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Calculate and analyze the model parameters including demand estimations for products S1, S2, and S3, as well as the optimization of production schedule considering resource constraints and sensitivity analysis, using regression models, linear programming, and classification tree methodology.

Paper For Above instruction

The process of developing a comprehensive model for production optimization involves multiple stages, beginning with the estimation of key parameters based on data analysis, progressing to demand forecasting, and culminating in resource allocation through linear programming. Furthermore, sensitivity analysis and quality classification provide critical insights into operational flexibility and product quality management, respectively. This paper systematically examines each component, emphasizing statistical modeling techniques and operational research tools essential for decision-making in manufacturing systems.

The initial step involves defining core model parameters such as demand, production costs, processing times, and resource availability. Values for these parameters are derived from empirical data—specifically, the production.csv file—which yields averages for machining, assembly, and finishing times, along with unit costs for each product type (S1, S2, S3). These parameters underpin the subsequent demand forecast, which is critical for efficient resource planning. By performing exploratory data analysis and plotting demand over time, linear trends were observed, warranting the employment of linear regression models to predict demands in the 53rd time period. The regression equations obtained—y = 459.5 + 3.4x for S1, y = 502.5 + 4x for S2, and y = 420 + 4x for S3—demonstrated high significance and fit (R-squared values approaching 1). Applying these models led to demand estimates of 640 units for S1, 715 units for S2, and 632 units for S3, respectively, which are pivotal for the planning process.

To translate these forecasts into an operational plan, a linear programming (LP) model was formulated with the objective of minimizing total production costs, incorporating constraints such as machine hours, assembly, finishing times, and the use of in-house versus outsourced production. Solving this LP model in Excel yielded an optimal schedule with a minimum cost of approximately $427,820. The produced unit quantities of S1, S2, and S3 balance in-house manufacturing and external procurement, adhering to resource limitations. The utilization of machine time (17,852 minutes), assembly (14,400 minutes), and finishing (13,685 minutes) was within the available hours, ensuring feasibility and efficiency.

Sensitivity analysis explored how variations in demand could impact overall costs. For instance, increasing demand for S1 by one unit results in an additional $185 in total production cost, illustrating the marginal cost implications of demand fluctuations. Conversely, a decrease in demand for S2 reduces costs by $228 per unit, emphasizing the importance of demand elasticity assessment. Of particular interest are potential resource adjustments; analyses indicated that the company would be willing to pay a maximum of $180 per hour for additional assembly time, while no additional costs are justified for extra machining or finishing times, reflecting the criticality of assembly capacity in the production process.

Lastly, the quality control process involved utilizing a classification tree generated via R’s rpart() function, trained on an 80% sample of data and tested on the remaining 20%. The decision rules—based on Test 2 and Test 3 metrics—accurately classified product batches into "POOR" and "GOOD" quality categories, with an impressive accuracy of over 99%. The classification rule "IF Test 2

In conclusion, integrating data-driven demand forecasting, linear programming for resource optimization, sensitivity analysis for operational flexibility, and classification models for quality management provides a comprehensive approach to manufacturing decision-making. The synergy of statistical analysis, operations research, and machine learning enhances the firm’s ability to meet customer demand efficiently, control costs, utilize resources effectively, and uphold high quality standards.

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