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

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


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.


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.


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


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:


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.


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

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

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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