Concept explainers
The monthly sales for Yazici Batteries, Inc., were as follows:
a) Plot the monthly sales data.
b)
i) Naive method.
ii) A 3-month moving average.
iii) A 6-month weighted average using .1, .1, .1, .2, .2, and .3, with the heaviest weights applied to the most recent months.
iv) Exponential smoothing using an α = .3 and a September forecast of 18.
v) A trend projection.
c) With the data given, which method would allow you to forecast next March’s sales?
a)
To determine: Plot and represent the monthly sales data in graphical form.
Introduction: Forecasting is used to predict future changes or demand patterns. It involves different approaches and varies with different time periods. A sequence of data points in successive order is known as a time series. Time series forecasting is the prediction based on past events which are at a uniform time interval.
Answer to Problem 6P
The monthly sales data is plotted and represented.
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Table 1
Graph:
The data to plot the sales is obtained from Table 1. Graph is plotted with the sales for January to December.
Thus, the sales data points are plotted and the graphical representation of sales data is presented.
b) i)
To determine: Forecast January sales using Naïve method.
Answer to Problem 6P
The forecast for January using Naïve method is 23
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Naïve Approach: This method assumes that the demand for a particular period will be the same as the demand in the most recent period.
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
January | 23 |
According to the naïve approach, the demand for January will be the same as the demand in the most recent past month. That is, the demand will be the same as that of December. Therefore, the demand for January will be same as the demand of December; 23.
Hence, the forecast for January using naïve approach is 23
ii)
To determine: Forecast January sales using 3-month moving average.
Answer to Problem 6P
The forecast for January using 3-month moving average is 50.67
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Formula to calculate the demand forecast:
Month | Sales | Moving Average |
January | 20 | |
February | 21 | |
March | 15 | |
April | 14 | 42.67 |
May | 13 | 36.00 |
June | 16 | 32.00 |
July | 17 | 33.67 |
August | 18 | 37.33 |
September | 20 | 40.33 |
October | 20 | 43.67 |
November | 21 | 46.00 |
December | 23 | 47.67 |
January | 50.67 |
Excel worksheet:
Calculation of the demand forecast for January sales:
Substitute the summation of the values 20, 21, and 23and divide it by the nth period; n=3
The January forecast is 50.67
Hence, the forecast of January sales using 3-month moving average is 50.67
iii)
To determine: Forecast January sales using 6-month weighted moving average.
Answer to Problem 6P
The forecast for January using 6-month moving average is 20.60
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Formula to calculate the demand forecast:
Month | Sales | Weighted moving average |
January | 20 | |
February | 21 | |
March | 15 | |
April | 14 | |
May | 13 | |
June | 16 | |
July | 17 | 15.80 |
August | 18 | 15.90 |
September | 20 | 16.20 |
October | 20 | 17.30 |
November | 21 | 18.20 |
December | 23 | 19.40 |
January | 20.60 |
Excel worksheet:
Calculation for the demand forecast of January sales:
To calculate the forecast for January, multiply the weights with the sales of recent year, i.e. multiply weight 0.3 with 23, 0.2 with 21, 0.2 with 20, 0.1 with 20, 0.1 with 18 and 0.1 with 17.
Divide the summation of the multiplied values with the summation of the weights i.e. (0.3+0.2+0.2+0.1+0.1+0.1). The corresponding result is 20.60which is the forecasted value for January. Therefore January forecast is 20.60.
Hence, the forecast of January sales using 6-month weighted moving average is 20.60
iv)
To determine: Forecast January sales using exponential smoothing method.
Answer to Problem 6P
The forecast for January using exponential smoothing method is 20.6298
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Formula to calculate the demand forecast
Where
Sl. No. | Month | Sales | Forecast |
1 | January | 20 | |
2 | February | 21 | |
3 | March | 15 | |
4 | April | 14 | |
5 | May | 13 | |
6 | June | 16 | |
7 | July | 17 | |
8 | August | 18 | |
9 | September | 20 | 18 |
10 | October | 20 | 18.6 |
11 | November | 21 | 19.02 |
12 | December | 23 | 19.614 |
13 | January | 20.6298 |
Excel worksheet:
Calculation of the forecast for October:
To calculate forecast for October, substitute the value of forecast of September, smoothing constant and difference of actual and forecasted demand of September. The result of forecast for October is 18.6.
Calculation of the forecast for November:
To calculate forecast for November, substitute the value of forecast of October, smoothing constant and difference of actual and forecasted demand of October. The result of forecast for November is 19.02.
Calculation of the forecast for December:
To calculate forecast for December, substitute the value of forecast of November, smoothing constant and difference of actual and forecasted demand of November. Therefore, the forecast for December is 19.614.
Calculation of the forecast for January:
To calculate forecast for January, substitute the value of forecast of December, smoothing constant and difference of actual and forecasted demand of December. Therefore, the forecast for January is 20.6298.
Hence, the forecast of January sales using exponential smoothing method is 20.6298
v)
To determine: Forecast January sales using trend projection.
Answer to Problem 6P
The forecast for January using trend projection is 20.754
Explanation of Solution
Given information:
Month | Sales |
January | 20 |
February | 21 |
March | 15 |
April | 14 |
May | 13 |
June | 16 |
July | 17 |
August | 18 |
September | 20 |
October | 20 |
November | 21 |
December | 23 |
Formula to calculate the demand forecast
Where,
Where
Month (x) | Sales (y) | xy | x2 |
1 | 20 | 20 | 1 |
2 | 21 | 42 | 4 |
3 | 15 | 45 | 9 |
4 | 14 | 56 | 16 |
5 | 13 | 65 | 25 |
6 | 16 | 96 | 36 |
7 | 17 | 119 | 49 |
8 | 18 | 144 | 64 |
9 | 20 | 180 | 81 |
10 | 20 | 200 | 100 |
11 | 21 | 231 | 121 |
12 | 23 | 276 | 144 |
∑=78 | ∑=218 | ∑=1474 | ∑=650 |
Substituting the values in the above formula
Calculation of average of x values
Average of x values is obtained by dividing the summation of x values i.e. (1+2+…+12) with the number of period n i.e.12. The value of
Calculation of average of y values
Average of y values is obtained by dividing the summation of sales with the number of period n i.e.12. The value of
Calculation of slope of regression line ‘b’:
Summation of product of sales (y) with x values is ∑xy = 1474, product of number of months (n), average of x values and average of y values is obtained i.e.
Summation of square of x values i.e. 650 is subtracted from the product of number of months i.e. 12 with average of x values i.e. 6.5. The resultant value is 143. The slope of regression line is obtained by dividing 57 with 143. The value of ‘b’ is 0.398.
Calculation of y axis intercept ‘a’:
The y axis intercept is obtained by the difference between average of y values and values obtained by the product of slope of regression line with average of x values. The resultant value of ‘a’ is 15.579.
Calculation of forecast of January:
The January forecast is obtained by summation of the product of slope of regression line and forecasted month, January i.e. 13 with the y-axis intercept. The forecasted value obtained is 20.754.
Hence, the forecast for January sales using trend projection is 20.754
c)
To determine: The best technique among time series methods to forecast March sales.
Explanation of Solution
The calculated results from the data revels that the trend projection (refer to equation (4)) is the best suitable technique to forecast March sales as it is useful in evaluating trends in the data.
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