Weiss’s paint store uses a (Q, R) inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are back-ordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss-of-goodwill costs. Fixed costs of replenishment are $15 per order, and holding costs are based on a 30 percent annual rate of interest. One of the products stocked at Weiss’s paint store, mentioned above, is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one year. AlWeiss purchases the paint thinner for $20 a gallon can and sells it for $50 a can. The supplier buys back cans not sold during the year for $8 for reprocessing. The demand for this thinner generally varies from 20 to 70 cans a year. Al assumes a holding cost for unsold cans at a 30 percent annual interest rate.a. Assuming that all values of the demand from 20 to 70 are equally likely, what is the optimal number of cans of paint thinner for Al to buy each year?b. More accurate analysis of the demand shows that a normal distribution gives a better fit of the data. The distribution mean is identical to that used in part (a), and the standard deviation estimator turns out to be 7. What policy do you now obtain?
Weiss’s paint store uses a (Q, R) inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are back-ordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss-of-goodwill costs. Fixed costs of replenishment are $15 per order, and holding costs are based on a 30 percent annual rate of interest.
One of the products stocked at Weiss’s paint store, mentioned above, is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one year. AlWeiss purchases the paint thinner for $20 a gallon can and sells it for $50 a can. The supplier buys back cans not sold during the year for $8 for reprocessing. The demand for this thinner generally varies from 20 to 70 cans a year. Al assumes a holding cost for unsold cans at a 30 percent annual interest rate.
a. Assuming that all values of the demand from 20 to 70 are equally likely, what is the optimal number of cans of paint thinner for Al to buy each year?
b. More accurate analysis of the demand shows that a normal distribution gives a better fit of the data. The distribution mean is identical to that used in part (a), and the standard deviation estimator turns out to be 7. What policy do you now obtain?
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