Central Perk orders their organic coffee filters from a South American supplier that mails them as inexpensively (hence, as slowly)as possible. Central Perk uses 80 filters a day with a standard deviation of 5 days. It would be disastrous if they ran out of these filters, years ago customers caught them using paper towels from the men's room and business suffered. They have set their service level at 99% in hopes of avoiding a similar situation. It takes a fortnight (14 days)to receive a shipment and the standard deviation of the shipping time is two days. What is their reorder point?
A)1120 filters
B)1450 filters
C)1495 filters
D)1515 filters

Question

Quizplus · Accepted Answer

To calculate the reorder point, we need to consider the lead time demand (i.e., the demand during the time it takes to receive a shipment). The lead time demand can be calculated as follows:

Lead time demand = Average daily demand x Lead time
Lead time demand = 80 x 14
Lead time demand = 1120

To this, we need to add safety stock to ensure that we don't run out of filters during the lead time. The safety stock can be calculated using the following formula:

Safety stock = Z x Standard deviation of lead time demand

Here, Z is the Z-score associated with the desired service level. For a service level of 99%, the Z-score is 2.33 (obtained from standard normal distribution table). The standard deviation of lead time demand can be calculated as follows:

Standard deviation of lead time demand = Standard deviation of daily demand x Square root of lead time
Standard deviation of lead time demand = 5 x sqrt(14)
Standard deviation of lead time demand = 18.7

Using these values, we can calculate the safety stock as follows:

Safety stock = 2.33 x 18.7
Safety stock = 43.6 (rounded up to 44)

Therefore, the reorder point is:

Reorder point = Lead time demand + Safety stock
Reorder point = 1120 + 44
Reorder point = 1495

Thus, the best choice is C) 1495 filters.

Central Perk Orders Their Organic Coffee Filters from a South