Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-02-118-4
DOI: https://dx.doi.org/10.15863/TAS.2023.02.118.4
Language: English
Citation: Opara, J., & Ojekudo, N. A. (2023). Reaching an optimal solution to a transportation problem involving a concave cost function. ISJ Theoretical & Applied Science, 02 (118), 17-28. Soi: http://s-o-i.org/1.1/TAS-02-118-4 Doi: https://dx.doi.org/10.15863/TAS.2023.02.118.4 |
Pages: 17-28
Published: 28.02.2023
Abstract: The work is on reaching an optimal solution to a transportation problem involving a concave cost function with specific objectives to develop a new approach for solving optimization problems of a transportation problem in a concave case; demonstrate the effectiveness of the new approach using real life examples from published works, and comparing the self developed approach with the existing method. One Least Cost Row Column Difference Method (OLCRCDM) was employed to obtain the initial basic feasible solution. The transportation concave simplex technique was modified for a better solution and its steps were clearly stated in this study. Four numerical examples were employed to demonstrate the effectiveness of the developed technique in this study. The results revealed that out of the four numerical problems, the existing Karush-Kuhn-Tucker (KKT) procedure of Modified Distribution (MODI) method could not produce optimality point in the first example with North West Corner Method (NWCM) and Vogel Approximation Method (VAM) as a means of obtaining the IBFS, but the self developed did using OLCRCDM to obtain the IBFS and it yielded an optimal value of N253,000 with an optimal solution as z12=13, z22=5, z23=8, z31=11, and z33=4. The remaining three examples were successfully solved with both the existing Karush-Kuhn-Tucker (KKT) procedure of MODI method and the new technique with optimal values of N377,000, GH? 236,000 and N509,000 respectively, but the new technique proved to be more efficient as it produced minimum number of iteration to optimality. The four problems were solved with Wolfram Mathematica and Anaconda Python programming softwares and the results agreed with the results obtained from the developed approach.
Key words: Concave Cost Function, OLCRCDM, Transportation Problem, Karush-Kuhn-Tucker, Optimal Solution, Proposed Algorithm.
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