A New Algorithm for Reaching an Optimal Solution to a Nonlinear Transportation Problem

J. Opara¹ , P.A. Esemokumo² , R. Bekesuoyeibo³

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.2 , pp.12-16, Apr-2022

Online published on Apr 30, 2022

Copyright © J. Opara, P.A. Esemokumo, R. Bekesuoyeibo . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The study was able to develop a technique to solve optimization transportation problems with nonlinear separable quadratic objective function with linear constraints. Transforming a nonlinear to linear approximation is not a new concept, but when it is to be employed, it starts with a large number of breakpoints for reason of solution accuracy. The algorithm employed only two breakpoints and also maintained accuracy of the solution. A numerical example was solved to demonstrate the effectiveness of the developed algorithm together with the time of execution. A Wolfram Mathematica Code for the Original Problem and that of the self developed algorithm was written with the time of execution and it was discovered that both of them gave the same optimal solution, but the time of execution (0.0312) for the self developed algorithm was far less than the time of execution (145.487) for the solution of the original problem using a system with 32 bit operating system, 2.00GB of RAM and processor Intel (R) (1.66GHz). Further investigation observed that the self developed algorithm can handle a higher number of variables and constraints with lesser time of execution, compared to the nonlinear.

Key-Words / Index Term :
Nonlinear Transportation Problem, Optimal Solution, Separable Quadratic Objective Function, Maclaurin’s series expansion, Dichotomous Breakpoints

References :
[1] F. L. Hitchcock, “The distribution of a product from several sources to numerous localities,”. Journal of Mathematical and Physics, Vol.20, Issue.3, pp. 224-230, 1941.
[2] S.C. Inyama, “Operation Research: Introduction,” Supreme Publisher, Nigeria, pp. 226-232, 2007.
[3] J. Opara, C. J. Ogbonna, S. O. Ihekuna, C. C. Ogbonna, “Proposed Piecewise Linear Approximation For Solving Nonlinear Transportation Problems,”. International Journal of Mathematics Trends and Technology, Vol.4, Issue.3, pp. 135-141, 2019.
[4] S. S. Dey, A. Gupte, “Analysis of MILP techniques for the pooling problem,”. Operations Research, Vol.63, Issue.2, 412-427, 2015.
[5] L. A. Wolsey, G. L. Nemhauser, “Integer and combinatorial optimization,”. John Wiley & Sons, USA, pp. 528–536, 1999.
[6] J. Opara, P.A. Esemokumo, R. Bekesuoyeibo, “Reaching an Optimal Solution to a Nonlinear Programming Problem Involving a Separable Quadratic Objective Function,” In the Proceedings of the 2022 FNAS Conference on Scientific Innovation, Nigeria, pp. 121-132, 2022.
[7] S. M. Abdul-Salam, “Transportation with volume discount - a case study of a logistic operator in Ghana,” Journal of Transport Literature, Vol.8, Issue.2, 7-37, 2014.
[8] D. D. Ekezie, J. Opara, “The Application of Transportation Algorithm with Volume Discount on Distribution Cost,” Journal of Emerging Trends in Engineering and Applied Sciences, Vol.4, Issue.2, 258 –272, 2013.