Application of stepping stone method for an optimal solution to a transportation problem

Abstract

The purpose of this study was to determine the optimal routes to apply in the distribution of Big Treat products so as to improve the profit obtained by the company. In this work, a transportation problem of the distribution of Big Treat bread (Happy Chef) was solved using the transportation tableau approach. The initial basic feasible solution was obtained using the Vogel’s approximation method and the stepping stone method was used to test and solve for optimality. From the data which was used to solve the six weeks distribution of bread to respective districts, the optimal cost of transportation obtained is ₦10,294,850 and the result was confirmed using TORA, a statistical software. The optimal allocations are;

X₁₁ = 9950
X₁₃ = 12600
X₁₄ = 10283
X₂₁ = 8033
X₂₂ = 2178
X₂₅ = 4500

Keywords: Optimal Solution, Stepping Stone Method, Feasible Solution, Slack Variable, Vogel’s Approximation Method