A Novel Approach Algorithm for Determining the Initial Basic Feasible Solution for Transportation Problems
Keywords:Balance and Unbalance Transportation Problem, Initial Basic Feasible Solution, Optimal Solution
In optimization, the transportation problem is of utmost significance. The fundamental idea for solving the transportation problem is to develop methods that lower the overall cost between the source and the destination. Numerous research techniques are given in the literature as solutions to transportation problems. The majority of strategies focus on locating the initial basic, feasible solution to the transportation problem, while some techniques concentrate on locating an optimal solution. To find an initial, basic, feasible solution, Vogel's approximation, the least-cost method, the northwest method, and other methods are used. The Modified Distribution Method and the Stepping Stone Method are gaining acceptance as the optimal solution to the transportation problem. In this research study, a model approach to figuring out the basic, feasible solution for transportation problems with balanced and unbalanced components is proposed based on the average unit cost value of columns and rows. A new table is created using the unit cost values and average unit cost values in the columns and rows and compared to the transportation problem to solve the problem by balancing demand and supply. The proposed methodology is effortless, easy to understand, and simple to use. Comparatively speaking, the algorithmic technique suggested by this work is less complex than the well-known meta-heuristic algorithms in the literature. Finally, provide a case study to demonstrate the proposed approach.
Abdelati, M. H., Khalil, M. I., Abdelgawwad, K. A., & Rabie, M. (2021). A case study of reducing the total wasted time for the bus movement of Public Transportation Authority in Cairo. SVU-International Journal of Engineering Sciences and Applications, 2(2), 82–87.
Ahmad, Q.S. (2020). A new approach for finding the initial solution of the unbalanced transportation problem. Asian Journal of Business and Management, 8 (4), 49-51.
Amaliah, B., Fatichah, C., & Suryani, E. (2020). A new heuristic method of finding the initial basic feasible solution to solve the transportation problem. Journal of King Saud University - Computer and Information Sciences. 34 (5), 2298-2307.
Babu, Md., A., Ahmmed, Md.,M, Salim, Z.R., Babu, Md., S., & Hoque, M.A. (2020). A brief overview of the classical transportation problem. Journal of Xi'an University of Architecture & Technology, 12 (4), 3425-3438.
Chandrakala, P. (2021). A comparative analysis for the solution of unbalanced transportation model by various methods. International Journal of Science and Research, 10 (2), 2319–7064.
Ekanayake E. M. U. S. B, Daundasekara W. B. & Perara S. P. C. (2021). Solution of a Transportation Problem using Bipartite Graph. Global Journal of Science Frontier Research, 21(1), 55.
Ekanayake E. M. U. S. B., Perera S. P. C., Daundasekara W. B., Juman Z. A. M. S. (2021). An effective alternative new approach in solving transportation problems. American Journal of Electrical And Computer Engineering, 5 (1), 1-8.
Ekanayake, E. M. U. S. B., Perera, S. P. C., Daundasekara, W. B., & Juman, Z. A. M. S. (2020). A Modified Ant Colony Optimization Algorithm for Solving a Transportation Problem. Journal of Advances in Mathematics and Computer Science, 35 (5), 83–101.
Febriani, A. (2021). Analysis of Transportation Method in Optimization of Distribution Cost Using Stepping Stone Method and Modified Distribution. Journal of Mathematics Technology and Education, 1(1), 103–112.
Geetha, T., & Anandhi, N. (2018). Method for solving unbalanced transportation problems using standard deviations. International Journal of Pure and Applied Mathematics, 119 (16), 4971–4989.
Gill, B., Solangi, M.A., Qureshi, S.A. (2020). An improved algorithm for optimal solution of unbalanced transportation problems. (2020). Mathematical Theory and Modeling. 10 (8), 8-15.
Hitchcock, f. l. (1941). The distribution of a product from several sources to numerous localities.
Hossain, Md. M., & Ahmed, M. M. (2020). A comparative study of initial basic feasible solution by a least cost mean method (lcmm) of transportation problem. American journal of operations research, 10(04), 122–131.
Kawser, R. (2016). New analytical methods for finding optimal solution of a transportation problems. Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh.
Latunde, Tolulope, Joseph Oluwaseun Richard, Opeyemi Odunayo Esan, and Damilola Deborah Dare. (2020). Optimal feasible solutions to a road freight transportation problem. Malaysian Journal of Computing, 5(1), 456–68.
Mallia, B., Das, M., & Das, C. (2021). Fundamentals of Transportation Problem. International Journal of Engineering and Advanced Technology, 10 (5), 90–103.
Mathirajan, M., & Meenakshi, B. (2004). Experimental analysis of some variants of Vogel's approximation method. Asia-Pacific Journal of Operational Research, 21 (4), 447-462.
Mhlanga, A., Nduna, I. S., Matarise, F., Machisvo, A., & Mhlanga, A. (2014). Innovative application of Dantzig’s North-West Corner Rule to solve a transportation problem. International Journal of Education and Research, 2 (2), 1-12.
Mishra, S. (2017). Solving transportation problem by various methods and their comparison. International Journal of Mathematics Trends and Technology, 44 (4), 270-275.
Parish, T. R. (1994). Case Studies of Market Research for Three Transportation Communication Products. Economic Analysis Division. Cambridge, Massachusetts.
Prasad, A. K., & singh, D. R. (2020). Modified least cost method for solving transportation problem. Proceedings on engineering sciences, 2(3), 269–280.
Seethalakshmy, A., & Srinivasan, N. (2018). The literature review for assignment and transportation problems. International journal of advanced research, 6(4), 1343–1349.
Shaikh, M. M., Soomro, A. S., Kalhoro, H. B. (2020). Comprehensive database of test transportation problems (balanced and unbalanced). Mendeley Data.
Sheth, I., Chhabra, G., Agarwal, G., Raka, H., & Saraf, I. (2021). Application of Operations Research in Steel Industry. International Journal of Innovative Science and Research Technology, 6 (10), 252-258.
Sridhar, A., & Pitchai, R. A. (2018). New approach to solve unbalanced transportation problems using least cost method, 5 (9), 397-403.
Subhikshaa, K., Arumugam, R. & Rajathi, M. (2019). A study on applications of transportation problem to minimize cost in various pharmacies. International Journal of Research and Analytical Reviews. 6(2), 507-512.
Sulaiman, A.S.A. (2019). Proposed methods for finding the basic acceptable solution for the transportation problems. Iraqi Journal of Statistical Science. (30), 73-84.
Sultana, M., Shohan, S., & Sufian, F. (2014). Aggregate Planning Using Transportation Method: A Case Study In Cable Industry. International Journal of Managing Value and Supply Chains, 5(3), 19–35.
Venkatesh, A. Manoj, A.B. (2020). A Mathematical Model for Diet control Using Ranking of Decagonal Fuzzy Number. Journal of Xi'an University of Architecture & Technology, 12 (7), 945-951.
How to Cite
Copyright (c) 2022 E.M.D.B. Ekanayake, E. M. U. S. B. Ekanayake
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.