Model Answer
0 min readIntroduction
Inventory management is a critical aspect of operations management, aiming to balance the costs associated with holding inventory against the costs of ordering or producing it. A key component of effective inventory control is determining the optimal production batch size, often represented by the Master Production Schedule (MPS). This schedule dictates the quantity of each product to be produced in a given period. Minimizing the total cost, encompassing setup costs, manufacturing costs, and inventory holding costs, is paramount for profitability. This response will analyze the given cost structure for product A and recommend an MPS that minimizes these combined costs.
Understanding the Cost Components
The problem presents three key cost elements:
- Setup Cost: ₹ 5,000 per batch. This is a fixed cost incurred each time a new batch of product A is produced, regardless of the batch size.
- Manufacturing Cost: ₹ 2,000 per unit. This is a variable cost, directly proportional to the number of units produced.
- Inventory Holding Cost: 20% of the manufacturing cost per unit per year. This represents the cost of storing and maintaining inventory, including warehousing, insurance, and obsolescence. Therefore, the holding cost per unit is ₹ 2,000 * 0.20 = ₹ 400 per unit per year.
Calculating Total Cost for Different Batch Sizes
To determine the optimal MPS, we need to calculate the total cost (TC) for various batch sizes. The total cost is the sum of setup costs, manufacturing costs, and inventory holding costs. Let 'Q' represent the batch size (number of units per batch).
Total Cost (TC) = Setup Cost + Manufacturing Cost + Holding Cost
TC = (5000/Q) + (2000 * Q) + (400 * Q/2) (Assuming average inventory is Q/2)
TC = (5000/Q) + 2000Q + 200Q
TC = (5000/Q) + 2200Q
We can now evaluate the total cost for different batch sizes. Since we don't have a demand forecast, we'll analyze a range of potential batch sizes to identify the minimum cost.
| Batch Size (Q) | Setup Cost (₹) | Manufacturing Cost (₹) | Holding Cost (₹) | Total Cost (₹) |
|---|---|---|---|---|
| 10 | 500 | 20,000 | 2,000 | 22,500 |
| 20 | 250 | 40,000 | 4,000 | 44,250 |
| 25 | 200 | 50,000 | 5,000 | 55,200 |
| 50 | 100 | 100,000 | 10,000 | 110,100 |
| 100 | 50 | 200,000 | 20,000 | 220,050 |
Determining the Optimal Batch Size
Based on the calculations above, the total cost is minimized when the batch size is 10 units. While a more rigorous approach would involve calculus to find the exact minimum (taking the derivative of the TC equation and setting it to zero), this table demonstrates the principle. As the batch size increases, the manufacturing cost increases linearly, but the setup cost decreases. However, the holding cost also increases with batch size. The optimal batch size balances these competing forces.
Recommendation for MPS
Therefore, I recommend an MPS that utilizes a batch size of 10 units for product A. This will minimize the combined setup, manufacturing, and inventory holding costs. It's important to note that this recommendation is based on the provided cost data and assumes a constant demand. In a real-world scenario, demand fluctuations and other factors would need to be considered when determining the optimal MPS.
Conclusion
In conclusion, minimizing the total cost associated with production and inventory requires a careful analysis of setup costs, manufacturing costs, and holding costs. By calculating the total cost for various batch sizes, we determined that a batch size of 10 units for product A results in the lowest overall cost. This recommendation provides a starting point for developing an effective MPS, but should be regularly reviewed and adjusted based on changing market conditions and demand forecasts. Further optimization could involve incorporating demand variability and lead times into the model.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.