Practice Problems: Chapter 4, Forecasting
ANSWER PROBLEM 8
Problem 1:
Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.
Week 1 2 3 4 5 6 7
Auto Sales 8 10 9 11 10 13 -
Answer
Week 1 2 3 4 5 6 7
Auto Sales 8 10 9 11 10 13 -
Three-Week Moving Average (8 + 9 + 10) / 3 = 9 (10 + 9 + 11) / 3 = 10 (9 + 11 + 10) / 3 = 10 (11 + 10 + 13) / 3 = 11 1/3
Problem 2:
Carmen’s decides to forecast auto sales by weighting the 3 weeks as follows:
Weights Applied 3 2 1 6
Period Last week 2 weeks ago 3 weeks ago Total
Answer
Week 1 2 3 4 5 6 7
Auto Sales 8 10 9 11 10 13 -
Three-Week Moving Average [(3 × 9) + (2 × 10) + (1 × 8)] / 6 = 9 1/6 [(3 × 11) + (2 × 9) + (1 × 10)] / 6 = 10 1/6 [(3 × 10) + (2 × 11) + (1 × 9)] / 6 = 10 1/6 [(3 × 13) + (2 × 10) + (1 × 11)] / 6 = 11 2/3
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.
Answer
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 January February March April May June
Actual Battery Sales 20 21 15 14 13 16
Forecast 22
Answer
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 2.95SE 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:
Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2015 sales.
Year 2008 2009 2010 2011 2012 2013 2014
Sales (Units) 100 110 122 130 139 152 164
To minimize computations, transform the value of x (time) to simpler numbers. In this case, designate 2008 as year 1, 2009 as year 2, etc.
Answer
Year Time Period (X) Sales (Units) (Y) X2 XY
2008 1 100 1 100
2009 2 110 4 220
2010 3 122 9 366
2011 4 130 16 520
2012 5 139 25 695
2013 6 152 36 912
2014 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 2015, we denote the year 2015 as and:
Sales in
Problem 6:
Given the forecast demand and actual demand for 3-metre fishing boats, compute the tracking signal and MAD.
Year 1 2 3 4 5 6
Forecast Demand 78 75 83 84 88 85
Actual Demand 71 80 101 84 60 73
Answer
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
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 as follows: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index.
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:
Meredith and Smunt Manufacturing expect sales of pumps to grow by 10% next year. Using the data in Problem 7, compute next year’s sales and the sales for each quarter.
Sample Solution