A company sells a group of items having a seasonal demand pattern. It is reasonable to assume that all items in the group have the same seasonal pattern. The forecasting procedure currently in use is as follows: From historical data on the whole group, reasonably accurate estimates are available for the fraction of annual demand that occurs in each of the 12 months. Let us call these F1, F2, ... , F12 and let Ck = 

k j=1 Fj be the cumulative fraction of annual demand historically experienced through month k, k =

1, 2, ... , 12.

Consider a particular item i and suppose that its actual demand in month j is Dij. At the end of month k, the annual demand projection for item i, denoted by Pik, is given by Pik =

k j=1 Dij Ck and the forecast for a single future month m in the same year is Pikm = pikFm

a. Illustrate the above forecasting method with annual rate projections and 1-month-ahead forecasts made at the end of each of Jan., Feb., ..., Dec. and Jan. for an item having the following monthly demands in a particular 13-month period:

Jan Feb Dec Jan Month, j 1 2 3 4 5 6 7 8 9 10 11 12 13 Dj 20 20 81 87 106 215 147 125 84 128 122 28 77 The historically determined F

i s for the associated group of items are Month, j 1 2 3 4 5 6 7 8 9 10 11 12 13 Fj 0.03 0.04 0.06. 0.07  0.09 0.16 0.14 0.12 0.11 0.09 0.06 0.03

b. The inventory manager claims that the method is very poor in the early months of a year, but gets better and better as one approaches the end of the year. Does this make sense? If so, how would you suggest modifying the method so as to improve matters early in the year? (There is no need to do a lot of numerical work here.)