The number of cases of merlot wine sold by the Connor Owen winery in an eight-year period is as follows. Using an exponential smoothing model with an alpha value of 0.20, estimate the smoothed value calculated as of the end of year 8. Use the average demand for years 1 through 3 as your initial forecast, and then smooth the forecast forward to year 8.

YEAR	CASES OF MERLOT WINE
1	270
2	356
3	398
4	456

YEAR	CASES OF MERLOT WINE
5	358
6	500
7	410
8	376

Not all the items in your office supply store are evenly distributed as far as demand is concerned, so you decide to forecast demand to help plan your stock. Past data for legal-sized yellow tablets for the month of August are as follows. Using a three-week moving average, what would you forecast the next week to be?

Assume an initial starting $F_t$ of $300$ units, a trend $(T)$ of eight units, an alpha of $0.30$, and a delta of $0.40$. If actual demand turned out to be $288$ , calculate the forecast for the next period.

Lakeside Bakery bakes fresh pies every morning. The daily demand for its apple pies is a random variable with (discrete) distribution, based on past experience, given below. Each apple pie costs the bakery $\$6.75$ to make and is sold for $\$17.99$. Unsold apple pies at the end of the day are purchased by a nearby soup kitchen for 99 cents each. Assume no goodwill cost. If the company decided to bake 15 apple pies each day, what would be its expected profit?

Given the following history, use a three-quarter moving average to forecast the demand for the third quarter of this year. Note, the first quarter is Jan, Feb, and Mar; second quarter Apr, May, Jun; third quarter Jul, Aug, Sep; and fourth quarter Oct, Nov, Dec.

The following tabulations are actual sales of units for six months and a starting forecast in January. Calculate MAD for the forecasts.

Assume that your stock of sales merchandise is maintained based on the forecast demand. If the distributor’s sales personnel call on the first day of each month, compute your forecast sales by each of the three methods requested here. Using a simple three-month moving average, what is the forecast for September?

The following table contains the number of complaints received in a department store for the first six months of operation.

$$\begin{array}{lc} \text { Month } & \text { Complaints } \\ \hline \text { January } & 36 \\ \text { February } & 45 \\ \text { March } & 81 \\ \hline \end{array} \begin{array}{lc} \text { Month } & \text { Complaints } \\ \hline \text { April } & 90 \\ \text { May } & 108 \\ \text { June } & 144 \\ \hline \end{array}$$

If a three-month moving average is used to smooth this series, what would have been the forecast for May?

Assume that your stock of sales merchandise is maintained based on the forecast demand. If the distributor's sales personnel call on the first day of each month, compute your forecast sales by each of the three methods requested here.

$$\begin{array}{lc} &\text { Actual }\\ \hline \text { June } & 140 \\ \text { July } & 180 \\ \text { August } & 170 \\ \hline \end{array}$$

a. Using a simple three-month moving average, what is the forecast for September?

b. Using a weighted moving average, what is the forecast for September with weights of $0.20,0.30$, and $0.50$ for June, July, and August, respectively?

c. Using single exponential smoothing and assuming that the forecast for June had been $130$ , forecast sales for September with a smoothing constant alpha of $0.30$.

Demand for stereo headphones and MP$3$ players for joggers has caused Nina Industries to grow almost $50$ percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for last year was as follows.

$$\begin{array}{lc} \text { Month } & \begin{array}{c} \text { Demand } \\ \text { (units) } \end{array} \\ \hline \text { January } & 4,200 \\ \text { February } & 4,300 \\ \text { March } & 4,000 \\ \text { April } & 4,400 \\ \text { May } & 5,000 \\ \text { June } & 4,700 \\ \hline \end{array} \begin{array}{ll} &\text { Demand }\\ \text { Month } & \text { (units) } \\ \hline \text { July } & 5,300 \\ \text { August } & 4,900 \\ \text { September } & 5,400 \\ \text { October } & 5,700 \\ \text { November } & 6,300 \\ \text { December } & 6,000 \\ \hline \end{array}$$

a. Using linear regression analysis, what would you estimate demand to be for each month next year? Using a spreadsheet, follow the general format in Exhibits $18.7$ and $18.8$. Compare your results to those obtained by using the forecast spreadsheet function.

b. To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. How many additional units should be held to meet this level of confidence?

Here are the data for the past 21 months for actual sales of a particular product. Develop a forecast for the fourth quarter using a three-quarter, weighted moving average. Weight the most recent quarter 0.5, the second most recent 0.25, and the third 0.25. Do the problem using quarters, as opposed to forecasting separate months.

Use regression analysis seasonal indexes to forecast next summer’s demand, given the following historical demand data.

The following table shows the past two years of quarterly sales information. Assume that there are both trend and seasonal factors and that the seasonal cycle is one year. Use time series decomposition to forecast quarterly sales for the next year.

A metal fabricator produces connecting rods with an outer diameter that has a $1 \pm .01$-inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be $1.002$ inches with a standard deviation of $.003$ inch.

a. Calculate the process capability index for this example.

b. What does this figure tell you about the process?