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 reciept is a $100 per order. The company uses an inventory carrying charge based on 28 percent annual interest rate. The monthly demand for the filters follows a normal distribution with mean 280 and a standard deviation 77. Order lead time is assumed to be 5 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 uncertanity 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 variances.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 reciept is a $100 per order. The company uses an inventory carrying charge based on 28 percent annual interest rate.
The monthly demand for the filters follows a
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 uncertanity 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 variances.
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