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?

Expando, Inc. is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $\$6$ million. If demand for new products is low, the company expects to receive $\$10$ million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $\$12$ million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $\$9$ million. Were demand to be low, the company would expect $\$10$ million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is .40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products. Construct a decision tree to help Expando make the best decision.

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 exponential smoothing with $\alpha=0.20$, if the exponential forecast for week 3 was estimated as the average of the first two weeks $[(300+400) / 2$ $=350]$, what would you forecast week 5 to be?

Historical demand for a product is as follows. Using simple linear regression, calculate the trend line for the historical data. Let's say the $X$ axis is April $=1$, May $=2$, and so on, while the $Y$ axis is demand.

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.

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?

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.

The following are sales revenues for a large utility company for years 1 through 11. Forecast revenue for years 12 through 15. Because we are forecasting four years into the future, you will need to use linear regression as your forecasting method.

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?

Southeast Soda Pop, Inc., has a new fruit drink for which it has high hopes. John Mittenthal, the production planner. has assembled the following cost data and demand forecast:

John's job is to develop an aggregate plan. The three initial options he wants to evaluate are:

• Plan A: a strategy that hires and fires personnel as necessary to meet the forecast.

• Plan B: a level strategy.

• Plan C: a level strategy that produces $1,200$ cases per quarter and meets the forecast demand with inventory and subcontracting.

Which strategy is the lowest-cost plan?

Southeast Soda Pop, Inc., has a new fruit drink for which it has high hopes. John Mittenthal, the production planner. has assembled the following cost data and demand forecast:

John's job is to develop an aggregate plan. The three initial options he wants to evaluate are:

• Plan A: a strategy that hires and fires personnel as necessary to meet the forecast.

• Plan B: a level strategy.

• Plan C: a level strategy that produces $1,200$ cases per quarter and meets the forecast demand with inventory and subcontracting.

If you are John's boss, the VP for operations, which plan do you implement and why?

U.S. Airfilter has hired you as a supply chain consultant. The company makes air filters for residential heating and air-conditioning systems. These filters are made in a single plant located in Louisville, Kentucky, in the United States. They are distributed to retailers through wholesale centers in 100 locations in the United States, Canada, and Europe. You have collected the following data relating to the value of inventory in the U.S. Airfilter supply chain. The company reported that it used $\$500$M worth of raw material during the year. On average, how many weeks of supply of raw material are on-hand at the factory?

A fast-food restaurant serves hamburgers, cheeseburgers, and chicken sandwiches. The restaurant counts a cheeseburger as equivalent to $1.25$ hamburgers and chicken sandwiches as $0.8$ hamburger. Current employment is five full-time employees who each work a $40$-hour week. If the restaurant sold $700$ hamburgers, $900$ cheeseburgers, and $500$ chicken sandwiches in one week, what is its productivity? What would its productivity have been if it had sold the same number of sandwiches $(2,100)$, but the mix was $700$ of each type?

U.S. Airfilter has hired you as a supply chain consultant. The company makes air filters for residential heating and air-conditioning systems. These filters are made in a single plant located in Louisville, Kentucky, in the United States. They are distributed to retailers through wholesale centers in 100 locations in the United States, Canada, and Europe. You have collected the following data relating to the value of inventory in the U.S. Airfilter supply chain. What is the average inventory turnover for the firm?