Köçken H. New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators. J. Inst. Sci. and Tech. September 2022;12(3):1776-1789. doi:10.21597/jist.1107648
Chicago Kara, Nurdan, and Hale Köçken. “New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators”. Journal of the Institute of Science and Technology 12, no. 3 (September 2022): 1776-89. https://doi.org/10.21597/jist.1107648.
EndNote Kara N, Köçken H (September 1, 2022) New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators. Journal of the Institute of Science and Technology 12 3 1776–1789.
IEEE N. Kara and H. Köçken, “New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators”, J. Inst. Sci. and Tech., vol. 12, no. 3, pp. 1776–1789, 2022, doi: 10.21597/jist.1107648.
ISNAD Kara, Nurdan - Köçken, Hale. “New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators”. Journal of the Institute of Science and Technology 12/3 (September 2022), 1776-1789. https://doi.org/10.21597/jist.1107648.
JAMA Kara N, Köçken H. New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators. J. Inst. Sci. and Tech. 2022;12:1776–1789.
MLA Kara, Nurdan and Hale Köçken. “New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators”. Journal of the Institute of Science and Technology, vol. 12, no. 3, 2022, pp. 1776-89, doi:10.21597/jist.1107648.
Vancouver Kara N, Köçken H. New Solution Approaches for Multi-Objective Solid Transportation Problem Using Some Aggregation Operators. J. Inst. Sci. and Tech. 2022;12(3):1776-89.