American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
American Journal of Applied Mathematics and Statistics. 2014, 2(5), 318-323
DOI: 10.12691/ajams-2-5-4
Open AccessArticle

Transportation Algorithm with Volume Discount on Distribution Cost (A Case Study of the Nigerian Bottling Company Plc Owerri Plant)


1Department of Statistics, Nnamdi Azikiwe University PMB 5025, Awka Anambra State Nigeria

2Department of Statistics, Federal University of Technology Owerri Nigeria PMB 1526, Owerri Nigeria

3Department of Statistics, Imo State University PMB 2000, Owerri Nigeria

Pub. Date: September 22, 2014

Cite this paper:
OSUJI GEORGE A., OGBONNA CHUKWUDI J. and OPARA JUDE. 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. 2014; 2(5):318-323. doi: 10.12691/ajams-2-5-4


This study is focused on the Application of Transportation Algorithm with volume Discount on distribution cost using Nigerian Bottling Company Plc Owerri Plant. This paper is intended to determine the quantity of Fanta (in crates), Coke (in crates) and Sprite (also in crates) that the Company should distribute in a month in order to minimize transportation cost and maximize profit. A problem of this nature was identified as a Nonlinear Transportation Problem (NTP), formulated in mathematical terms and solved by the Karush-Kuhn-Tucker (KKT) optimality condition for the NTP. A statistical software package was used to obtain the initial basic feasible solution using the Least Cost Method. Thus, analysis revealed that the optimal solution that gave minimum achievable cost of supply was the supply of 5000 crates of Fanta and 6000 crates of the same product to Umuahia market zone and Afikpo respectively. 7000 crates of Coke, 9000 crates and 1000 crates of the same product should be supplied to Orlu, Mbaise, and Afikpo market zones respectively. 6000, and 5000 crates of Sprite should be allocated to Mbaise and Umuahia market zones respectively, at a total cost of N377, 000.

Karush-Kuhn-Tucker nonlinear transportation volume discount concave cost

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Caputo, A.C. (2006). A genetic approach for freight transportation planning, Industrial Management and Data Systems, Vol. 106 No. 5.
[2]  Frank, S. J. (1970). A Decomposition Algorithm for multifacility production transportation problem with nonlinear production costs, Econometrics, Vol. 38 No. 3.
[3]  Kidist, T. (2007). Nonlinear Transportation Problems. A paper submitted to the department of mathematics of Addis Asaba University.
[4]  Kikuchi, S.A. (2000). A method to defuzzify the number: transportation problem application, Fuzzy Sets and Systems, vol. 116.
[5]  Lau, H.C.W.; Chan, T.M.; Tsui, W.T.; Chan, F.T.S.; HO, G.T.S and Choy K.L. (2009). A fuzzy guided multi-objective evolutionary algorithm model for solving Transportation problem. Expert System with Applications: An International Journal. Vol. 36.
[6]  Lohgaonkar, M.H. and Bajaj, V.H. (2010). Fuzzy approach to solve multi-objective capacitated transportation problem, International Journal of Bioinformatics Research. Vol. 2.
[7]  Reep, J. and Leaengood S. (June 2002). Transportation problem: A Special Case of Linear Programming Problems, Operations Research Society of America.
[8]  Shetty, C.M. (1959). A Solution to the Transportation Problem with Nonlinear Costs," Operation Research. Vol. 7. No. 5.
[9]  Simons, A.R. (2006). Nonlinear Programming for Operation research, Society for Industrial and Applied Mathematics, Vol. 10, No. 1.
[10]  Mohamed, A. (1983). An iterative procedure for solving the incapacitated production distribution problem under concave cost function, International Journal of operations and management, Vol. 16. No. 3.
[11]  Zangiabadi, M. and Maleki, H.R. (2007). Fuzzy goal programming for multi-objective transportation problems. Applied Mathematics and Computation, vol. 24, pp. 449-460.