Harlen Industries has a simple forecasting model: Take the actual demand for the same month last year and divide that by the number of fractional weeks in that month. This gives the average weekly demand for that month. This weekly average is used as the weekly forecast for the same month this year. This technique was used to forecast eight weeks for this year, which are shown as follows, along with the actual demand that occurred.

The following eight weeks show the forecast (based on last year) and the demand that actually occurred:

$$\begin{array}{ccc} \text { Week } & \begin{array}{c} \text { Forecast } \\ \text { Demand } \end{array} & \begin{array}{c} \text { Actual } \\ \text { Demand } \end{array} \\ \hline 1 & 140 & 137 \\ 2 & 140 & 133 \\ 3 & 140 & 150 \\ 4 & 140 & 160 \\ 5 & 140 & 180 \\ 6 & 150 & 170 \\ 7 & 150 & 185 \\ 8 & 150 & 205 \\ \hline \end{array}$$

a. Compute the MAD of forecast errors.

b. Using the RSFE, compute the tracking signal.

c. Based on your answers to parts (a) and (b), comment on Harlen's method of forecasting.

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.

The following tabulations are actual sales of units for six months and a starting forecast in January. (Answers in Appendix D)

a. Calculate forecasts for the remaining five months using simple exponential smoothing with $\alpha=0.2$.

b. Calculate MAD for the forecasts.

$$\begin{array}{lcc} & \text { Actual } & \text { Forecast } \\ \hline \text { January } & 100 & 80 \\ \text { February } & 94 & \\ \text { March } & 106 & \\ \text { April } & 80 & \\ \text { May } & 68 & \\ \text { June } & 94 & \\ \hline \end{array}$$

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.

Here are the actual tabulated demands for an item for a nine-month period (January through September). Your supervisor wants to test two forecasting methods to see which method was better over this period. Forecast April through September using a three-month moving average.

Mark Price, the new productions manager for Speakers and Company, needs to find out which variable most affects the demand for their line of stereo speakers. He is uncertain whether the unit price of the product or the effects of increased marketing are the main drivers in sales and wants to use regression analysis to figure out which factor drives more demand for its particular market. Pertinent information was collected by an extensive marketing project that lasted over the past 12 years (year 1 is data from 12 years ago) and was reduced to the data that follow. Perform a regression analysis based on these data using Excel. Answer the following questions based on your results.

A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for four homes per acre, but she is planning to request new zoning. What she builds depends on approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the decision process has been reduced to the following costs, alternatives, and probabilities: Cost of land: $\$ 2$ million Probability of rezoning: .$60$ If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of $\$ 1$ million.

If the land is rezoned, the contractor must decide whether to build a shopping center or $1,500$ apartments that the tentative plan shows would be possible. If she builds a shopping center, there is a $70$ percent chance that she can sell the shopping center to a large department store chain for $\$ 4$ million over her construction cost, which excludes the land; and there is a $30$ percent chance that she can sell it to an insurance company for $\$ 5$ million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to build the $1,500$ apartments, she places probabilities on the profits as follows: There is a $60$ percent chance that she can sell the apartments to a real estate investment corporation for $\$ 3,000$ each over her construction cost; there is a $40$ percent chance that she can get only $\$ 2,000$ each over her construction cost. (Both exclude the land cost.)

If the land is not rezoned, she will comply with the existing zoning restrictions and simply build $600$ homes, on which she expects to make $\$ 4,000$ over the construction cost on each one (excluding the cost of land).

Draw a decision tree of the problem and determine the best solution and the expected net profit.

Historical demand for a product is shown below. Using a weighted moving average with weights of 0.60, 0.30, and 0.10, find the July forecast.

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?

Historical demand for a product is shown below. Using a simple three-month moving average, find the July forecast.

Historical demand for a product is shown below. Using the regression equation in part (d), calculate the forecast for July.

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?

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

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.

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.