Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2 1 2014 01 05 Paradox Algorithm in Application of a Linear Transportation Problem 10 15 EN Osuji George A. Department of Statistics, Nnamdi Azikiwe University, Awka Anambra State Nigeria Opara Jude Nwobi Anderson C. Onyeze Vitus Iheagwara Andrew I. AJAMS2014213 10.12691/ajams-2-1-3 2013 12 14 2013 12 23 2014 01 05 Paradox seldom occurs in a linear transportation problem, but it is related to the classical transportation problem. For specific reasons of this problem, an increase in the quantity of goods or number of passengers (as used in this paper) to be transported may lead to a decrease in the optimal total transportation cost. Two numerical examples were used for the study. In this paper, an efficient algorithm for solving a linear programming problem was explicitly discussed, and it was concluded that paradox does not exist in the first set of data, while paradox exists in the second set of data. The Vogel's Approximation Method (VAM) was used to obtain the initial basic feasible solution via the Statistical Software Package known as TORA. The first set of data revealed that paradox does not exist, while the second set of data showed that paradox exists. The method however gives a step by step development of the solution procedure for finding all the paradoxical pair in the second set of data.