Model Answer
0 min readIntroduction
Inventory management is a critical component of operations management, particularly in industries dealing with perishable or time-sensitive goods like fast food. Maintaining optimal inventory levels is crucial to balance the costs of holding inventory against the risks of stockouts. The Economic Order Quantity (EOQ) model helps determine the ideal order quantity to minimize total inventory costs, while the Reorder Point (ROP) specifies when to place a new order to avoid shortages. This question tests the application of these concepts in a practical scenario, considering demand variability, lead time, and service level requirements.
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 holding costs. The formula for EOQ is:
EOQ = √(2DS / H)
Where:
- D = Annual demand
- S = Ordering cost per order
- H = Holding cost per unit per year
In this case:
- D = 8 pizzas/day * 300 days/year = 2400 pizzas/year
- S = Rs. 200/order
- H = We need to calculate the holding cost. Assuming a cost of capital of 10% and a pizza cost of Rs. 300, the holding cost is 10% of Rs. 300 = Rs. 30/pizza/year.
Therefore:
EOQ = √(2 * 2400 * 200 / 30) = √(32000) ≈ 178.89 pizzas
Rounding to the nearest whole number, the optimal order quantity is 179 pizzas.
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. The formula for ROP with safety stock is:
ROP = (Average daily demand * Lead time) + Safety Stock
Safety Stock = Z * σd * √Lead Time
Where:
- Z = Z-score corresponding to the desired service level
- σd = Standard deviation of daily demand
In this case:
- Average daily demand = 8 pizzas
- Lead time = 3 days
- Service level = 99%
- σd = 2.5 pizzas
For a 99% service level, the Z-score is approximately 2.33 (obtained from a standard normal distribution table).
Safety Stock = 2.33 * 2.5 * √3 ≈ 10.06 pizzas
Rounding to the nearest whole number, the safety stock is 10 pizzas.
ROP = (8 pizzas/day * 3 days) + 10 pizzas = 24 + 10 = 34 pizzas
Therefore, the reorder point with a lead time of 3 days and a service level of 99% is 34 pizzas.
Implications and Considerations
The calculated EOQ of 179 pizzas suggests that the fast-food outlet should place orders for this quantity to minimize its total inventory costs. The ROP of 34 pizzas indicates that when the inventory level drops to 34 pizzas, a new order should be placed to ensure sufficient stock during the 3-day lead time, while maintaining a 99% service level. It's important to note that these calculations are based on certain assumptions, such as constant demand and lead time. In reality, these factors may vary, and the outlet should regularly review and adjust its inventory policies accordingly.
Conclusion
In conclusion, the optimal order quantity for the fast-food outlet is 179 pizzas, and the reorder point is 34 pizzas, given the specified demand, costs, lead time, and service level. Implementing these inventory management strategies will help the outlet minimize costs, reduce the risk of stockouts, and improve overall operational efficiency. Continuous monitoring and adjustments based on actual demand patterns and lead time variations are crucial for maintaining optimal inventory control.
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.