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. a. What are the optimal lot sizes and reorder points for this brand of paint? b. What is the optimal safety stock for this paint?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Solve Problem 14 assuming that the lead time demand follows a Laplace distribution with mean and variance equal to the mean and variance of lead time demand you computed for Problem 14. What difference do you see in the (Q, R) values as compared to those for the normal case?

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.
a. What are the optimal lot sizes and reorder points for this brand of paint?
b. What is the optimal safety stock for this paint?
Transcribed Image Text: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. a. What are the optimal lot sizes and reorder points for this brand of paint? b. What is the optimal safety stock for this paint?
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