After using your forecasting model for six months, you decide to test it using MAD and a tracking signal. Here are the forecast and actual demands for the six-month period:

$$\begin{array}{lcc} \text { Period } & \text { Forecast } & \text { Actual } \\ \hline \text { May } & 450 & 500 \\ \text { June } & 500 & 550 \\ \text { July } & 550 & 400 \\ \text { August } & 600 & 500 \\ \text { September } & 650 & 675 \\ \text { October } & 700 & 600 \\ \hline \end{array}$$

a. Find the tracking signal.

b. Decide whether your forecasting routine is acceptable.

In this problem, you are to test the validity of your forecasting model. Here are the forecasts for a model you have been using and the actual demands that occurred. Use the method stated in the text to compute MAD and tracking signal. Then decide whether the forecasting model you have been using is giving reasonable results.

The Fast Track Ski Shoppe sells ski goggles during the four months of the ski season. Average demand follows:

a. Calculate the deseasonalized sales and the seasonal index for each of the four months.
b. If next year’s demand is forecast at $1200$ pairs of goggles, what will be the forecast sales for each month?

In this problem, you are to test the validity of your forecasting model. Here are the forecasts for a model you have been using and the actual demands that occurred:

$$\begin{array}{ccr} \text { Week } & \text { Forecast } & \text { Actual } \\ \hline 1 & 800 & 900 \\ 2 & 850 & 1,000 \\ 3 & 950 & 1,050 \\ 4 & 950 & 900 \\ 5 & 1,000 & 900 \\ 6 & 975 & 1,100 \\ \hline \end{array}$$

Use the method stated in the text to compute MAD and the tracking signal. Then, decide whether the forecasting model you have been using is giving reasonable results.

A company has a fixed cost of $30,000 and a production cost of$6 for each unit it manufactures. A unit sells for $10.

What is the profit function?

A company has a fixed cost of $30,000 and a production cost of$6 for each unit it manufactures. A unit sells for $10.

What is the cost function?

Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.

a. Calculate the simple three-month moving average forecast for periods $4$ to $12$ .

b. Calculate the weighted three-month moving average using weights of $0.50,0.30$, and $0.20$ for periods $4$ to $12$ .

c. Calculate the single exponential smoothing forecast for periods $2$ to $12$ using an initial forecast $\left(F_1\right)$ of $61$ and an $\alpha$ of $0.30$.

d. Calculate the exponential smoothing with trend component forecast for periods $2$ to $12$ using an initial trend forecast $\left(T_1\right)$ of $1.8$, an initial exponential smoothing forecast $\left(F_1\right)$ of $60$ , an $\alpha$ of $0.30$, and a $\delta$ of $0.30$.

e. Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods $4$ to $12$ . Which forecasting method do you prefer?

$$\begin{array}{cccc} \text { Month } & \begin{array}{c} \text { Actual } \\ \text { Demand } \end{array} & \text { Month } & \begin{array}{c} \text { Actual } \\ \text { Demand } \end{array} \\ 1 & 62 & 7 & 76 \\ 2 & 65 & 8 & 78 \\ 3 & 67 & 9 & 78 \\ 4 & 68 & 10 & 80 \\ 5 & 71 & 11 & 84 \\ 6 & 73 & 12 & 85 \\ \hline \end{array}$$

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 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?

The following table shows predicted product demand using your particular forecasting method along with the actual demand that occurred. Discuss whether your forecasting method is giving good predictions

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 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?

Calculate the deseasonalized demands for the following:

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?

Using the data in above problem and the seasonal indices you have calculated, calculate expected monthly demand if the annual forecast is $2000$ units.