Description
the need of forecasting and different types of forecasting methods. It explains various quantitative and qualitative methods of forecasting.
Demand Forecasting
Demand Forecasting
• A forecast is an estimate of the occurrence and magnitude of a future event by systematically combining and casting forward in a predetermined way data about the past.
Need for Forecasting
• Forecasting is an important input to corporate long run planning • Forecasting is an important component of strategic and operational planning and provides basis for budgetary planning and cost control • It establishes the link between planning and controlling systems.
Selection of a Forecasting Model
• Dependent Vs Independent Demand
• The time horizon for the forecast (short-term, intermediate- term or long-term) • Level of detail or how much aggregation there will be (product or product group, company’s division or the entire company) • Number of items • Nature of demand pattern ( stable and unstable) • Cost of forecasting and accuracy.
Types of Forecasts
• Qualitative (Judgmental) • Quantitative
– – –
Time Series Analysis Causal Relationships Simulation
A Classification of Basic Forecasting Methods
Qualitative Approaches
• Usually based on judgments about causal factors that underlie the demand of particular products or services • Do not require a demand history for the product or service, therefore are useful for new products/services • Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events • The approach/method that is appropriate depends on a product’s life cycle stage
Qualitative Methods
• • • • • • •
Executive Judgment Historical analogy Market research Survey of sales force Survey of customers Delphi method Nominal group technique
Delphi Method
Developed by Rand Corporation in 1950s l. Choose the experts to participate representing a variety of knowledgeable people in different areas 2. A coordinator through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants 3. He summarizes the results and redistribute them to the participants along with appropriate new questions 4. Repeat Step 3 as necessary till consensus is reached and distribute the final results to all participants
Time Series Analysis
• Time series forecasting models try to predict the future based on past data • You can pick models based on: 1. Time horizon to forecast 2. Data availability 3. Accuracy required 4. Size of forecasting budget 5. Availability of qualified personnel
Components of Demand
• Average demand for a period of time • Trend (General pattern of change over time eg. Linear, exponential etc.) • Seasonal element (Any regular pattern recurring within a time period of not more than a year) • Cyclical elements ( Arise from the changes in economy as it moves from phases of growth and decline) • Random variation
Example of Linear and Nonlinear Trend Patterns
Some Time Series Techniques
• • • • •
Simple Moving Average Weighted Moving Average Exponential Smoothing Regression Analysis Trend Projections
Simple Moving Average Formula
• The simple moving average model assumes an average is a good estimator of future behaviour • The formula for the simple moving average is:
A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Ft = Forecast for the coming period N = Number of periods to be averaged A t-1 = Actual occurrence in the past period for up to “n” periods
Simple Moving Average Problem
A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Week 1 2 3 4 5 6 7 8 9 10 11 12 Demand 650 678 720 785 859 920 850 758 892 920 789 844
Question: What are the 3-week and 6-week moving average forecasts for demand? Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
Calculating the moving averages gives us:
Week 1 2 3 4 5 6 7 8 9 10 11 12
Demand 3-Week 6-Week 650 F4=(650+678+720)/3 678 =682.67 720 F7=(650+678+720 +785+859+920)/6 785 682.67 859 727.67 =768.67 920 788.00 850 854.67 768.67 758 876.33 802.00 892 842.67 815.33 920 833.33 844.00 789 856.67 866.50 844 867.00 854.83
©The McGraw-Hill Companies, Inc., 2004
Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
Weighted Moving Average Formula
While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods
The formula for the moving average is:
Ft = w 1 A t -1 + w 2 A t - 2 + w 3 A t -3 + ...+ w n A t - n
wt = weight given to time period “t” occurrence (weights must add to one)
?w
i=1
n
i
=1
Weighted Moving Average Problem Data
Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?
Week 1 2 3 4 Demand 650 678 720
Weights: t-1 .5 t-2 .3 t-3 .2
Note that the weights place more emphasis on the most recent data, that is time period “t-1”
Weighted Moving Average Problem Solution
Week 1 2 3 4
Demand Forecast 650 678 720 693.4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
Exponential Smoothing Model
Ft = Ft-1 + a(At-1 - Ft-1)
Where : Ft ? Forcast va for thecoming t time period lue Ft - 1 ? Forecast v in 1 past time period alue At - 1 ? Actual occurancein the past t time period
a ? Alpha smoothing constant
Or
Ft = a At-1 + (1- a) Ft-1
Exponential Smoothing Problem (1) Data
Week 1 2 3 4 5 6 7 8 9 10
Demand 820 775 680 655 750 802 798 689 775
Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60? Assume F1=A1
Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.
Week 1 2 3 4 5 6 7 8 9 10
Demand 820 775 680 655 750 802 798 689 775
0.1 820.00 820.00 815.50 801.95 787.26 783.53 785.38 786.64 776.88 776.69
0.6 820.00 820.00 793.00 725.20 683.08 723.23 770.49 787.00 728.20 756.28
Exponential Smoothing Problem Plotting
Note that the smaller alpha results in a smoother line in this example
Exponential Smoothing Advantages
• More accurate • Formulation of the model is easy • User can understand how the model works • Little computation is required to use the model • Computer storage requirements are small • Tests for accuracy can be done easily
Simple Linear Regression
• Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables. • In simple linear regression analysis there is only one independent variable. • If the data is a time series, the independent variable is the time period. • The dependent variable is whatever we wish to forecast.
Simple Linear Regression
• Regression Equation This model is of the form:
Y = a + bX
Y = dependent variable X = independent variable a = y-axis intercept b = slope of regression line
Simple Linear Regression Formulas for Calculating “a”
and “b”
a = y - bx
? xy - n
(x) ? x - n(x )
2 2
b=
Simple Linear Regression Problem Data
Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?
Week 1 2 3 4 5
Sales 150 157 162 166 177
30
Answer: First, using the linear regression formulas, we can compute “a” and “b”
Week Week*Week Sales Week*Sales 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 3 55 162.4 2499 Average Sum Average Sum ? xy - n( y)(x) = 2499 - 5(162.4)(3) ? 63 = 6.3 b= 55 ? 5(9 ) 10 x 2 - n(x )2 ?
a = y - bx = 162.4 - (6.3)(3) = 143.5
31
The resulting regression model is:
Yt = 143.5 + 6.3x
Now if we plot the regression generated forecasts against the actual sales we obtain the following chart: 180 175 170 165 Sales 160 155 Forecast 150 145 140 135 1 2 3 4 5 Perio d Sales
Coefficient of Correlation (r)
• The coefficient of correlation, r, explains the relative importance of the relationship between x and y. • The sign of r shows the direction of the relationship. • The absolute value of r shows the strength of the relationship. • r can take on any value between –1 and +1.
Coefficient of Correlation (r)
• r is computed by:
r? n? xy ? ? x ? y
? n ? x 2 ? ( ? x )2 ? ? n ? y 2 ? ( ? y ) 2 ? ? ?? ?
Coefficient of Correlation (r)
• Meanings of several values of r: -1 a perfect negative relationship (as x goes up, y goes down by one unit, and vice versa) +1 a perfect positive relationship (as x goes up, y goes up by one unit, and vice versa) 0 no relationship exists between x and y +0.3 a weak positive relationship -0.8 a strong negative relationship
Incorporating Trend and Seasonal Components
•
•
•
•
•
Determine the seasonality index SI = Seasonal demand/ Average demand Deseasonalize the original data (Divide the original data by SI Develop least square regression line for the deseasonalized data Project the regression line through the period to be forecast Create final forecast by adjusting the regression line by the seasonal factor
Exercise
• For the following data use seasonalised time series regression analysis to develop a forecast for next year's quarterly sales revenues for personal computers:
QUARTERLY SALES ($ MILLION) ???????????????????????????????????? YEAR Q1 Q2 Q3 Q4 ?????????????????????????????????????????????????????? ????? 1 9.2 5.4 4.3 14.1 2 10.3 6.4 5.4 16.0 ?????????????????????????????????????????????????????? ?????
•
• • • • • • •
Step 1
First, compute the seasonal indexes:
????????????????????????????????????????????????????????????????? QUARTERLY SALES ($ MILLION) ???????????????????????????????????? ANNUAL YEAR Q1 Q2 Q3 Q4 TOTAL ????????????????????????????????????????????????????????????????? 1 9.2 5.4 4.3 14.1 33.0 2 10.3 6.4 5.4 16.0 38.1 ????????????????????????????????????????????????????????????????? TOTALS 19.5 11.8 9.7 30.1 71.1 QUARTER AVERAGE 9.75 5.90 4.85 15.05 8.8875 ????????????????????????????????????????????????????????????????? SEASONAL INDEX (SI) 1.097 .664 .546 1.693 ?????????????????????????????????????????????????????????????????
SIQ1 = 9.75/8.8875, SIQ2 = 5.9/8.8875, SIQ3 = 4.85/8.8875
Next, deseasonalize the data by dividing each observation by its SI:
??????????????????????????????????????????????????????????? QUARTERLY SALES ($ MILLION) ???????????????????????????????????? YEAR Q1 Q2 Q3 Q4 ???????????????????????????????????????????????????????????? 1 8.39 8.13 7.88 8.33 2 9.39 9.64 9.89 9.45 ????????????????????????????????????????????????????????????
Next, perform time series regression on the deseasonalized data:
???????????????????????????????????????????????????????????? YEAR QUARTER x y x2 xy ???????????????????????????????????????????????????????????? 1 1 1 8.39 1 8.39 2 2 8.13 4 16.26 3 3 7.88 9 23.64 4 4 8.33 16 33.32 2 1 5 9.39 25 46.95 2 6 9.64 36 57.84 3 7 9.89 49 69.23 4 8 9.45 64 75.60 ?????????????????????????????????????????????????????????? Totals 36 71.10 204 331.23 ??????????????????????????????????????????????????????????
?x = 36, ?y = 71.10, ?x2 = 204, ?xy= 331.23, n = 8 ?x2?y - ?x?xy 204(71.10) - 36(331.23) a = ??????????? = ????????????????? n?x2 - (?x)2 8(204) - (36)2 14,504.40 - 11,924.28 2,580.12 a = ??????????????? = ?????????? = 7.679 1,632 - 1,296 336 n?xy - ?x?y 8(331.23) - 36(71.10) b = ?????????? = ???????????????? n?x2 - (?x)2 336 2,649.84 - 2,559.6 b = ????????????? = .26857 336 Y8 = a + bX8 = 7.679 + .26857(X) Next, compute the deseasonalized forecasts for periods 9 - 12: Y9 Y10 Y11 Y12 = 7.679 + .26857(9) = = 7.679 + .26857(10) = = 7.679 + .26857(11) = = 7.679 + .26857(12) = 10.096 10.365 10.633 10.902
Next, use the seasonal indexes to seasonalize the forecasts:
?????????????????????????????????????????????????????????? SEASONALIZED DESEASONALIZED FORECASTS QUARTER SI FORECASTS ($ MILLION) (1) (2) (3) [COL 2 X COL 3] ?????????????????????????????????????????????????????????? Q1 Q2 Q3 Q4 1.097 .664 .546 1.693 10.096 10.365 10.633 10.902 11.08 6.88 5.81 18.46
Causal Methods for Forecasting
• Regression analysis (Forecast is caused by the occurrence of other events) • Econometric models (attempts to describe some sector of the economy by a series of interdependent equations • Input/output models ( Indicate the change that a producer industry might expect because of the purchasing changes by another industry) • Leading indicators ( Statistics that move in the same direction as the series being forecast but move before the series.
Chapter 11 Forecasting and Demand Planning
•
Forecast error (et) is the difference between the
observed value of the time series and the forecast, or At – Ft. • Mean Square Error (MSE)
Mean Square Error =
?(et )
t=1
n
n
2
•
Mean Absolute Deviation Error (MAD)
Mean Absolute Error =
n ?|e |
t t=1
n
MAD Example
Month 1 2 3 4 5
Sales 220 250 210 300 325
Forecast Abs Error n/a 255 5 205 5 20 320 315 10
40
?A
MAD =
t=1
n
t
- Ft
n
40 = = 10 4
Computer Software for Forecasting
• Examples of computer software with forecasting capabilities
– – – – – – – – Forecast Pro Autobox SmartForecasts for Windows SAS SPSS SAP Minitab POM Software Library
Primarily for forecasting Have Forecasting modules
doc_979141579.pptx
the need of forecasting and different types of forecasting methods. It explains various quantitative and qualitative methods of forecasting.
Demand Forecasting
Demand Forecasting
• A forecast is an estimate of the occurrence and magnitude of a future event by systematically combining and casting forward in a predetermined way data about the past.
Need for Forecasting
• Forecasting is an important input to corporate long run planning • Forecasting is an important component of strategic and operational planning and provides basis for budgetary planning and cost control • It establishes the link between planning and controlling systems.
Selection of a Forecasting Model
• Dependent Vs Independent Demand
• The time horizon for the forecast (short-term, intermediate- term or long-term) • Level of detail or how much aggregation there will be (product or product group, company’s division or the entire company) • Number of items • Nature of demand pattern ( stable and unstable) • Cost of forecasting and accuracy.
Types of Forecasts
• Qualitative (Judgmental) • Quantitative
– – –
Time Series Analysis Causal Relationships Simulation
A Classification of Basic Forecasting Methods
Qualitative Approaches
• Usually based on judgments about causal factors that underlie the demand of particular products or services • Do not require a demand history for the product or service, therefore are useful for new products/services • Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events • The approach/method that is appropriate depends on a product’s life cycle stage
Qualitative Methods
• • • • • • •
Executive Judgment Historical analogy Market research Survey of sales force Survey of customers Delphi method Nominal group technique
Delphi Method
Developed by Rand Corporation in 1950s l. Choose the experts to participate representing a variety of knowledgeable people in different areas 2. A coordinator through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants 3. He summarizes the results and redistribute them to the participants along with appropriate new questions 4. Repeat Step 3 as necessary till consensus is reached and distribute the final results to all participants
Time Series Analysis
• Time series forecasting models try to predict the future based on past data • You can pick models based on: 1. Time horizon to forecast 2. Data availability 3. Accuracy required 4. Size of forecasting budget 5. Availability of qualified personnel
Components of Demand
• Average demand for a period of time • Trend (General pattern of change over time eg. Linear, exponential etc.) • Seasonal element (Any regular pattern recurring within a time period of not more than a year) • Cyclical elements ( Arise from the changes in economy as it moves from phases of growth and decline) • Random variation
Example of Linear and Nonlinear Trend Patterns
Some Time Series Techniques
• • • • •
Simple Moving Average Weighted Moving Average Exponential Smoothing Regression Analysis Trend Projections
Simple Moving Average Formula
• The simple moving average model assumes an average is a good estimator of future behaviour • The formula for the simple moving average is:
A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Ft = Forecast for the coming period N = Number of periods to be averaged A t-1 = Actual occurrence in the past period for up to “n” periods
Simple Moving Average Problem
A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Week 1 2 3 4 5 6 7 8 9 10 11 12 Demand 650 678 720 785 859 920 850 758 892 920 789 844
Question: What are the 3-week and 6-week moving average forecasts for demand? Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
Calculating the moving averages gives us:
Week 1 2 3 4 5 6 7 8 9 10 11 12
Demand 3-Week 6-Week 650 F4=(650+678+720)/3 678 =682.67 720 F7=(650+678+720 +785+859+920)/6 785 682.67 859 727.67 =768.67 920 788.00 850 854.67 768.67 758 876.33 802.00 892 842.67 815.33 920 833.33 844.00 789 856.67 866.50 844 867.00 854.83
©The McGraw-Hill Companies, Inc., 2004
Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
Weighted Moving Average Formula
While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods
The formula for the moving average is:
Ft = w 1 A t -1 + w 2 A t - 2 + w 3 A t -3 + ...+ w n A t - n
wt = weight given to time period “t” occurrence (weights must add to one)
?w
i=1
n
i
=1
Weighted Moving Average Problem Data
Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?
Week 1 2 3 4 Demand 650 678 720
Weights: t-1 .5 t-2 .3 t-3 .2
Note that the weights place more emphasis on the most recent data, that is time period “t-1”
Weighted Moving Average Problem Solution
Week 1 2 3 4
Demand Forecast 650 678 720 693.4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
Exponential Smoothing Model
Ft = Ft-1 + a(At-1 - Ft-1)
Where : Ft ? Forcast va for thecoming t time period lue Ft - 1 ? Forecast v in 1 past time period alue At - 1 ? Actual occurancein the past t time period
a ? Alpha smoothing constant
Or
Ft = a At-1 + (1- a) Ft-1
Exponential Smoothing Problem (1) Data
Week 1 2 3 4 5 6 7 8 9 10
Demand 820 775 680 655 750 802 798 689 775
Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60? Assume F1=A1
Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.
Week 1 2 3 4 5 6 7 8 9 10
Demand 820 775 680 655 750 802 798 689 775
0.1 820.00 820.00 815.50 801.95 787.26 783.53 785.38 786.64 776.88 776.69
0.6 820.00 820.00 793.00 725.20 683.08 723.23 770.49 787.00 728.20 756.28
Exponential Smoothing Problem Plotting
Note that the smaller alpha results in a smoother line in this example
Exponential Smoothing Advantages
• More accurate • Formulation of the model is easy • User can understand how the model works • Little computation is required to use the model • Computer storage requirements are small • Tests for accuracy can be done easily
Simple Linear Regression
• Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables. • In simple linear regression analysis there is only one independent variable. • If the data is a time series, the independent variable is the time period. • The dependent variable is whatever we wish to forecast.
Simple Linear Regression
• Regression Equation This model is of the form:
Y = a + bX
Y = dependent variable X = independent variable a = y-axis intercept b = slope of regression line
Simple Linear Regression Formulas for Calculating “a”
and “b”
a = y - bx
? xy - n
(x) ? x - n(x )2 2
b=
Simple Linear Regression Problem Data
Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?
Week 1 2 3 4 5
Sales 150 157 162 166 177
30
Answer: First, using the linear regression formulas, we can compute “a” and “b”
Week Week*Week Sales Week*Sales 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 3 55 162.4 2499 Average Sum Average Sum ? xy - n( y)(x) = 2499 - 5(162.4)(3) ? 63 = 6.3 b= 55 ? 5(9 ) 10 x 2 - n(x )2 ?
a = y - bx = 162.4 - (6.3)(3) = 143.5
31
The resulting regression model is:
Yt = 143.5 + 6.3x
Now if we plot the regression generated forecasts against the actual sales we obtain the following chart: 180 175 170 165 Sales 160 155 Forecast 150 145 140 135 1 2 3 4 5 Perio d Sales
Coefficient of Correlation (r)
• The coefficient of correlation, r, explains the relative importance of the relationship between x and y. • The sign of r shows the direction of the relationship. • The absolute value of r shows the strength of the relationship. • r can take on any value between –1 and +1.
Coefficient of Correlation (r)
• r is computed by:
r? n? xy ? ? x ? y
? n ? x 2 ? ( ? x )2 ? ? n ? y 2 ? ( ? y ) 2 ? ? ?? ?
Coefficient of Correlation (r)
• Meanings of several values of r: -1 a perfect negative relationship (as x goes up, y goes down by one unit, and vice versa) +1 a perfect positive relationship (as x goes up, y goes up by one unit, and vice versa) 0 no relationship exists between x and y +0.3 a weak positive relationship -0.8 a strong negative relationship
Incorporating Trend and Seasonal Components
•
•
•
•
•
Determine the seasonality index SI = Seasonal demand/ Average demand Deseasonalize the original data (Divide the original data by SI Develop least square regression line for the deseasonalized data Project the regression line through the period to be forecast Create final forecast by adjusting the regression line by the seasonal factor
Exercise
• For the following data use seasonalised time series regression analysis to develop a forecast for next year's quarterly sales revenues for personal computers:
QUARTERLY SALES ($ MILLION) ???????????????????????????????????? YEAR Q1 Q2 Q3 Q4 ?????????????????????????????????????????????????????? ????? 1 9.2 5.4 4.3 14.1 2 10.3 6.4 5.4 16.0 ?????????????????????????????????????????????????????? ?????
•
• • • • • • •
Step 1
First, compute the seasonal indexes:
????????????????????????????????????????????????????????????????? QUARTERLY SALES ($ MILLION) ???????????????????????????????????? ANNUAL YEAR Q1 Q2 Q3 Q4 TOTAL ????????????????????????????????????????????????????????????????? 1 9.2 5.4 4.3 14.1 33.0 2 10.3 6.4 5.4 16.0 38.1 ????????????????????????????????????????????????????????????????? TOTALS 19.5 11.8 9.7 30.1 71.1 QUARTER AVERAGE 9.75 5.90 4.85 15.05 8.8875 ????????????????????????????????????????????????????????????????? SEASONAL INDEX (SI) 1.097 .664 .546 1.693 ?????????????????????????????????????????????????????????????????
SIQ1 = 9.75/8.8875, SIQ2 = 5.9/8.8875, SIQ3 = 4.85/8.8875
Next, deseasonalize the data by dividing each observation by its SI:
??????????????????????????????????????????????????????????? QUARTERLY SALES ($ MILLION) ???????????????????????????????????? YEAR Q1 Q2 Q3 Q4 ???????????????????????????????????????????????????????????? 1 8.39 8.13 7.88 8.33 2 9.39 9.64 9.89 9.45 ????????????????????????????????????????????????????????????
Next, perform time series regression on the deseasonalized data:
???????????????????????????????????????????????????????????? YEAR QUARTER x y x2 xy ???????????????????????????????????????????????????????????? 1 1 1 8.39 1 8.39 2 2 8.13 4 16.26 3 3 7.88 9 23.64 4 4 8.33 16 33.32 2 1 5 9.39 25 46.95 2 6 9.64 36 57.84 3 7 9.89 49 69.23 4 8 9.45 64 75.60 ?????????????????????????????????????????????????????????? Totals 36 71.10 204 331.23 ??????????????????????????????????????????????????????????
?x = 36, ?y = 71.10, ?x2 = 204, ?xy= 331.23, n = 8 ?x2?y - ?x?xy 204(71.10) - 36(331.23) a = ??????????? = ????????????????? n?x2 - (?x)2 8(204) - (36)2 14,504.40 - 11,924.28 2,580.12 a = ??????????????? = ?????????? = 7.679 1,632 - 1,296 336 n?xy - ?x?y 8(331.23) - 36(71.10) b = ?????????? = ???????????????? n?x2 - (?x)2 336 2,649.84 - 2,559.6 b = ????????????? = .26857 336 Y8 = a + bX8 = 7.679 + .26857(X) Next, compute the deseasonalized forecasts for periods 9 - 12: Y9 Y10 Y11 Y12 = 7.679 + .26857(9) = = 7.679 + .26857(10) = = 7.679 + .26857(11) = = 7.679 + .26857(12) = 10.096 10.365 10.633 10.902
Next, use the seasonal indexes to seasonalize the forecasts:
?????????????????????????????????????????????????????????? SEASONALIZED DESEASONALIZED FORECASTS QUARTER SI FORECASTS ($ MILLION) (1) (2) (3) [COL 2 X COL 3] ?????????????????????????????????????????????????????????? Q1 Q2 Q3 Q4 1.097 .664 .546 1.693 10.096 10.365 10.633 10.902 11.08 6.88 5.81 18.46
Causal Methods for Forecasting
• Regression analysis (Forecast is caused by the occurrence of other events) • Econometric models (attempts to describe some sector of the economy by a series of interdependent equations • Input/output models ( Indicate the change that a producer industry might expect because of the purchasing changes by another industry) • Leading indicators ( Statistics that move in the same direction as the series being forecast but move before the series.
Chapter 11 Forecasting and Demand Planning
•
Forecast error (et) is the difference between the
observed value of the time series and the forecast, or At – Ft. • Mean Square Error (MSE)
Mean Square Error =
?(et )
t=1
n
n
2
•
Mean Absolute Deviation Error (MAD)
Mean Absolute Error =
n ?|e |
t t=1
n
MAD Example
Month 1 2 3 4 5
Sales 220 250 210 300 325
Forecast Abs Error n/a 255 5 205 5 20 320 315 10
40
?A
MAD =
t=1
n
t
- Ft
n
40 = = 10 4
Computer Software for Forecasting
• Examples of computer software with forecasting capabilities
– – – – – – – – Forecast Pro Autobox SmartForecasts for Windows SAS SPSS SAP Minitab POM Software Library
Primarily for forecasting Have Forecasting modules
doc_979141579.pptx