Practice Problems: Chapter 4, Forecasting
Problem 1:
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.
Week / Auto Sales1 / 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 / Period3 / 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 / ForecastJanuary / 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 2008 sales.
Year / Sales (Units)2001 / 100
2002 / 110
2003 / 122
2004 / 130
2005 / 139
2006 / 152
2007 / 164
To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate year 2001 as year 1, 2002 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 Demand1 / 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 7, 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 Average1 / 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:
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:
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 / 15 / 1
Sum = / 15 / 16
/ 2.5 / 2.75
SE / 3.7 / 4.1
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:
2001 / 1 / 100 / 1 / 100
2002 / 2 / 110 / 4 / 220
2003 / 3 / 122 / 9 / 366
2004 / 4 / 130 / 16 / 520
2005 / 5 / 139 / 25 / 695
2006 / 6 / 152 / 36 / 912
2007 / 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 2008, we denote the year 2008 as and:
Sales in 2008 = 89.16 + 10.46 * 8 = 172.84
Problem 6:
Year / Forecast Demand / Actual Demand / Error / RSFE1 / 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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