Proposed Piecewise Linear Approximation
For Solving Nonlinear Transportation
Problems

Opara Jude; Ogbonna Chukwudi; J.; Ihekuna Stephen; O.; Ogbonna Christopher; C.

doi:https://doi.org/10.14445/22315373/IJMTT-V65I6P519

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P519

Proposed Piecewise Linear Approximation For Solving Nonlinear Transportation Problems

Opara Jude, Ogbonna Chukwudi, J., Ihekuna Stephen, O., Ogbonna Christopher, C.

Citation :

Opara Jude, Ogbonna Chukwudi, J., Ihekuna Stephen, O., Ogbonna Christopher, C., "Proposed Piecewise Linear Approximation For Solving Nonlinear Transportation Problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 135-141, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P519

Abstract

The study has developed an algorithm that can be employed to tackle optimization problems with nonlinear transportation problem. The algorithm used two breakpoints. After transforming the nonlinear objective function to linear function, Wolfram Mathematica was employed to get the optimal solution. The two problems solved in this study showed that the proposed algorithm converged faster than solving the original problem directly via Wolfram Mathematica, though with the same optimal solution. In the study, a program code via Wolfram Mathematica for evaluating a nonlinear transportation problem with multiple linear variables and constraints of different sizes up to 70,000 variables and 35,000 constraints was written using the proposed technique. The study demonstrated the effectiveness of the proposed approach using the written program code as compared to the written program code for the original problem as it converged faster via the time of execution.

Keywords

Transportation Algorithm, Nonlinear Transportation Problem, Piecewise Linear Approximation, Total Minimum Transportation Cost.

References

[1] Abdul-Salam, S.M. (2014). Transportation with volume discount. Journal of Transport Literature. Vol. 8, N. 2, pp. 7-37, Apr. 2014.
[2] Ekezie, D.D and Opara, J. (2013). The Application of Transportation Algorithm with Volume Discount on Distribution Cost in Port Harcourt Flour Mills. Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS). 4(2): 258-272.
[3] Opara, J., Iheagwara, A. I., and Nwobi, A.C. (2015). Nonlinear Transportation Problems‟ Algorithm (A Case Study of the Nigerian Bottling Company Ltd Owerri Plant). International Journal of Research, Volume 02 Issue 02 February 2015.
[4] Osuji, G. A., Ogbonna, C. J., and Opara, J. (2014). “Transportation Algorithm with Volume Discount on Distribution Cost (A Case Study of the Nigerian Bottling Company Plc Owerri Plant).” American Journal of Applied Mathematics and Statistics, vol. 2, no. 5 (2014): 318-323. doi: 10.12691/ajams-2-5-4.