Can the Fixed-Cost Transportation Problem Be Solved with the Initial Solution Methods of the Transportation Problem?

Year 2024, Volume: 11 Issue: 3, 944 - 959, 30.09.2024

Kenan Karagül

https://doi.org/10.30798/makuiibf.1389617

Abstract

Abstract
From the dawn of humanity's existence to the present day and beyond, there will always be production and service systems to meet the demands at every point of consumption. In this context, transporting goods from production and service resources to consumption points will continue to play a significant role. Supply Chain Management and its sub-systems, particularly logistics and hence the Transportation Problem, will be crucial for the functioning of these systems. This study focuses on the Fixed-Cost Transportation Problem. A novel heuristic approach has been proposed for this problem, and the success of the heuristic has been analyzed through a group of test problems compared with similar methods in the literature. The proposed heuristic has shown promising results.

Keywords

Fixed-Cost Transportation Problem, Transportation Problem, Heuristics, VAM, MODI

References

• Abdelati, M.H. (2023). Improving solution quality in transportation problems: A novel algorithm for efficient resource allocation. Agpe The Royal Gondwana Research Journal of History, Science, Economic, Political and Social Science, 4(8), 1–10.
• Adlakha, V., Kowalski, K., & Vemuganti, R.R. (2006). Heuristic algorithms for the fixed-charge transportation problem. OPSEARCH, 43, 132–151. https://doi.org/10.1007/BF03398770
• Akbar, Y.R., Zain, I., Septianingsih, R.., & Nuraini, P. (2023). The transportation method for efficient cost of shipping goods. International Journal of Economics, Management, Business, And Social Science (IJEMBIS), 3(1), 67–76. https://doi.org/10.59889/ijembis.v3i1.114
• Angmalisang, H.Y., Angmalisang, H., & Sumarauw, S.J. (2023). Leaders and followers algorithm for balanced transportation problem. Computer Engineering and Applications Journal, 12(2), 79-87. https://doi.org/10.18495/COMENGAPP.V12I2.436
• Aroniadi C, Beligiannis G.N. (2023). Applying particle swarm optimization variations to solve the transportation problem effectively. Algorithms, 16(8), 372. https://doi.org/10.3390/a16080372
• Balinski, M. L. (1961). Fixed-cost transportation problems. Naval Research Logistics, 8(1), 41-54.
• Dantzig, G.B. (1951). Application of the simplex method to a transportation problem, In Koopmans, T.C. (Ed), Activity Analysis of Production and Allocation (pp. 359-373). John Wiley and Sons.
• Demircioğlu, M., & Coşkun, İ. T. (2018). Sabit maliyetli ulaştırma problemleri için Balinski yöntemi uygulaması. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, (31), 275-284. https://doi.org/10.30794/pausbed.414850
• Hitchcock F.L. (1941). The distribution of a product from several sources to numerous localities, Journal of Mathematics and Physics, 20, 224−230.
• Jamali, J., Rahma, T.M. (2023). Investigating the pitfalls of the least cost and Vogel’s approximate methods: Understanding the impact of cost matrix pattern. Journal of Engineering Science, 14(1), 123-135. https://doi.org/10.3329/jes.v14i1.67641
• Kalaivani, K., Kaliyaperumal, P. (2023). A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers. Proyecciones (Antofagasta), 42(2), 533-547. https://dx.doi.org/10.22199/issn.0717-6279-5374
• Karagül, K. (2022, December 10-13). Sabit maliyetli ulaştırma problemi için yeni bir çözüm yaklaşımı [Conference Paper]. 1st International Conference on Scientific and Academic Research, Konya, Türkiye.
• Karagül, K., Şahin, Y. (2020). A novel approximation method to obtain initial basic feasible solution of transportation problem. Journal of King Saud University - Engineering Sciences, 32(3), 211-218.
• Khani, A.R., Vilcu, A., Uddini, M.D.S., & Ungureanu, F. (2015). A competent algorithm to find the initial basic feasible solution of cost minimization transportation problem. Buletinul Institutului Politehnic Din Iaşi, Publicat de Universitatea Tehnica, Georghe Asachi Din Iaişi Tomul, LXI (LXV), Fasc. 2.
• Kirca, O., Satir, A. (1990). A heuristic for obtaining an initial solution for the transportation problem. Journal of the Operational Research Society, 41, 865–871.
• Lestari, S., Mustari,G.I., & Muttaqien, Z. (2023). Implementation of transportation methods in optimization of rubber product distribution costs in PT. IRC INOAC. Jurnal Teknik, 12(1), 26-33.
• Mallick, C., Bhoi, S.K., Singh, T., Swain, P., Ruskhan, B., Hussain, K., & Sahoo, K.S. (2023). Transportation problem solver for drug delivery in pharmaceutical companies using steppingstone method. International Journal of Intelligent Systems and Applications in Engineering,11(5), 343–352.
• Muhtarulloh, F., Meirista, M., & Cahyandari, R. (2022). Penyelesaian masalah transportasi menggunakan metode Sumathi-Sathiya dan metode pendekatan Karagul-Sahin (KSAM). Jurnal Eureka Matika, 10(1), 43-52.
• Mutlu, Ö, Karagül, K., & Şahin, Y. (2022). Avoid maximum cost method for determining the initial basic feasible solution of the transportation problem. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 28(4), 569-576.
• Sarhani, M., Voß, Ma., & Jovanovic, R. (2022). Initialization of metaheuristics: comprehensive review, critical analysis, and research directions. International Transactions in Operational Research, 30(6), 3361-3397. https://doi.org/10.1111/itor.13237
• Shivani, R.D. (2023a). Solving non-linear fixed-charge transportation problems using nature inspired non-linear particle swarm optimization algorithm. Applied Soft Computing, 146, https://doi.org/10.1016/j.asoc.2023.110699
• Shivani, R.D. (2023b). A method to solve fractional transportation problems with rough interval parameters. In Kumar, R., Verma, A.K., Sharma, T.K., Verma, O.P., Sharma, S. (Eds.), Soft Computing: Theories and Applications. Lecture Notes in Networks and Systems, (Vol. 627). Springer. https://doi.org/10.1007/978-981-19-9858-4_59
• Shivani, R.D., Ebrahimnejad, A. (2023a). On solving fully rough multi-objective fractional transportation problem: development and prospects. Computational and Applied Mathematics, 42, 266. https://doi.org/10.1007/s40314-023-02400-z
• Shivani, R.D., Ebrahimnrjad, A. (2023b). An approach for unbalanced fully rough interval transportation problem. Hacettepe Journal of Mathematics and Statistics, 52(5), 1408-1424. https://doi.org/10.15672/hujms.980108
• Szkutnik-Rogoz, J., Malachowski, J. (2023). Optimization programming tools supporting supply chain management. Bulletin of The Polish Academy of Sciences Technical Sciences, 71(3). https://doi.org/10.24425/bpasts.2023.145570
• Tarigan, M.L., Tastrawati, N. K. T., & Utari, I. A. P. A. (2023). Optimisasi biaya transportasi menggunakan metode stepping stone dengan solusi awal TOC-SUM approach dan KSAM. E-Jurnal Matematika, 12(1), 77-86. https://doi.org/10.24843/MTK.2023.v12.i01.p403
• Yılmaz Soydan, N.T., Çilingirtürk, A. & Can, T. (2023). Simulation for appropriate mean selection for Can's approximation method in transportation models. Manisa Celal Bayar Üniversitesi Sosyal Bilimler Dergisi, 21(1), 189-200. https://doi.org/10.18026/cbayarsos.1117589
• Yousefi, K., Afshari, A.J., & Hajiaghaei-Keshteli, M. (2017). Solving the fixed-charge transportation problem by new heuristic approach. Journal of Optimization in Industrial Engineering, 12(1), 41-52. https://doi.org/10.22094/joie.2017.738.1469
• Yousefi, K.J., Afshari, A., & Hajiaghaei-Keshteli, M. (2018). Fixed-charge transportation problem with discount. Journal of Industrial and Production Engineering, 35(7), 444-470.