Because the exponential smoothing model is very simple, it is widely used in companies. However, choosing the appropriate exponential smoothing coefficient α to achieve an accurate forecast is an important issue. To choose a reasonable coefficient α as well as to evaluate the accuracy of the forecast, we compare the forecast results with the actual demand. The forecast error is calculated as follows:
Forecast error = Actual demand – Forecast = A t -F t
In addition, to evaluate the overall forecast error, the mean absolute deviation MAD is also used. The mean absolute deviation MAD is calculated as follows:
nA i - F i
MAD =i=1 (2.4)
n
Test the accuracy for the two values α = 0.1 and α = 0.9 in the following table:
Table 2.5: Calculating the mean absolute deviation (MAD)
Month
Real needs | α = 0.1 | α = 0.9 | |||||
Forecast | Absolute error opposite to | Forecast error | Forecast | Absolute error opposite to | Forecast error | ||
1 | 405 | 405 | 0 | 0 | 405 | 0 | 0 |
2 | 410 | 405 | 5 | 5 | 405 | 5 | 5 |
3 | 395 | 405.5 | 10.5 | - 10.5 | 409.5 | 14.5 | - 14.5 |
4 | 450 | 395 | 55 | 55 | 396.5 | 53.5 | 53.5 |
5 | 410 | 400.5 | 9.5 | 9.5 | 444.6 | 34.6 | - 34.6 |
6 | 430 | 410.5 | 28.5 | 28.5 | 413.5 | 16.6 | 16.6 |
7 | 450 | 404.5 | 45.5 | 45.5 | 428.5 | 21.5 | 21.5 |
8 | 461 | 409 | 52 | 52 | 448 | 13 | 13 |
9 | 470 | 414 | 56 | 56 | 460 | 10 | 10 |
10 | 600 | 420 | 180 | 180 | 469 | 131 | 131 |
11 | 630 | 438 | 192 | 192 | 587 | 43 | 43 |
12 | 610 | 457 | 153 | 153 | 626 | 16 | - 16 |
Total | 787 | 766 | 358.6 | 228.4 | |||
Maybe you are interested!
-
Research on the treatment of seafood wastewater by electrocoagulation method combined with USBF - 19 tank -
Revenue Forecast of Nam Viet Corporation 2014 Using Brown Method -
Equivalent Annual Payment Method -
Teaching Process of Science Subject Using Btnb Method -
Barium-Based Gastroduodenal X-ray: Good Method for Diagnosing Lesser Curvature and Duodenal Ulcers, Less Sensitive for Superficial Ulcers or Inflammation, Now Gradually
From the results in the table above we have: MAD α= 0.1 = 787/12 = 65.6
MAD α= 0.9 = 358.6/12 = 29.88
Comparing the two values above, we confirm that the forecast with α = 0.9 is more accurate than with α = 0.1. So we choose α = 0.9 in the above case.
2.2.2.5. Trend-adjusted exponential smoothing method
The simple exponential smoothing method cannot accurately represent the fluctuation trend of the demand flow, so it is necessary to use additional trend correction techniques. In this method, the forecast demand is determined by the formula:
FIT t = F t + T t (2.5)
In there:
FIT t : Forecast demand level by trend-adjusted exponential smoothing method; F t : Forecast demand level by simple exponential smoothing method;
T t : Trend adjustment amount
T t = T t-1 + β(F t - F t-1 ) (2.6)
In there:
T t : Adjustment amount according to the trend in the period;
T t-1 : Trend adjustment amount in period t-1; β: Trend smoothing coefficient.
Thus, to forecast demand using the trend-adjusted exponential smoothing method, the following steps need to be taken:
- Forecast demand by simple exponential smoothing method F t in period t.
- Calculating the trend adjustment: To calculate the trend adjustment, the initial trend adjustment value must be determined and entered into the formula. This value can be suggested by judgment or by data that has been observed over time.
- Calculate forecast demand using the exponential smoothing method with trend adjustment.
Returning to the above example, we can create a forecast table using the exponential smoothing method with trend adjustment with β = 0.1 as follows:
Table 2.6: Forecasting demand for store X using the exponential smoothing method with trend adjustment
Month
Actual needs | Forecast (F t) | Adjust the trend T t with β = 0.1; α = 0.9 | Forecast with trend adjustment FIT t direction | |
1 | 405 | 405 | 0 | 405 |
2 | 410 | 405 | 0 = 0 + 0.1(405 – 405) | 405 |
3 | 395 | 409.5 | 0.45 = 0 + 0.1(409.5 – 405) | 410 |
4 | 450 | 396.5 | -0.85 = 0.45 + 0.1(396.5 – 409.5) | 395.65 |
5 | 410 | 444.6 | 3.96 = -0.85 + 0.1(444.6 – 396.5) | 448.6 |
6 | 430 | 413.5 | 0.85 = 3.96 + 0.1(413.5 – 444.6) | 414.4 |
450 | 428.5 | 2.35 = 0.85 + 0.1(428.5 – 413.5) | 431 | |
8 | 461 | 448 | 4.3 = 2.35 + 0.1(448 – 428.5) | 452.3 |
9 | 470 | 460 | 5.5 = 4.3 + 0.1(460 – 448) | 565.5 |
10 | 600 | 469 | 6.4 = 5.5 + 0.1(469 – 460) | 475.5 |
11 | 630 | 587 | 18.2 = 6.4 + 0.1(587 – 469) | 605.2 |
12 | 610 | 626 | 22.1 = 18.2 + 0.1(626 – 587) | 648.1 |
7
To test whether the forecasting by the trend-adjusted exponential smoothing method is better than the above methods, we can use the mean absolute deviation (MAD) indicator.
To calculate MAD we have the following table:
Table 2.7: Calculating MAD for the exponential smoothing method with trend adjustment
Month
Actual needs | Forecast with trend adjustment FIT t direction | Absolute deviation A t - FIT t | |
1 | 405 | 405 | 0 |
2 | 410 | 405 | 5 |
3 | 395 | 410 | 15 |
4 | 450 | 395.65 | 54.35 |
5 | 410 | 448.6 | 38.6 |
6 | 430 | 414.4 | 15.6 |
7 | 450 | 431 | 19.0 |
8 | 461 | 452.3 | 8.7 |
9 | 470 | 565.5 | 4.5 |
10 | 600 | 475.5 | 124.6 |
11 | 630 | 605.2 | 24.8 |
12 | 610 | 648.1 | 22.1 |
Total | 332.25 |
According to the table above, we have:
MAD =
332.25
12 =27.69
Compared with the results in section 4, the results here are more accurate because they have a smaller MAD.
2.2.2.6. Trend-based planning
Trend-based planning helps us forecast future demand based on time series.
The time series allows to determine the theoretical trend line on the basis of the least squares technique, i.e. the sum of the distances from the points representing the actual demand
past economic data to the trend line taken along the vertical axis is the smallest. Then based on the theoretical trend line to forecast future demand.
To determine the theoretical trend line, we first need to represent the past needs on the chart and analyze the development trend of those data. Through analysis, if we see that the data increases or decreases relatively regularly in a certain direction, we can draw a straight line to represent that direction. If the data fluctuates in a more special direction, such as increasing and decreasing more and more quickly or increasingly slowly, we can use appropriate curves to describe that fluctuation, such as parabola, hyperbola, logarithm...
Some common product demand trend curves are: linear, logistic and exponential... Below will consider the method of forecasting product demand according to the linear trend line.
The form of the linear model is represented by the following formula:
Y t = a +bt (2.7)
In which: Y t : Product demand calculated for the period, b: Parameters
t : Time variable
Using the least squares method, a and b are determined as follows:
i 1
i
i
nY
nY . t
i
b = n
i 1
t 2
2
n . t
and a= Y
b . t
(2.8)
n
n
n
Y n 1 t 1
Y i and
i 1
In which: Y i : Actual demand of stage i
n: Number of observation periods
t i i 1
(2.9)
Example: The output of numbered mail over the years is given in the following table. Forecast the demand for numbered mail for the next 5 years using the trend planning method.
Unit: thousand pieces
Year
1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | |
Output | 130 | 255 | 298 | 300 | 370 | 400 | 459 | 494 | 541 | 652 | 738 | 798 |
We make the following table:
Table 2.8: Demand forecasting using trend planning method
Unit: product
Output (Y i ) | t i | t i 2 | Y i t i | |
1994 | 130 | 1 | 1 | 130 |
1995 | 255 | 2 | 4 | 510 |
1996 | 298 | 3 | 9 | 894 |
1997 | 300 | 4 | 16 | 1200 |
1998 | 370 | 5 | 25 | 1850 |
1999 | 400 | 6 | 36 | 2400 |
2000 | 459 | 7 | 49 | 3213 |
2001 | 494 | 8 | 64 | 3952 |
2002 | 541 | 9 | 81 | 4869 |
2003 | 652 | 10 | 100 | 6520 |
2004 | 738 | 11 | 121 | 8118 |
2005 | 798 | 12 | 144 | 9576 |
5435 | 78 | 650 | 43232 |
Year
Based on the data in the table, determine the coefficients: b = 51.43 and a = 126.95. Thus, the trend line has the form: Y = 126.95 +51.43 t.
2.2.2.7. Seasonal demand forecasting method
There are many types of goods whose demand varies with the seasons, such as clothing, heating, agricultural machinery, etc. The following example shows how to use the seasonal index to adjust seasonal demand.
For example: The Electromechanical Factory has recorded the number of electric fans sold in the past as follows:
Month
Real needs | Average demand military month | Average demand simple month | Seasonal index | ||
Year 1 | Year 2 | ||||
1 | 0 | 0 | 0 | 1,789 | 0 |
2 | 0 | 0 | 0 | 1,789 | 0 |
3 | 0 | 0 | 0 | 1,789 | 0 |
4 | 800 | 1,100 | 950 | 1,789 | 0.531 |
5 | 5,500 | 7,300 | 6,400 | 1,789 | 3,577 |
6 | 7,600 | 8,200 | 7,900 | 1,789 | 4,416 |
7 | 4,100 | 4,300 | 4,200 | 1,789 | 2,348 |
8 | 1,500 | 1,600 | 1,550 | 1,789 | 0.866 |
9 | 400 | 510 | 455 | 1,789 | 0.254 |
10 | 10 | 12 | 11 | 1,789 | 0.006 |
11 | 0 | 0 | 0 | 1,789 | 0 |
12 | 0 | 0 | 0 | 1,789 | 0 |
Total average demand = 21,466 | |||||
Average monthly demand =
Monthly demand by year 2
Monthly demand by year 1 +
37
/ 2 (2.10)
Simple average monthly demand =
21,466
12 = 1.789
Average monthly demand
Seasonal index = Simple monthly average demand (2.11) Total seasonal index = Total seasonal period
If the demand for the third year is forecasted to be 23,500 units, then using the above seasonal indices we can forecast the monthly demand for that year as follows:
Table 2.9: Monthly demand forecast using seasonal index
Unit: product
Month
Demand | Month | Demand | |
1 | (23,500/12)x0 = 0 | 7 | (23,500/12)x2,348 = 4598 |
2 | (23,500/12)x0 = 0 | 8 | (23,500/12)x0.866 = 1698 |
3 | (23,500/12)x0 = 0 | 9 | (23,500/12)x0.254 = 498 |
4 | (23,500/12)x0.531 = 1040 | 10 | (23,500/12)x0.006 = 12 |
5 | (23,500/12)x0.577 = 700 | 11 | (23,500/12)x0 = 0 |
6 | (23,500/12)x4,416 = 8648 | 12 | (23,500/12)x0 = 0 |
2.2.2.8. Causal forecasting methods: regression and correlation analysis
Causal forecasting models usually study many events related to the forecasted demand. Once the relevant variables are found, a model is built and used for forecasting. This approach reflects the factors that influence demand. There are many factors that influence demand. The manager’s job is to build a model that reflects the correlation between these factors. The most commonly used quantitative causal forecasting model is the “Linear Regression Analysis Model”.
In the linear regression analysis model, the dependent variable is demand y and the independent variable is x. The forecasting equation is the same as in the trend forecasting equation, but the time factor is replaced by the x factor.
y = a + bx (2.12)
In there:
y: Value of dependent variable; a: Intercept coefficient;
b: Slope coefficient;
x: Independent variable.
We can find the mathematical equation expressing the above linear regression relationship as follows:
n x
y nx y
i 1 i i
n
b =
and a= y b . x
(2.13)
i
2
n
i 1
x 2 n . x
n
y n1
y y 1
x iand
i 1
i 1 i n
(2.14)
In which: Y i: Actual demand of stage i
n: Number of observation periods
SUMMARY OF CHAPTER CONTENT
1. Forecasting is a scientifically based, probabilistic prediction of the level, content, relationships, state, and development trends of the research object or of the method and time limit for achieving certain goals set in the future.
2. When forecasting, the following principles must be followed:
- Principle of dialectical relationship
- Principle of historical inheritance
- Principle of specificity of the nature of the forecast object
- Principles of optimal description of the forecast object
- Principle of similarity of forecasting objects
3. Based on time, there are 3 types of forecasts:
- Short term forecast
- Medium term forecast
- Long term forecast
4. The main qualitative forecasting methods include:
- Get the opinion of the executive management
- Method of collecting opinions from sales force
- Consumer market research methods
- Expert method
5. The main quantitative forecasting methods include:
- Time series method:
+ Simple average method
+ Moving average method
+ Weighted moving average method
+ Simple exponential smoothing method
+ Trend-adjusted exponential smoothing method
+ Forecasting by trend line
- Correlation regression method