Using a Linear Programming Model to Minimize Costs and Improve Production Quality in Industrial Enterprises

Abstract

In this study, linear programming was used to optimize the inputs for product manufacturing, cement production was chosen as a case study. The cement industry faces a continuous challenge of balancing the reduction of production costs, where the cost of raw materials constitutes a significant portion of these costs, with the necessary quality of the product. The linear programming model was applied as a scientific tool to find the optimal raw material mix that achieves the lowest possible cost while ensuring compliance with all technical requirements and limitations. To achieve this objective, a mathematical model for linear programming was built using the Simplex Method with actual data from the Souk El Khemis Msehel cement plant. The solution was implemented using Excel Solver due to its ability to handle multivariable linear models and constraints. The study and analysis were conducted for the production of a standard batch weighing 100 tons. The results demonstrated the model's success in finding optimal and low-cost solutions. The optimal raw material mix consisted of 82,448 tons of limestone, 11,531 tons of clay, 0.155 tons of iron ore, and 5,866 tons of sand, at a cost of 767 Libyan dinars (7.67 dinars per ton). This optimal solution met all the key requirements. The study concluded that linear programming is not only a cost optimization tool, but a strategic analytical tool capable of assessing production feasibility and identifying operational risks related to raw material quality before the production process begins. The study provided a quantitative basis for factory management to make more accurate and reliable decisions in production processes and procurement management. The research demonstrated that the linear programming model serves a dual purpose: it is an optimization tool for reducing costs and a diagnostic tool for identifying operational and production constraints.