Question

A large electronics repair shop uses an average of 85 capacitors a day. The standard deviation is 5 units per day. The buyer follows this rule: Order when the amount on hand and on order drops to 625 units. Orders are delivered approximately six days after being placed. The delivery time is Normal with a mean of six days and a standard deviation of 1.10 days. What is the probability that the inventory of capacitors will be exhausted before the shipment is received?

Answer 1

Average daily demand(d) =85 units

Standard deviation of daily demand(d) = 5 units

Lead time (L) = 6 days

Standard deviation of lead time(L) = 1.10 days

Reorder point(ROP) = 625 units

Rop = d x L + {Z x sqrt of[(L x square of d)+(square of d x square of L)]}

=> 625 =85 x 6 + {Z x sqrt of [(6 x square of 5) + (square of 85 x square of 1.10)]}

=> 625 = 510 +{ Z x sqrt of [(6 x 25) + (7225 x 1.21)]}

=> 625 = 510 + [Z x sqrt of (150 + 8742.25)]

=> 625 = 510 + (Z x sqrt of 8892.25)

=> 625 = 510 + (Z x 94.30)

=> 625-510 = Z x 94.30

=> 115 = Z x 94.30

=> Z = 115/94.30

=> Z = 1.22

with a Z value of 1.22 the service level is approximately 89%

So probability of stockout = 100% - 89% = 11%

So the probability that the inventory of capacitors will be exhausted before the shipment is received is 11%