Question

After graduation, you decide to go into a partnership in an office supply store that has existed for a number of years. Walking through the store and stockrooms, you find a great discrepancy in service levels. Some spaces and bins for items are completely empty; others have supplies that are covered with dust and have obviously been there a long time. You decide to take on the project of establishing consistent levels of inventory to meet customer demands. Most of your supplies are purchased from just a few distributors that call on your store once every two weeks. You choose, as your first item for study, computer printer paper. You examine the sales records and purchase orders and find that demand for the past 12 months was 5,000 boxes. Using your calculator you sample some days' demands and estimate that the standard deviation of daily demand is 10 boxes. You also search out these figures:

Cost per box of paper: $11.
Desired service probability: 98 percent.
Store is open every day.
Salesperson visits every two weeks.
Delivery time following visit is three days.

Using your procedure, how many boxes of paper would be ordered if, on the day the salesperson calls, 60 boxes are on hand?

Answer 1

To determine how many boxes of computer printer paper to order, calculate the reorder point by adding the lead time demand to the safety stock. Subtract the current on-hand inventory from the reorder point to determine the number of boxes to order.

Step-by-step explanation:

To determine how many boxes of computer printer paper to order, we need to consider the desired service level and the demand variability. Since the desired service probability is 98 percent, we need to calculate the safety stock using the z-score corresponding to a 98 percent service level. For a 98 percent service level, the z-score is approximately 2.05 (using a standard normal distribution table). Next, we calculate the reorder point by adding the lead time demand (demand during the lead time) to the safety stock. The lead time demand is the average daily demand multiplied by the lead time, which in this case is 3 days. So the reorder point is the average daily demand multiplied by 3 plus 2.05 times the standard deviation of daily demand. Finally, we subtract the current on-hand inventory (60 boxes) from the reorder point to determine the number of boxes of paper to order.

Let's calculate the reorder point:

Average daily demand: 5,000 / 365 = 13.70 boxes

Reorder point = (Average daily demand * Lead time) + (Z-score for 98% service level * Standard deviation of daily demand) = (13.70 * 3) + (2.05 * 10) = 41.10 + 20.50 = 61.60 boxes

Number of boxes to order = Reorder point - Current on-hand inventory = 61.60 - 60 = 1.60 boxes

Answer 2

257 boxes

Step-by-step explanation:

The computation is given below;

Daily Demand would be

= 5000 ÷ 365

Standard Deviation = 10 boxes

Lead Time = 2 Weeks + 3 Days = 17 Days

Service Level = 0.98

Reorder Point = avg(d) × LT + z × σd × sqrt(LT)

= 5000 ÷ 365 × 17 + 2.05 × 10 × 170.5

= 317

So, the number of boxes should be ordered is

= 317 - 60

= 257 boxes