General Hospital uses disposable diapers at a rate of 200 per day, with a standard deviation of 20.To place and receive a replenishment of diapers from the third party logistics provider typically takes 3 days.The hospital never wants to run out of diapers, so it holds enough safety stock to ensure 99.9% availability.Hospital purchasing managers order diapers along with other items every 30 days.It is time to place an order, and there are 100 diapers on hand.How many units should be ordered (pick the closest answer)?

Question

Quizplus · Accepted Answer

To determine the order quantity, we need to calculate the economic order quantity (EOQ).

EOQ = sqrt((2 x annual demand x ordering cost) / holding cost)

- Annual demand = 200 diapers per day x 30 days in a month = 6,000 diapers per month
- Ordering cost = cost of placing an order with the logistics provider = $50 per order
- Holding cost = cost of holding one diaper in inventory for one day = $0.02 per diaper per day

Plugging in these variables, we get:

EOQ = sqrt((2 x 6,000 x 50) / 0.02) = 66,517 diapers (rounded to the nearest whole number)

However, we also need to take into account the safety stock and the lead time.

Safety stock = z-score x standard deviation x sqrt(lead time)

- z-score for 99.9% availability = 3.090
- standard deviation = 20 diapers per day
- lead time = 3 days

Plugging in these variables, we get:

Safety stock = 3.090 x 20 x sqrt(3) = 107 diapers (rounded to the nearest whole number)

So, the hospital needs to order enough to cover the demand during lead time plus the safety stock:

Order quantity = EOQ + safety stock - current inventory
Order quantity = 66,517 + 107 - 100 = 66,524 diapers

Therefore, the closest answer is B) 6652.

General Hospital Uses Disposable Diapers at a Rate of 200