Starbucks has a large, global supply chain that must efficiently supply over $17,000$ stores.

Although the stores might appear to be very similar, they are actually very different. Depending

on the location of the store, its size, and the profile of the customers served, Starbucks

management configures the store offerings to take maximum advantage of the space available

and customer preferences.

Starbucks' actual distribution system is much more complex, but for the purpose of our

exercise let's focus on a single item that is currently distributed through five distribution

centers $($DC$)$ in the United States. Our item is a logo$-$branded coffeemaker that is sold at some

of the larger retail stores. The coffeemaker has been a steady seller over the years due to its

reliability and rugged construction. Starbucks does not consider this a seasonal product, but

there is some variability in demand. Demand for the product over the past $13$ weeks is shown

in the following table. The current quarter's data are pretty close to the demand shown in the

table.

Management would like you to experiment with some forecasting models to determine

what should be used in a new system to be implemented. The new system is programmed to

use one of two forecasting models: simple moving average or exponential smoothing.

a$.$ Consider a simple moving average model using three weeks' past data. The past data

in each region are given as follows $($week $-1$ is the week before week $1$ in the table, $-2$

is two weeks before week $1,$ etc.$).$ Evaluate the forecasts that would have been made

over the $13$ weeks using the overall $($at the end of the $13$ weeks$)$ mean absolute