Practice Problems: Chapter 4, Forecasting

Problem 1:

Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.

Week Auto Sales

1 8

2 10

3 9

4 11

5 10

6 13

7 -

Problem 2:

Carmen’s decides to forecast auto sales by weighting the three weeks as follows:

Weights Applied

Period

3 Last week

2 Twoweeks ago

1 Three weeks ago

6 Total

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Problem 3:

A firm uses simple exponential smoothing with to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.

Problem 4:

Exponential smoothing is used to forecast automobile battery sales. Two value of are examined, and Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:

Month Actual Battery Sales

Forecast

January 20 22

February 21 

March 15 

April 14 

May 13 

June 16 

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Problem 5:

Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2003 sales.

Year Sales (Units)

1996 100

1997 110

1998 122

1999 130

2000 139

2001 152

2002 164

To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 1996 as year 1, 1997 as year 2, etc.

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Problem 6:

Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD.

Year Forecast Demand

Actual Demand

1 78 71

2 75 80

3 83 101

4 84 84

5 88 60

6 85 73

Problem: 7

Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index.

Problem: 8

Using the data in Problem, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year. Compute next year’s sales and the sales for each quarter.

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ANSWERS:

Problem 1:

Week Auto Sales

Three-Week Moving Average

1 8 

2 10 

3 9 

4 11 (8 + 9 + 10) / 3 = 9

5 10 (10 + 9 + 11) / 3 = 10

6 13 (9 + 11 + 10) / 3 = 10

7 - (11 + 10 + 13) / 3 = 11 1/3

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Problem 2:

Week Auto Sales

Three-Week Moving Average

1 8 

2 10 

3 9 

4 11 [(3*9) + (2*10) + (1*8)] / 6 = 9 1/6

5 10 [(3*11) + (2*9) + (1*10)] / 6 = 10 1/6

6 13 [(3*10) + (2*11) + (1*9)] / 6 = 10 1/6

7 - [(3*13) + (2*10) + (1*11)] / 6 = 11 2/3

Problem 3:

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Problem 4:

Month Actual Battery Sales

Rounded Forecast with a =0.8

Absolute Deviation with a =0.8

Rounded Forecast with a =0.5

Absolute Deviation with a =0.5

January 20 22 2 22 2

February 21 20 1 21 0

March 15 21 6 21 6

April 14 16 2 18 4

May 13 14 1 16 3

June 16 13 3 14.5 1.5

           

      S = 15   S = 16

2.56   2.95

SE 3.5   3.9

On the basis of this analysis, a smoothing constant of a = 0.8 is preferred to that of a = 0.5 because it has a smaller MAD.

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Problem 5:

Year Time Period (X)

Sales (Units) (Y)

X2 XY

1996 1 100 1 100

1997 2 110 4 220

1998 3 122 9 366

1999 4 130 16 520

2000 5 139 25 695

2001 6 152 36 912

2002 7 164 49 1148

 S X = 28

S Y =917

S X2=140

S XY = 3961

Therefore, the least squares trend equation is:

To project demand in 2003, we denote the year 2003 as and:

Sales in

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Problem 6:

Year Forecast Demand

Actual Demand

Error RSFE

1 78 71 -7 -7

2 75 80 5 -2

3 83 101 18 16

4 84 84 0 16

5 88 60 -28 -12

6 85 73 -12 -24

Year Forecast Demand

Actual Demand

|Forecast Error|

Cumulative Error

MAD Tracking Signal

1 78 71 7 7 7.0 -1.0

2 75 80 5 12 6.0 -0.3

3 83 101 18 30 10.0 +1.6

4 84 84 0 30 7.5 +2.1

5 88 60 28 58 11.6 -1.0

6 85 73 12 70 11.7 -2.1

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Problem 7:

Sales of 10,000 units annually divided equally over the 4 seasons is and the seasonal index for each quarter is: spring summer

fall winter

Problem 8:

Next years sales should be 11,000 pumps Sales for each quarter should be 1/4 of the annual sales the quarterly index.

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