Main Article Content
The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following License
CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
- Abdelati, M. H., Khalil, M. I., Abdelgawwad, K. A. and Rabie, M. (2020). Alternative Algorithms for Solving Classical Transportation Problems. Journal of Advanced Engineering Trends, Vol. 39, No. 1, pp. 13-24, ISSN: 2682 2091.
- Ackora Prah, J., Acheson, V., Barnes, B., Takyi, I., Owusu-Ansah, E. (2022). A 2-Phase Method for Solving Transportation Problems with Prohibited Routes. Pakistan Journal of Statistics and Operation Research,18(3), 749-758. https://doi.org/10.18187/pjsor.v18i3.3911
- Amaliah, B., Fatichah, C., Suryani, E. (2019) Total opportunity cost matrix- Minimal total: A new approach to determine initial basic feasible solution of a transportation problem, Egyptian Informatics Journal, Vol. 20, No. 2, 2019, Pages 131-141, ISSN 1110-8665, htpps://doi.org/10.1016/j.eij.2019.01.002.
- Charnes, A. and Cooper, W. W. (1954). The stepping stone method of explaining linear programming calculations in transportation problems, Management Science 1, 49-69.
- Dantzig, G. B. (1951). Application of the simplex method to a transportation problem, In Activity Analysis of Production and Allocation (Edited by T.C. Koopmans), John Wiley and Sons, New York.
- Hasan, M., K. (2012). Direct Methods for Finding Optimal Solution of a Transportation Problem are not Always Reliable. International Refereed Journal of Engineering and Science (IRJES), ISSN (Online) 2319- 183X (Print) 2319-1821, Vol. 1, No. 2 (October 2012), PP.46-52.
- Hanif, M. and Rafi, F., S. (2018). A New Method for Optimal Solutions of Transportation Problems in LPP. Journal of Mathematics Research; Vol. 10, No. 5; ISSN 1916-9795, E-ISSN 1916-9809, Published by Canadian Center of Science and Education.
- Hitchcock, F.L. (1941). The Distribution of a Product from Several Sources to Numerous Localities, MIT Journal of Mathematics and Physics 20:224–230 MR0004469.
- Hosseini, E. (2017). Three new methods to find initial basic feasible solution of transportation problems. Applied Mathematical Sciences, 11(37), 1803-1814.
- Kamal, M., Alarjani, A., Haq, A., Yusufi, F. N. K., and Ali, I. (2021). Multi-Objective Transportation Problem under Type-2 Trapezoidal Fuzzy Numbers with Parameters Estimation and Goodness of Fit. Transport, 36(4), 317-338. htpps://doi.org/10.3846/transport.2021.15649.
- Kantorovich, L. V. (1939). Mathematical Methods of Organizing and Planning Production. Management Science 6 (4) 366-422 htpps://doi.org/10.1287/mnsc.6.4.366.
- Mishra, S. (2017). Solving Transportation Problem by Various Methods and Their Comaprison. International Journal of Mathematics Trends and Technology, 44, 270-275.
- Monge, G. (1781). Dissertation on the theory of cuttings and embankments. History of the Royal Academy of Sciences of Paris, with the Memories of Mathematics and Physics for the same year, pages 666–704.
- Opara J., Oruh B. I., Iheagwara A. I. and Esemokumo P. A. (2017). “A New and Efficient Proposed Ap- proach to Find Initial Basic Feasible Solution of a Transportation Problem.” American Journal of Applied Mathematics and Statistics, Vol. 5, No. 2: 54-61. doi: 10.12691/ajams-5-2-3.
- Prasad, A. and Singh, D. (2020). Modified Least Cost Method for Solving Transportation Problem. Proceedings on Engineering Sciences. 2. 269-280.
- Ravi, K., R., Radha G. and Karthiyayini O. (2018). A New Approach to Find The Initial Basic feasible Solution of A Transportation Problem. International Journal of Research - Granthaalayah, 6(5), 321-325. htpps://doi.org/10.29121/granthaalayah.v6.i5.2018.1457.
- Reinfeld, N. V., and Vogel, W. R. (1958). Mathematical Programming, Prentice-Hall, New Jersey.
- Saleh, Z. and Shiker, M. (2022). A New VAM Modification for Finding an IBFS for Transportation Problems. 7(2), 984-990.
- Shaikh, M., S., R., Shah, S., F. and Memon, Z. (2018). An Improved Algorithm to Solve Transportation Problems for Optimal Solution, Mathematical Theory and Modeling, Vol.8, No.8, ISSN 2224-5804 (Paper), ISSN 2225-0522 (Online).
- Taha. H.A. (2004). Operations Research- Introduction, Prentice Hall of India (PVT), New Delhi.
- Sharma, J. K. (2010). Quantitative Methods: Theory and Applications. Macmillan Publishers India. ISBN 10: 0230-32871-7.
- Taylor, B. W. III (1999) Introduction to Management Science, 6th ed., Prentice Hall Inc., New Jersey.
- Yeola, M., C. and Jahav, V., A. (2016). Solving Multi-Objective Transportation Problem Using Fuzzy Pro-
- gramming Technique-Parallel Method. International Journal of Recent Scientific Research, Vol. 7, No. 1, pp. 8455-8457.
- Zangiabadi, M., and Rabie, T. (2012). A New Model for Transportation Problem with Qualitative Data, Iranian Journal of Operations Research Vol. 3, No. 2, 2012, pp. 33-46.