Question

A company uses 86 circuit boards a day in a manufacturing process. The person who orders the boards follows this rule: Order when the amount on hand drops to 626 boards. 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 supply of circuit boards will be exhausted before the order is received if boards are reordered when the amount on hand drops to 626 boards? (Round your answer to the nearest whole percent. Omit the "%" sign in your response.) Use Table Probability %

Answer 1

Average daily demand (d) = 86 boards

Lead time(L) = 6 days

Standard deviation of lead time($\sigma$L) = 1.10 day

Reorder point = 626 boards

Reorder point = d × L + (Z × d × $\sigma$L)

=> 626 = 86 × 6 + (Z × 86 × 1.10)

=> 626 = 516 + (Z × 94.6)

=> 626 = 516 + 94.6Z

=> 94.6Z = 626-516

=> 94.6Z = 110

=> Z = 110/94.6

=> Z = 1.16

The Z value of 1.16 corresponds to the service probability of 87.6% or 88%

So risk of stock out = 100% - service probability = 100% - 88% = 12%

So there is a probability of 12% that the supply of current boards will be exhausted before the order is received