Question

Daily demand for a certain product is normally distributed with a mean of 179 and a standard deviation of 14. The supplier is reliable and maintains a constant lead time of 3 days. The cost of placing an order is $25 and the cost of holding inventory is $0.50 per unit per year. There are no stock-out costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over 362 days of the year. Your goal here is to find the order quantity and reorder point to satisfy a 92 percent probability of not stocking out during the lead time.

a. To manage inventory, the company is using
- Continuous review system
- Periodic review system

Answer 1

The student's question pertains to determining the reorder point and order quantity for inventory management using a 92% service level. The reorder point calculation involves finding the lead time demand and then applying the z-score corresponding to the desired service level to determine safety stock and reorder point. The order quantity typically would be calculated using the EOQ model, but the question lacks necessary information for this calculation.

Step-by-step explanation:

The scenario presented relates to inventory management in operations management, which is a field of study within business. The student is seeking to determine the order quantity and the reorder point for a product given a daily demand that is normally distributed, specifying the mean, standard deviation, lead time, and other cost factors.

To calculate the reorder point (ROP), we first need to establish the lead time demand, and then find the z-score that corresponds to the 92 percent service level. Afterward, we can calculate the number of standard deviations above the mean that corresponds to the desired service level and determine the safety stock and reorder point accordingly.

1. Determine the daily demand and lead time:

• Daily demand mean (μm): 179
• Daily demand standard deviation (σ): 14
• Lead time: 3 days

2. Calculate lead time demand:

• Lead time demand mean = μm * lead time = 179 * 3
• Lead time demand standard deviation = σ * √(lead time) = 14 * √(3)

3. Find the z-score corresponding to a 92% service level (using statistical tables or software).

4. Calculate the safety stock:

• Safety stock = z-score * lead time demand standard deviation

5. Determine the reorder point:

• Reorder point = Lead time demand mean + safety stock

The order quantity can be determined using inventory models like the Economic Order Quantity (EOQ) model, which minimizes the total costs of ordering and holding inventory. However, specific information required to calculate EOQ (like demand rate and holding cost) is not provided in the question.