4.1 The following gives the number of pints of type A

blood used at Woodlawn Hospital in the past 6 weeks:

a) Forecast the demand for the week of October 12 using a 3-week

moving average.

Weeks of

Pints

21-Sep

381

28-Sep

368

total of pints / 3 weeks

5-Oct

374

Total

1123

3 week moving avg.

374.33 pints

b) Use a 3-week weighted moving average, with weights of .1, .3,

and .6, using .6 for the most recent week. Forecast demand for

the week of October 12.

Weeks of

21-Sep

28-Sep

5-Oct

Total weighted average

Pints

381

368

374

Weights

0.1

0.3

0.6

Weighted moving avg

38.1

110.4

224.4

372.9

Forecast demand for week October 12

372.9

c) Compute the forecast for the week of October 12 using exponential

smoothing with a forecast for August 31 of 360 and α = .2

Weeks of

Pints

Forecast

31-Aug

7-Sep

14-Sep

21-Sep

28-Sep

5-Oct

12-Oct

360

389

410

381

368

374

360

360

365.8

374.64

375.91

374.33

374.26

Forecasted for the week of Oct 12

374.26

New forecast = Last period’s forecast

+α (Last period’s actual demand - Last period’s forecast)

360+0.2*(360-360)

4.3 Refer to Problem4.2.Develop a forecast for years 2 through

12 using exponential smoothing with α = .4 and a forecast for year 1 of

6. Plot your new forecast on a graph with the actual data and the naive

forecast. Based on a visual inspection, which forecast is better?

α

year 1

Year

1

2

3

4

5

6

7

8

9

10

11

Demand

7

9

5

9

13

8

12

13

9

11

7

Naïve forecast

0.4

6

Exponential smoothing

6

6.40

7.44

6.46

7.48

9.69

9.01

10.21

11.32

10.39

10.64

7

9

5

9

13

8

12

13

9

11

14

12

10

8

Column D

Column E

Exponential smoothing

6

4

2

0

1

2

3

4

5

6

7

8

9

10

11

The exponential smoothing forecast shows a steady trend vs. the other two forecast which show more ups and downs.

4.5 The Carbondale Hospital is considering the purchase

of a new ambulance. The decision will rest partly on the anticipated

mileage to be driven next year. The miles driven during the past 5

years are as follows:

a) Forecast the mileage for next year using a 2-year moving average.

Year

1

2

3

4

5

6

Mileage 2- year moving avg Absolute Deviation

3,000

4,000

3,400

3500

100

3,800

3700

100

3,700

3600

100

3750

b) Find the MAD based on the 2-year moving average forecast in

part (a). (Hint: You will have only 3 years of matched data.)

c) Use a weighted 2-year moving average with weights of .4 and .6

to forecast next year’s mileage. (The weight of .6 is for the most

recent year.) What MAD results from using this approach to

forecasting? (Hint: You will have only 3 years of matched data.)

d) Compute the forecast for year 6 using exponential smoothing, an

initial forecast for year 1 of 3,000 miles, and α = .5

4.27 Mark Cotteleer owns a company that manufactures

sailboats. Actual demand for Mark’s sailboats during each season in

2006 through 2009 was as follows:

Mark has forecasted that annual demand for his sailboats in 2011

will equal 5,600 sailboats. Based on this data and the multiplicative

seasonal model, what will the demand level be for Mark’s sailboats

in the spring of 2011?

Season

2006

Years

2007

Winter

Spring

Summer

Fall

1,400

1,500

1,000

600

4,500

1,200

1,400

2,100

750

5,450

Average over all season=

2009

1,000

1,600

2,000

650

5,250

900

1,500

1,900

500

4,800

1,250

Average over spring =

2008

1,500

Spring index=

Demand level

1.2

1680 sailboats forcasted for 2011

4.31 Coffee Palace’s manager, Joe Felan, suspects that

demand for mocha latte coffees depends on the price being charged.

Based on historical observations, Joe has gathered the following

data, which show the numbers of these coffees sold over six different

price values:

Using these data, how many mocha latte coffees would be forecast

to be sold according to simple linear regression if the price per cup

were $2.80?

x

y

Price Number sold

$2.70

760

$3.50

510

$2.00

980

$4.20

250

$3.10

320

$4.05

480

Slope =

-277.628

Intercept

1454.604

The regression equation is

Y=1454.604 -277.628

When X=

Y=

$2.80

677.2462 lattes

4.37 Sales of music stands at Johnny Ho’s music store in

Columbus, Ohio, over the past 10 weeks are shown in the table below.

a) Forecast demand for each week, including week 10, using exponential

smoothing with α = .5 (initial forecast = 20).

b) Compute the MAD.

c) Compute the tracking signal

a)

Week

1

2

3

4

5

6

7

8

9

10

Demand Forecast (α=0.5)

20

20.0

21

20.0

28

20.5

37

24.3

25

30.6

29

27.8

36

28.4

22

32.2

25

27.1

28

26.1

256.9

b)

MAD=∑│Error│/n=49.91/10

4.99

c)

Tracking signal=∑(Actual- Forcast)/MAD=

2.82

Tracking Signal

Absolute Deviation

0.00

1.00

7.50

12.75

-5.63

1.19

7.59

-10.20

-2.10

1.95

0.00

1.00

7.50

12.75

5.63

1.19

7.59

10.20

2.10

1.95

14.05

49.91