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4.5 The Carbondale Hospital is consideri...
This question was answered on Sep 03, 2012. View the Answer
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:
Year Mileage
1 3,000
2 4,000
3 3,400
4 3,800
5 3,700
6
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


Excel Tab Problem 4.5 - I have started this problem but I do not understand question B C & D, I think I have part A correct.
Problems 4.xlsx

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 periods forecast
+α (Last periods actual demand - Last periods 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 years 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 Marks 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 Marks 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 Palaces 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 Hos 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

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