Abstract
Blending problem is one of production problems that can be formulated to a linear programming model and solved by the simplex method, which begins with choosing an initial basic variables set. In the blending problem, it is not easy in practice to choose basic variables since the original point is not a feasible point. Therefore, artificial variables are added in order to get the origin point as the initial basic feasible solution. This addition brings to increase the size of the problem. In this paper, we present a new initial basis without adding artificial variables. The first step of the proposed technique is to rewrite the blending problem. Then, it is divided into sub-problems depend on the number of products. The variable associated with the maximum profit, together with all slack variables of each sub-problem are selected to be a basic variable. This selection can guarantee that the dual feasible solution is obtained. Therefore, artificial variables are not required.
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Acknowledgment
This work was supported by Thammasat University Research Unit in Fixed Points and Optimization.
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Boonmalert, C., Boonperm, Aa., Sintunavarat, W. (2021). A New Initial Basis for Solving the Blending Problem Without Using Artificial Variables. In: Vasant, P., Zelinka, I., Weber, GW. (eds) Intelligent Computing and Optimization. ICO 2020. Advances in Intelligent Systems and Computing, vol 1324. Springer, Cham. https://doi.org/10.1007/978-3-030-68154-8_108
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DOI: https://doi.org/10.1007/978-3-030-68154-8_108
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