For purposes of calculating the safety stock of a particular item, we are interested in having an estimate of the MAD or MSE of forecast errors. No historical forecasts are available, but historical monthly demand data for 3 years are available. An analyst on your staff has proposed using the MAD with the following procedure for estimating it:

Step 1 Plot the 3 years of data.

Step 2 Fit the best straight line to it (either by eye or through a statistical fit).

Step 3 For each month find the absolute deviation

|t|=|xt − ˜xt|

where xt is the actual demand in month t and x˜t is the value read off the straight line

(found in Step 2) at month t.

Step 4 MAD = average value of |t| over the 36 months.

a. Discuss why the MAD found by the above procedure might be lower than that actually achievable by statistical forecasting.

b. Discuss why the MAD found by the above procedure might be substantially higher than that actually achievable by a forecasting procedure. Hint: The use of diagrams may be helpful.

c. Why might the MSE be a better choice?