Model Answer
0 min readIntroduction
Inventory management is a critical aspect of supply chain operations, aiming to balance the costs of holding inventory with the risks of stockouts. Two fundamental concepts in this domain are the Economic Order Quantity (EOQ) and the Reorder Point (ROP). EOQ determines the optimal order quantity to minimize total inventory costs, while ROP indicates when to place a new order to avoid shortages. This question requires us to calculate both EOQ and ROP, considering a specified service level, to ensure efficient component assembly supply for a firm operating on a defined schedule.
Economic Order Quantity (EOQ) Calculation
The Economic Order Quantity (EOQ) is the order quantity that minimizes the total inventory costs, which include ordering costs and carrying costs. The formula for EOQ is:
EOQ = √(2DS / H)
Where:
- D = Annual demand (120 units/day * 5 days/week * 52 weeks/year = 31,200 units)
- S = Ordering cost per order (₹45)
- H = Annual carrying cost per unit (₹0.75)
Substituting the values:
EOQ = √(2 * 31,200 * 45 / 0.75) = √(18,640,000 / 0.75) = √24,853,333.33 ≈ 4985.2 units
Therefore, the Economic Order Quantity is approximately 4985 units.
Reorder Point (ROP) Calculation
The Reorder Point (ROP) is the inventory level at which a new order should be placed. It considers the lead time and the demand during the lead time, along with a safety stock to account for demand variability. The formula for ROP is:
ROP = (d * L) + SS
Where:
- d = Daily demand (120 units)
- L = Lead time (4 days)
- SS = Safety stock
To calculate the safety stock (SS) for a 95% service level, we need to determine the Z-score corresponding to this service level. For a 95% service level, the Z-score is approximately 1.645 (obtained from standard normal distribution tables).
SS = Z * σL
Where:
- Z = Z-score (1.645)
- σL = Standard deviation of demand during lead time. Since lead time is constant, σL = σd * √L
- σd = Standard deviation of daily demand (15 units)
σL = 15 * √4 = 15 * 2 = 30 units
SS = 1.645 * 30 = 49.35 ≈ 49 units
Now, we can calculate the ROP:
ROP = (120 * 4) + 49 = 480 + 49 = 529 units
Therefore, the Reorder Point is 529 units.
Summary of Results
| Parameter | Value |
|---|---|
| Economic Order Quantity (EOQ) | 4985 units |
| Reorder Point (ROP) | 529 units |
Conclusion
In conclusion, the firm should order approximately 4985 units of the component assembly item each time to minimize total inventory costs. Orders should be placed when the inventory level reaches 529 units to maintain a 95% service level, ensuring a low probability of stockouts. Regular review of these parameters is crucial, as changes in demand, lead time, or costs can necessitate adjustments to the EOQ and ROP.
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.