Briley Cosmetics Case Paper (Partial Write-Up)

Briley Cosmetics Case Paper (partial write up)

Based on the provided data, the value of the objective function, which represents the total production and subcontracting costs, was obtained through a detailed linear programming optimization model. This model considers various variables such as the number of cartons to be produced in each shift for different types of creams (face, body, hand), alongside subcontracting figures. The goal was to minimize the total costs associated with production and subcontracting while satisfying multiple constraints like demand requirements, labor hours, and raw material availability. By inputting these constraints into the optimization algorithm, the model generated an optimal production schedule which resulted in a total cost of approximately $1,066,546, as indicated in the results. This total reflects the sum of costs incurred from manufacturing, labor, raw materials, and subcontracting, adjusted to meet the specified demand and resource constraints effectively.

In determining why certain resources such as labor hours and raw materials are completely utilized, the model's output shows that the available labor hours at Stage 1 in the first shift are entirely consumed, as the optimal schedule has allocated enough production to exhaust the shift’s capacity. Similarly, raw material B is also fully consumed in the process, signifying that the production plan maximizes the use of scarce resources to meet the demand efficiently. This complete utilization occurs because the optimization process seeks to minimize costs; thus, it prioritizes the use of these critical resources up to their maximum availability to avoid surplus or underutilized capacity, ultimately ensuring production costs are minimized while fulfilling demand constraints.

Paper For Above instruction

Briley Cosmetics has implemented a comprehensive linear programming approach to optimize their production scheduling for their three main product categories: face, body, and hand creams. The primary objective is to minimize the total costs associated with manufacturing and subcontracting while ensuring that product demands are met within the constraints of available labor hours and raw materials. The data provided includes the number of cartons to produce in different shifts, costs per unit, labor hours needed at each stage of production, and raw material availability. Through this mathematical model, the company can determine the optimal quantities to produce in each shift and whether to subcontract portions of production, ultimately achieving cost efficiency.

The model's results indicate that 10,000 cartons of face cream and 1,250 cartons of body cream should be subcontracted to an external vendor. The production scheduling specifies that labor hours at Stage 1 during the first shift are fully utilized, signifying that the labor capacity is a critical constraint influencing the production plan. Additionally, raw Material B supplies are exhausted in the process, which reflects the importance of raw material management in cost minimization. The optimal solution demonstrates a balance between internal production and subcontracting, ensuring demand fulfillment at the lowest possible total cost while respecting the constraints of labor hours and raw materials. This strategic approach helps Briley Cosmetics optimize resource utilization and contain production costs effectively.

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