Question

A hospital manager knows the surgical glove has a Normal distribution with a mean of five boxes of surgical gloves per day and a standard deviation of one-half box of surgical gloves per day. Two days are required to fill an order surgical glove and ordering cost is $10 per order, annual holding cost is $10 per box. The hospital reorders when the surgical gloves on hand and on order is 12 boxes.

1. Calculate the risk of a stock-out during a lead time.

2. What shortage risk does the hospital incur if it orders 36 boxes when the amount on hand is 12 boxes If a fixed interval of seven days is used for reordering?

Answer 1

Daily demand, d = 5

SD of daily demand, s = 0.5 (one-half box)

Lead time, L = 2 days

Average demand during lead time, d*L = 5*2 = 10

SD of demand during lead time, s*sqrt(L) = 0.5*sqrt(2) = 0.707

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1)

Given reorder point, R = 12

z value = (R - Average demand during lead time) / SD of demand during lead time

= (12 - 10) / 0.707

= 2.828

P(z) = NORMSDIST(2.828) = 0.99766

Risk of stock-out during a lead time = 1 - 0.99766

= 0.00234 or, 0.234 %

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2)

Order interval, P = 7 days

Protection interval = P+L = 7+2 = 9 days

Average demand during protection interval = d*(P+L) = 5*9 = 45

SD of demand during protection interval = s*sqrt(P+L) = 0.5*sqrt(9) = 1.5

Order up to level = Amount on hand + order quantity = 12+36 = 48

z value = (Order up to level - Average demand during protection interval) / SD of demand during protection interval

= (48 - 45)/1.5

= 2

P(z) = NORMSDIST(2) = 0.97725

Shortage risk incurred = 1 - P(z) = 1 - 0.97725

= 0.02275 or, 2.275 %