Paradox Algorithm in Application of a Linear Transportation Problem

Osuji George A.¹, Opara Jude², Nwobi Anderson C.³, Onyeze Vitus² and Iheagwara Andrew I.⁴

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

²Department of Statistics, Imo State University, Owerri Nigeria

³Department of Statistics, Abia State Polytechnic, Aba Nigeria

⁴Department of Planning, Research and Statistics, Ministry of Petroleum and Environment Owerri Imo State Nigeria

Cite this paper:
Osuji George A., Opara Jude, Nwobi Anderson C., Onyeze Vitus and Iheagwara Andrew I.. Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics. 2014; 2(1):10-15. doi: 10.12691/ajams-2-1-3

Abstract

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.

Keywords:
transportation paradox paradoxical range of flow transportation problem linear programming paradoxical pair VAM

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