Propuesta de un modelo de programación lineal para una empresa productora de componentes de acristalamiento automotriz en Quito – Ecuador

Abstract

This thesis presents a linear programming model designed to optimize the production process of InnovaGlass, a company that manufactures automotive glazing components in Quito, Ecuador. The research stems from operational inefficiencies observed at the plant, such as poor machinery layout, inaccurate standard times for subprocesses, and inefficient material flow. These issues result in financial losses and reduced competitiveness in the domestic market. The primary objective was to develop a linear programming optimization model to improve operational efficiency and resource management in the production of three products: automotive windows, rear windows, and oven doors. To achieve this, production times were recorded for each process stage—cutting and sizing, polishing, washing, drilling, painting, and oven treatment—while installed capacity was quantified and data on costs and monthly demand were collected. The mathematical model was formulated with an objective function aimed at maximizing revenue, subject to constraints regarding processing time, minimum demand, and product mix combinations. The model was solved using three methods—the graphical method, the analytical Simplex method, and Microsoft Excel's Solver tool—all of which yielded the same optimal values, thereby validating the model's formulation. The results indicated an optimal monthly production of 3,240 windows, 810 rear windows, and 750 oven doors, resulting in a projected maximum monthly revenue of Z = $105,570 USD. Since the objective function coefficients correspond to unit selling prices, the resulting figure represents total sales revenue rather than the period's profit (which would require deducting associated production costs); therefore, the calculated value ($105,570 USD) represents the projected gross revenue. Sensitivity analysis revealed that the washing process is the primary bottleneck, with a shadow price of $12.2 per additional unit of capacity, identifying it as the best investment opportunity to increase profitability. The other processes have a margin of up to 5,346 available minutes, meaning there is idle capacity that can be leveraged to increase 3 production without incurring financial risk