An automotive warehouse stocks a variety of parts that are sold at neighborhoodstores. One particular part, a popular brand of oil filter, is purchased by thewarehouse for $1.50 each. It is estimated that the cost of order processing andreceipt is $100 per order. The company uses an inventory carrying charge based on warehouse for $1.50 each. It is estimated that the cost of order processing andreceipt is $100 per order. The company uses an inventory carrying charge based ona 28 percent annual interest rate.The monthly demand for the filter follows a normal distribution with mean280 and standard deviation 77. Order lead time is assumed to be five months.Assume that if a filter is demanded when the warehouse is out of stock, then thedemand is back-ordered, and the cost assessed for each back-ordered demand is$12.80. Determine the following quantities:a. The optimal values of the order quantity and the reorder level.b. The average annual cost of holding, setup, and stock-out associated with thisitem assuming that an optimal policy is used.c. Evaluate the cost of uncertainty for this process. That is, compare the averageannual cost you obtained in part (b) with the average annual cost that would beincurred if the lead time demand had zero variance.
An automotive warehouse stocks a variety of parts that are sold at neighborhood
stores. One particular part, a popular brand of oil filter, is purchased by the
warehouse for $1.50 each. It is estimated that the cost of order processing and
receipt is $100 per order. The company uses an inventory carrying charge based on warehouse for $1.50 each. It is estimated that the cost of order processing and
receipt is $100 per order. The company uses an inventory carrying charge based on
a 28 percent annual interest rate.
The monthly demand for the filter follows a
280 and standard deviation 77. Order lead time is assumed to be five months.
Assume that if a filter is demanded when the warehouse is out of stock, then the
demand is back-ordered, and the cost assessed for each back-ordered demand is
$12.80. Determine the following quantities:
a. The optimal values of the order quantity and the reorder level.
b. The average annual cost of holding, setup, and stock-out associated with this
item assuming that an optimal policy is used.
c. Evaluate the cost of uncertainty for this process. That is, compare the average
annual cost you obtained in part (b) with the average annual cost that would be
incurred if the lead time demand had zero variance.
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