Question: Crazy Charlie's, a discount stereo shop, uses simple exponential smoothing with a smoothing constant of α = 2 to track the mean and the MAD of monthly item demand. One particular item, a stereo receiver, has experienced the following sales over the last three months: 126, 138, 94. Three months ago the computer had stored values of mean = 135 and MAD = 18.5.
a. Using the exponential smoothing equations given in Section 5.1, determine the current values for the mean and the MAD of monthly demand. (Assume that the stored values were computed prior to observing the demand of 126.)
b. Suppose that the order lead time for this particular item is 10 weeks (2.5 months). Assuming a normal distribution for monthly demand, determine the current estimates for the mean and the standard deviation of lead time demand.
c. This particular receiver is ordered directly from Japan, and as a result there has been considerable variation in the replenishment lead time from one order cycle to the next. Based on an analysis of past order cycles, it is estimated that the standard deviation of the lead time is 3.3 weeks. All other relevant figures are given in parts (a) and (b). Find the mean and the standard deviation of lead time demand in this case.
d. If Crazy Charlie's uses a Type 1 service objective of 98 percent to control the replenishment of this item, what is the value of the reorder level? (Assume that the lead time demand has a normal distribution.)