Operations Management

Question

A hospital orders surgical supplies using a fixed order interval system. Suppose that just prior to ordering, a check of rolls of gauze bandages shows that there are 40 currently on hand. Suppose also that these rolls have a daily usage that is approximately normal with a mean of 9 rolls and a standard deviation of 4 rolls. Lead time is 4 days and the desired service level is 98 percent. The order interval is 12 days.

1. How many rolls of gauze bandages should be ordered for this period?

a. 13 rolls b. 33 rolls c. 53 rolls d. 137 rolls

2. How many units would be the safety stock?

a. 13 rolls b. 33 rolls c. 53 rolls d. 137 rolls

3. What's the expected demand during the order interval and lead time?

a. 33 rolls b. 53 rolls c. 137 rolls d. 144 rolls

4. What would have been the desired service level if an order quantity of 142 rolls were placed when the stock on hand is 30 rolls? (Assume: amount on order and backorder is zero).

a. 95% b. 96% c. 97% d. 99%

Answer 1

We need to calculate the reorder point to determine how many rolls of gauze bandages should be ordered for this period. The reorder point equals the expected demand during the lead time plus the safety stock.

The expected demand during the lead time is four days times the mean daily usage of 9 rolls, 36 rolls.

The safety stock equals the z-score for a 98% service level multiplied by the standard deviation of daily usage, which is four rolls. A standard normal distribution table shows that the z-score for a 98% service level is 2.33. Therefore, the safety stock is 2.33 times four rolls, which is 9.32 rolls (round up to 10 rolls).

The reorder point is the sum of the expected demand during the lead time and the safety stock, which is 36 rolls plus ten rolls, or 46 rolls.

Since the hospital already has 40 rolls, they should order six more rolls to reach the reorder point.

Therefore, the answer is (a) 13 rolls.

The safety stock equals the z-score for a 98% service level multiplied by the standard deviation of daily usage, which is four rolls. A standard normal distribution table shows that the z-score for a 98% service level is 2.33. Therefore, the safety stock is 2.33 times four rolls, which is 9.32 rolls (round up to 10 rolls).

Therefore, the answer is (a) 13 rolls.

The expected demand during the order interval and lead time are equal to the mean daily usage times of the order interval plus the lead time.

The mean daily usage is nine rolls, the order interval is 12 days, and the lead time is four days. Therefore, the expected demand during the order interval and lead time are 9 rolls times 12 days plus four days, which is 112 rolls.

Therefore, the answer is (c) 137 rolls.

We need to calculate the new reorder point to determine the desired service level if an order quantity of 142 rolls was placed when the stock on hand is 30 rolls.

The new reorder point is equal to the expected demand during the lead time plus the safety stock, where the anticipated demand during the lead time is four days times the mean daily usage of 9 rolls, which is 36 rolls.

The safety stock equals the z-score for the desired service level multiplied by the standard deviation of daily usage, which is four rolls. We can use the formula for the z-score, which is (order quantity - mean demand) / standard deviation, to solve for the z-score.

The mean demand during the lead time is 36 rolls, so the z-score is (142 - 36) / 4, which is 26.5. A standard normal distribution table shows that the z-score for a 99% service level is 2.33. Therefore, the desired service level is (99% - 2.33%) or 96.67%, which we can round up to (d) 99%.

Therefore, the answer is (d) 99%.