Question

a firm uses a fixed time period model to manage a type of bolts they keep in inventory. the average daily demand for the bolts is 43 with a standard deviation of 6 . an order is placed every 21 days and is received 7 days later. they use a 99 percent service level and currently have 72 on hand. how many should they order ?

Answer 1

The firm should order 1206 bolts to maintain a 99 percent service level, considering the average demand, standard deviation, order cycle, lead time, and current inventory.

Step-by-step explanation:

To calculate how many bolts a firm should order using a fixed time period model with a given average daily demand, standard deviation, order cycle, lead time, current inventory on hand, and desired service level, we can follow these steps:

1. Calculate the average demand over the order cycle plus lead time.
2. Determine the safety stock required for the desired service level.
3. Compute the reorder point.
4. Calculate the order quantity by subtracting the on-hand inventory from the sum of the average demand during the reorder period and safety stock.

Step 1: The average demand over the order cycle plus lead time (28 days in total) is 43 bolts per day * 28 days = 1204 bolts.

Step 2: To calculate the safety stock, you need to find the z-score corresponding to the 99% service level and multiply it by the standard deviation of the demand during the reorder period. The z-score for a 99% service level is approximately 2.33. The standard deviation of the demand during the reorder period is 6 bolts per day * sqrt(28 days) = 6 * 5.29 = 31.74 bolts.

So the safety stock is 2.33 * 31.74 = approximately 74 bolts.

Step 3: The reorder point is just the average demand over the order cycle plus lead time, which is 1204 bolts.

Step 4: The order quantity is 1204 + 74 - 72 = 1206 bolts.

Therefore, the firm should order 1206 bolts to maintain a 99 percent service level.