# Question

A manufacturing company regularly consumes a special type of glue purchased from a foreign supplier. Because the supplier is foreign, the time gap between placing an order and receiving the shipment against that order is long and uncertain.

This time gap is called "lead time." From past experience, the materials manager notes that the company's demand for glue during the uncertain lead time is normally distributed with a mean of 187.6 gallons and a standard deviation of 12.4 gallons. The company follows a policy of placing an order when the glue stock falls to a predetermined value called the "reorder point." Note that if the reorder point is x gallons and the demand during lead time exceeds x gallons, the glue would go "stock-out" and the production process would have to stop. Stock-out conditions are therefore serious.

a. If the reorder point is kept at 187.6 gallons (equal to the mean demand during lead time) what is the probability that a stock-out condition would occur?

b. If the reorder point is kept at 200 gallons, what is the probability that a stockout condition would occur?

c. If the company wants to be 95% confident that the stock-out condition will not occur, what should be the reorder point? The reorder point minus the mean demand during lead time is known as the "safety stock." What is the safety stock in this case?

d. If the company wants to be 99% confident that the stock-out condition will not occur, what should be the reorder point? What is the safety stock in this case?

This time gap is called "lead time." From past experience, the materials manager notes that the company's demand for glue during the uncertain lead time is normally distributed with a mean of 187.6 gallons and a standard deviation of 12.4 gallons. The company follows a policy of placing an order when the glue stock falls to a predetermined value called the "reorder point." Note that if the reorder point is x gallons and the demand during lead time exceeds x gallons, the glue would go "stock-out" and the production process would have to stop. Stock-out conditions are therefore serious.

a. If the reorder point is kept at 187.6 gallons (equal to the mean demand during lead time) what is the probability that a stock-out condition would occur?

b. If the reorder point is kept at 200 gallons, what is the probability that a stockout condition would occur?

c. If the company wants to be 95% confident that the stock-out condition will not occur, what should be the reorder point? The reorder point minus the mean demand during lead time is known as the "safety stock." What is the safety stock in this case?

d. If the company wants to be 99% confident that the stock-out condition will not occur, what should be the reorder point? What is the safety stock in this case?

## Answer to relevant Questions

The daily price of orange juice 30-day futures is normally distributed. In March through April 2007, the mean was 145.5 cents per pound, and standard deviation = 25.0 cents per pound.4 Assuming the price is independent from ...For X ~ N(32, 72), find two values x1 and x2, symmetrically lying on each side of the mean, with P(x1 < X < x2) = 0.99. Private consumption as a share of GDP is a random quantity that follows a roughly normal distribution. According to an article in Business Week, for the United States that was about 71%. Assuming that this value is the mean ...A large state university sends recruiters throughout the state to recruit graduating high school seniors to enroll in the university. University records show that 25% of the students who are interviewed by the recruiters ...Weekly rates of return (on an annualized basis) for certain securities over a given period are believed to be normally distributed with mean 8.00% and variance 0.25. Give two values x1 and x2 such that you are 95% sure that ...Post your question

0