SOLUTION TO NONLINEAR TRANSPORTATION PROBLEM
Abstract
This study focused on solution to nonlinear transportation problem using Unilever Nigeria Plc as case
study. This study aimed at solving transportation problem with volume discount on quantity of goods
transported which is a non-linear transportation problem. This study applied KKT optimality technique
to solve the company’s problem. Using KKT optimality algorithm, with data from a Nigerian
company, it was observed that the optimal solution that gave minimum achievable cost of supply was
achieved for the two numerical examples. In the first practical example solved, the nonlinear
transportation problem was optimal at iteration two by using Least Cost Method (LCM) to obtain the
initial basic feasible solution, while it was optimal at iteration three by using Vogel Approximation
Method (VAM) and North West Corner Method (NWCM) to obtain the initial basic feasible solution.
In the second example, the nonlinear transportation problem was optimal at iterations six, four and
three by using NWCM, VAM and LCM respectively to obtain the initial basic feasible solution. The
LCM in this study has proven more efficient (close to optimality) than the other two techniques. This
study therefore suggests that future researchers should propose a nonlinear transportation technique
that will produce a lesser iteration to optimality than the existing once encountered in this study.
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