A New And Efficient Proposed Approach For
Optimizing The Initial Basic Feasible Solution
Of A Linear Transportation Problem

Opara Jude; Oruh Ben Ifeanyichukwu; Ihekuna Stephen; O.; Okenwe Idochi

doi:https://doi.org/10.14445/22315373/IJMTT-V65I6P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P517

A New And Efficient Proposed Approach For Optimizing The Initial Basic Feasible Solution Of A Linear Transportation Problem

Opara Jude, Oruh Ben Ifeanyichukwu, Ihekuna Stephen, O., Okenwe Idochi

Citation :

Opara Jude, Oruh Ben Ifeanyichukwu, Ihekuna Stephen, O., Okenwe Idochi, "A New And Efficient Proposed Approach For Optimizing The Initial Basic Feasible Solution Of A Linear Transportation Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 104-118, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P517

Abstract

In this research, a new approach (Loop Product Difference) for optimizing the initial basic feasible solution of a balanced transportation problem is proposed. The proposed technique has been tested and proven efficient by solving several number of cost minimizing transportation problems and it was discovered that the method gives the same result as that of optimal solution obtained by using MODI/Stepping stone methods. Conclusively, it can be said that proposed technique is easy to adopt and close to optimality if employed with the Inverse Coefficient of Variation Method as an improved technique of obtaining Initial Basic Feasible Solution.

Keywords

Transportation Problem, Inverse Coefficient of Variation Method, Initial Basic Feasible Solution, Optimal Solution, Loop Product Difference.

References

[1] Abul, K. A., and Mosharraf, H. (2018). An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Mathematics Letters. Vol. 4, No. 1, 2018, pp. 1-5. doi: 10.11648/j.ml. 20180401.11
[2] Amaravathy, A., Thiagarajan, K. and Vimala, S. (2018). Optimal Solution of OFSTF, MDMA Methods with Existing Methods Comparison. International Journal of Pure and Applied Mathematics. Volume 119 No. 10 2018, 989-1000.
[3] Deshabrata, R. M., Sankar, K. R., Mahendra, P.B. (2013). Multi-choice stochastic transportation problem involving extreme value distribution. 37(4).
[4] Gurupada, M., Sankar, K. R., and José, L. V. (2016). Multi-Objective Transportation Problem With Cost Reliability Under Uncertain Environment. International Journal of Computational Intelligence Systems, 9(5).
[5] Hakim, M.A. (2012). An Alternative Method to Find Initial Basic Feasible Solution of a Transportation Problem, Annals of Pure and Applied Mathematics, Vol. 1, No. 2, 2012, 203-209.
[6] Opara, J., Oruh, B. I., Iheagwara, A. I., and Esemokumo, P. A. (2017). A New and Efficient Proposed Approach to Find Initial Basic Feasible Solution of a Transportation Problem. American Journal of Applied Mathematics and Statistics, 2017, Vol. 5, No. 2.
[7] Roy, S.K. (2016). Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply J. Operations Research of China (2016) 4(2), 193-204, DOI 10.1007/s40305-016-0125-3
[8] Roy, S.K., Maity, G. & Weber, G.W. (2017). Multi-objective two-stage grey transportation problem using utility function with goals Cent Eur. J. Oper. Res. (2017) 25: 417.
[9] Sankar, K.R., Gurupada, M., Gerhard, W.W., Sirma, Z.A.G. (2016). Conic Scalarization Approach to solve Multi-choice Multi-objective Transportation Problem with interval goal. Annals of Operations Research · August 2016 DOI: 10.1007/s10479-016-2283-4.
[10] Sudipta, M. & Sankar, K. R. (2014). Solving Single-Sink, Fixed-Charge, Multi-Objective, Multi-Index Stochastic Transportation Problem. American Journal of Mathematical and Management Sciences. 33(4).