Forecast Models and Calculations

FORECAST STRATEGIES AND CALCULATIONS IN SAP APO Model Constant Model

APO Forecast Strategy code 10 (or) 11

Forecast Strategy & Calculation Spread Sheet First Order Exponential Smoothing (FOES)

FOES.xlsx

Explanation on the Model Exponential smoothing methods are the most widely accepted time series techniques in use today. They were originally called "exponentially weighted moving averages." The basic premise of single exponential smoothing is that the sales values for more recent periods have more impact on the forecast and should therefore be given more weight, while the weights for older periods will decrease at an exponential rate. In addition, because the calculations require more recent sales history, data storage is minimized (or at least reduced) as a result of the minimal historical data required. First-order exponential smoothing, also known as single exponential smoothing, uses a smoothing constant (alpha) to which a value between 0 and 1 is assigned. The larger its value (closer to 1), the more weight it assigns to recent sales history. A large alpha (.8) is comparable to using a small number of time periods (n) in a moving average model. A small n allows greater emphasis to be placed on recent periods. Conversely, a small alpha (.1) is similar to using a large number of time periods in the moving average, because the impact of recent data is lessened. The strengths of exponential smoothing models are that they: - Are reasonably simple to understand and use - Provide more weight to recent data periods - Do not require much data storage - Have fairly good accuracy for short-term forecasts (one to three periods out into the future) The weaknesses of exponential smoothing models are that: - A great deal of research may be required to find the correct alpha value - They are usually weak models to use for medium or long-range forecasting

(three periods and beyond) - Forecasts can be thrown into great error because of large random fluctuations in recent data. Because they rely heavily on past history and on a smoothing factor to predict the future, exponential smoothing models cannot easily predict turning points in recent data. At least one to three periods are usually needed to correct for extreme fluctuations in recent data. The principles of first-order exponential smoothing are: 

The older the time series values, the less important they are for the calculation of the forecast.



The present forecast error is taken into account in subsequent forecasts.

The constant model with first-order exponential smoothing (forecast strategies 11 and 12) can be derived from the above two considerations. A simple transformation gives the basic formula for exponential smoothing (see below). Determining the Basic Value

To calculate the forecast value, the system uses the preceding forecast value, the last historical value, and the alpha smoothing factor. This smoothing factor weights the more recent historical values more than the less recent ones, so that they have a greater influence on the forecast. How quickly the forecast reacts to a change in pattern depends on the smoothing factor. If you choose 0 for alpha, the new average is equal to the old one and the basic value calculated previously remains; that is, the forecast does not react to current data. If you choose 1 for the alpha value, the new average equals the last value in the time series. The most common values for alpha lie, therefore, between 0.1 and 0.5. For example, an alpha value of 0.5 weights historical values as follows: 1st historical value: 50% 2nd historical value: 25% 3rd historical value: 12.5% 4th historical value: 6.25% The weightings of historical data can be changed by a single parameter. Therefore, it is relatively easy to respond to changes in the time series.

Use Use the constant model with first-order exponential smoothing for time series that do not have trend-like patterns or seasonal variations.

Constant Model

12

First Order Exponential Smoothing (FOES) with Automatic Alpha adaptation

Uses First Order Exponential Smoothing and adapts the alpha factor.

Use In this forecast strategy, the alpha factor is adapted in every ex-post period based on the mean absolute deviation (MAD) and the error total (ET).

FOES with auto Alpha.xlsx

Features The minimum alpha factor is 0.05. The maximum alpha factor is 0.90. The initial alpha factor ( 0) is either the default of 0.3, or a value that you have entered in the Univariate forecast profile.

Activities The system uses the following iterative formula to calculate the alpha factor in each ex-post period:

TS is the tracking signal.    

TS = 0 if MAD(i) = 0. TS = ABS [ET (i) / MAD (i)] if MAD (i)  0. i = 1 … n, where n is the number of periods in the ex-post forecast.  i is used to calculate the ex-post forecast in the period i+1.

Constant Model

13

Moving Average

Features

Moving Average.xlsx

The system calculates the average of the values in the historical time horizon as defined in the master forecast profile. This average for n periods of history is the forecast result for every period in the forecast horizon; that is, the forecast is the same in every period

Definition The moving average model is used to exclude irregularities in the time series pattern. This strategy calculates the average of the time series values in the historical time horizon. You define the historical time horizon in the master forecast profile. Formula for the Moving Average

Use This forecast strategy is only suitable for time series that are constant; that is, for time series with no trend-like or season-like patterns. As all historical data is equally weighted with the factor 1/n, it takes precisely 'n' periods for the forecast to adapt to a possible level change. No ex-post forecast is calculated with this forecast strategy.

Constant Model

14

Weighted Moving Average

Weighted Moving Average.xlsx

The system weights every time series value with a weighting factor. For example, you can define the factors such that recent data is weighted more heavily than older data. You define the weighting factor in a weighting group.

Definition In the weighted moving average model (forecast strategy 14), every historical value is weighted with a factor from the weighting group in the Univariate forecast profile. Formula for the Weighted Moving Average

The weighted moving average model allows you to weight recent historical data more heavily than older data when determining the average. You do this if the more recent data is more representative of what future demand will be than older data. Therefore, the system is able to react more quickly to a change in level.

Use The accuracy of this model depends largely on your choice of weighting factors. If the time series pattern changes, you must also adapt the weighting factors. When creating a weighting group, you enter the weighting factors as percentages. The sum of the weighting factors does not have to be 100%. No ex-post forecast is calculated with this forecast strategy.

Trend

20 (or) 21

With First Order Exponential Smoothing

Definition: The following formula is used in forecast strategies 20, 21, 30, 31, 40 and 41, and in forecast strategies 50 to 56 where a trend, seasonal or seasonal trend model is determined. The calculation takes into account both trend and seasonal variations. The basic value, the trend value and the seasonal index are calculated after the initial period. See also Model Initialization as well as the definition of exponential smoothing in the APO Glossary. Formula for First-Order Exponential Smoothing in a Trend, Seasonal or Seasonal Trend Model

Use Use the trend, seasonal or seasonal trend model with first-order exponential smoothing for time series that have trend-like patterns and/or seasonal variations.

Trend

22

With Second Order Exponential Smoothing

SOES.xlsx

The method of first-order exponential smoothing is theoretically appropriate when the data series contains a horizontal pattern (that is, it does not have a trend). If first-order exponential smoothing is used with a data series that contains a consistent trend, the forecasts will trail behind (lag) that trend. Second-order exponential smoothing, also known as Holt's linear exponential smoothing, avoids this problem by explicitly recognizing and taking into consideration the presence of a trend. It prepares a smoothed estimate of the trend in a data series.

Definition Second-order exponential smoothing is used in forecast strategies 22 and 23. It is based on a linear trend and consists of two equations. The first equation corresponds to that of first-order exponential smoothing except for the bracketed indices. In the second equation, the values calculated in the first equation are used as initial values and are smoothed again. Formulas for Second-Order Exponential Smoothing

Use

Trend

23

With Second Order Exponential Smoothing

If, over several periods, a time series shows a change in the average value such that a trend pattern is revealed, first-order exponential smoothing produces forecast values that lag behind the actual values by one or several periods. You can achieve a more efficient adjustment of the forecast to the actual values pattern by using second-order exponential smoothing. Uses Second Order Exponential Smoothing and adapts the alpha factor.

Use SOES with Auto Alpha.xlsx

In forecast strategies 12 and 23, the alpha factor is adapted in every ex-post period based on the mean absolute deviation (MAD) and the error total (ET).

Features The minimum alpha factor is 0.05. The maximum alpha factor is 0.90. The initial alpha factor (a 0) is either the default of 0.3, or a value that you have entered in the Univariate forecast profile. The system uses the following iterative formula to calculate the alpha factor in each ex-post period:

TS is the tracking signal. TS = 0 if MAD(i) = 0. TS = ABS [ET (i) / MAD (i) ] if MAD (i) ¹ 0. i = 1 … n, where n is the number of periods in the ex-post forecast. Alpha(i) is used to calculate the ex-post forecast in the period i+1.

Seasonal

30 (or) 31

Seasonal model based on Winters' method

Definition: The following formula is used in forecast strategies 20, 21, 30, 31, 40 and 41, and in forecast strategies 50 to 56 where a trend, seasonal or seasonal trend model is determined. The calculation takes into account both trend and seasonal variations. The basic value, the trend value and the seasonal index are calculated after the initial period. See also Model Initialization as well as the definition of exponential smoothing in the APO Glossary. Formula for First-Order Exponential Smoothing in a Trend, Seasonal or Seasonal Trend Model

Use Use the trend, seasonal or seasonal trend model with first-order exponential smoothing for time series that have trend-like patterns and/or seasonal variations.

Seasonal

35

Seasonal Linear Regression

Calculates seasonal indices, removes the seasonal influence from the data, performs linear regression, and reapplies the seasonal influence to the calculated linear regression line. See also Seasonal Linear Regression

Use Seasonal linear regression, forecast strategy 35, can be used as an alternative to forecast strategies 30 and 31, which return large basic values if the seasonal index is zero or nearly zero. Do not use strategy 35 if your historical data has strong trend patterns.

Activities The system calculates the seasonal linear regression line as follows: 1. The seasonal indices are calculated: Determination of the starting seasonal index for each historical period t a) The number n k of seasons available within the whole historical time series is calculated: n k = n total / n season Where n season is the number of periods per season and n total is the total number of historical values. b) The average value A k of each season k is calculated: A k = Σ V(t) / n season Where V(t) is the historical value of period t and n season is the number of periods per season.

c) The starting seasonal index s start (t) is calculated for each period t within each season. S start (t) = V(t) / A k If a non-completed season exists that is, if n k is not an integer number the starting seasonal index s start (t) of the oldest historical data is calculated with the average A k of the n k th season. Determination of the average seasonal index d) If k complete seasons are available, the starting seasonal indices are averaged: s average (s) = (s start (s) + s start (n season + s) + ....+s start ((k-1) n season +s))/k, s = 1, ... , n season Smoothing of the average seasonal indices e) If you have entered a smoothing factor in field PERSMO of the Univariate forecast profile, the result of step (d) is smoothed. SAP recommends that you enter a smoothing factor of ‘1‘. If the smoothing factor is 0, no seasonal influence is calculated and only linear regression is carried out. 2. The actual data is corrected on the basis of the seasonal indices calculated in step 1. 3. Linear regression is performed on the non-seasonal actual values. 4. The seasonal indices are applied to the results of the linear regression calculation, which produces the forecast results.

Seasonal Trend

40 (or) 41

Forecast with Seasonal trend Model

Definition: The following formula is used in forecast strategies 20, 21, 30, 31, 40 and 41, and in forecast strategies 50 to 56 where a trend, seasonal or seasonal trend model is determined. The calculation takes into account both trend and seasonal variations. The basic value, the trend value and the seasonal index are calculated after the initial period. See also Model Initialization as well as the definition of exponential smoothing in the APO Glossary. Formula for First-Order Exponential Smoothing in a Trend, Seasonal or Seasonal Trend Model

Use Use the trend, seasonal or seasonal trend model with first-order exponential smoothing for time series that have trend-like patterns and/or seasonal variations.

Automatic model selection

50

Forecast with automatic model selection

Choose this strategy if you have no knowledge of the patterns in your historical data.

Test for constant, trend, seasonal and seasonal trend (model selection procedure 1)

The system tests the historical data for constant, trend, seasonal and seasonal trend patterns. The system applies the model that corresponds most closely to the pattern detected. If no regular pattern is detected, the system runs the forecast as if the data revealed as a constant pattern. In this process, the alpha, beta and gamma factors are determined as follows:

Automatic Model Selection Procedure 1.docx

  

Automatic model selection

51

Forecast with automatic model selection Test for trend using model selection procedure 1

Automatic Model Selection Procedure 1.docx

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

See also Automatic Model Selection Procedure 1 (Attached in the previous column). Choose this strategy if you think that there is a trend pattern in your historical data, and if you know that there is no other pattern. The system subjects the historical values to a regression analysis and checks to see whether there is a significant trend pattern. If not, the system runs the forecast as if the data revealed a constant pattern. The alpha and beta factors are determined as follows:   

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

Automatic model selection

52

Forecast with automatic model selection Test for Season using model selection procedure 1

Choose this strategy if you think that there is a seasonal pattern in your historical data, and if you know that there is no other pattern. The system clears the historical values of any possible trends and carries out an autocorrelation test. If no seasonal pattern is detected, the system runs the forecast as if the data revealed a constant pattern. The alpha and gamma factors are determined as follows:

Automatic Model Selection Procedure 1.docx

  

Automatic model selection

53

Forecast with automatic model selection Test for Trend and Season using model selection procedure 1

Automatic Model Selection Procedure 1.docx

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

Choose this strategy if you think that there is a seasonal and/or a trend pattern in your historical data. The system subjects the historical values to a regression analysis and checks to see whether there is a significant trend pattern. It also clears the historical values of any possible trends and carries out an autocorrelation test to see whether there is a significant seasonal pattern. If a seasonal and/or trend pattern is detected, a trend model, seasonal model or seasonal trend model is used. If no regular pattern is detected, the system runs the forecast as if the data revealed a constant pattern. The alpha, beta and gamma factors are determined as follows:   

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

Manual model selection with test for an additional pattern

54

Seasonal model and test for trend (model selection procedure 1)

Automatic Model Selection Procedure 1.docx

Choose this strategy if you think that there is a trend pattern in your historical data, and if you know that there is a seasonal pattern. The system subjects the historical values to a regression analysis and checks to see whether there is a significant trend pattern. If there is, a seasonal trend model is used. Otherwise, a seasonal model is used. The alpha, beta and gamma factors are determined as follows:   

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

See also Automatic Model Selection Procedure 1. Manual model selection with test for an additional pattern

55

Trend model and test for seasonal pattern (model selection procedure 1)

Automatic Model Selection Procedure 1.docx

Choose this strategy if you think that there is a seasonal pattern in your historical data, and if you know that there is a trend pattern. The system clears the historical values of any possible trends and carries out an autocorrelation test. If the test is positive, a seasonal trend model is used. Otherwise, a trend model is used. The alpha, beta and gamma factors are determined as follows:   

The smoothing factors are taken from the Univariate profile. The settings in the demand planning desktop if these are different than the ones in the Univariate profile. If you have made no settings either in the Univariate profile or on the demand planning desktop, the default factors of 0.3 are used.

See also Automatic Model Selection Procedure 1.

Automatic model selection

56

Model selection procedure 2

Choose this strategy if you wish highly detailed tests of the historical data to be carried out. The system tests for constant, trend, seasonal and seasonal trend patterns, using all possible combinations for the alpha, beta, and gamma smoothing factors where the factors are varied between 0.1 and 0.5 in intervals of 0.1. The system then chooses the model with the lowest mean absolute deviation (MAD). Procedure 2 is more precise than procedure 1, but takes longer time.

Copy History

60

Historical data used as a Forecast Data

Manual forecast

70

Manual Forecast

Croston

80

Croston Model

Choose this strategy if demand does not change at all and you want to opt for the least performance- or work-intensive strategy. No forecast is calculated. Instead, the historical data from the previous year is copied. Choose this strategy if you wish to set the basic value, trend value and/or seasonal indices yourself

Choose this strategy if demand is sporadic Definition The Croston method is a forecast strategy for products with intermittent demand. In the Univariate forecast profile, choose forecast strategy 80. The Croston method consists of two steps. First, separate exponential smoothing estimates are made of the average size of a demand. Second, the average interval between demands is calculated.

Use Exponential smoothing is often used to forecast demand in stock control systems. If demand is intermittent, however, this method almost always produces inappropriate stock levels. The Croston method is suitable if demand appears at random, with many or even most time periods having no demand; where demand does occur, the historical data is randomly distributed, independently or almost independently of the demand interval. Such demand patterns are known as "lumpy demand" or intermittent, irregular, random or sporadic demand. One example might be demand for spare parts or equipment that is usually ordered in batches to replenish downstream inventories. No ex-post forecast is calculated with this forecast strategy.

Linear Regression

Simple Linear Regression

94

The system calculates a line of best fit for the equation y = a + bx, where a and b are constants. The ordinary least squares method is used.

FORECAST ACCURACY MEASUREMENT / EVALUATION CRITERIA

Monitoring of Forecast Accuracy Purpose You monitor forecast accuracy:   

To find out whether you are using the right forecast models To identify what adjustments are needed to the forecast models To project expected deviation from the planned forecast

APO offers the following ways to monitor forecast accuracy:     

Statistical error analysis Univariate forecast error measurements Multiple linear regression model measures of fit Planned/actual comparison Viewing purpose-designed KPIs with a BW front end (BW is the SAP Business Information Warehouse)

Statistical Error Analysis Purpose

Statistical error analysis is a technqiue used in forecast accuracy reporting. A series of previous forecasts for a particular period is stored and each deviation of this series is compared to the actuals for the same period. The deviation can then be projected into the future. This visualization of expected deviation not only places the forecast in context; it also enables "what if" planning. For example, it enables your company to evaluate future scenarios for maximum, planned and minimum production volumes, stock, sales revenue, and cash flow. The real impact of forecast accuracy reporting is realized when coupled with a simulation at the significant nodes of the supply chain, in particular, for S&OP.

Prerequisites The analyst must have a comprehensive understanding of the both the historical and projected business environment including market behavior, competitor activity, the product, product life cycle, and activities relating to pricing, promotion and distribution. In addition the analyst should understand the business constraints relating to supply, production and distribution. This comprehensive understanding will enhance the quality of the corrected historical data and ensure that projections are kept in context. 1. You have stored the forecasts from previous periods. See also Forecast Storage. In Demand Planning, use macros for this purpose. For example, you might have one macro that stores for a given month what was forecasted in the prior month, a second macro that stores for a given month what was forecasted two months prior to that month, and a third macro that stores for a given month the sum of three months' forecasts ending with the forecast for that month. The following forecasts would be seen in the month of March: January

February

Forecast

March March's forecast for March

Prev Month

December's forecast for January

January's forecast for February

February's forecast for March

-2 Month

November's forecast for January

December's forecast for February

January's forecast for March

3 Month Rolling

November’s forecast for Nov+Dec+Jan

December’s forecast for Dec+Jan+Feb

January’s forecast for Jan+Feb+Mar

Include this information in your data view, if you wish to use it while forecasting. Otherwise, create a separate data view.

2. You have updated your historical data by loading actuals for the period(s) just completed. 3. You have corrected history such that outliers are suppressed, previous promotion impacts removed, and business issues like previous stock transfers, refurbishments and so on, are not counted as sales.

Process Flow 1. Review the corrected history to validate that it makes sense in the business context. 2. Review the business dynamics and decide which data range is relevant. For instance, if the cumulative procurement lead time for the significant components is only one month, it may not make sense to include errors generated by forecasts prior to one month, as strictly they are irrelevant from a procurement standpoint. In the table below, the errors from months (-3) and (-2) should therefore not be included in any statistical average calculation as they would make the forecast error worse. This would lead to unnecessary contingency in the forecast projections. In this example, a product has three original forecasts for the month of November. The actual consumption for the month of November was 150 units. Month

Units forecast for November

August (-3)

100

-33

September (-2)

110

-27

October (-1)

120

-20

November (1)

3. Run standard macros to calculate the forecast errors.

Actual sales

150

% Error compared to actual sales

The % error for each of forecast is calculated as the percentage difference between the forecast and the actual. A positive error indicates an over-forecast while a negative error indicates an under-forecast.

Result An understanding by your company not only of the accuracy of the forecast, but also of how to provide for the variance.

The magnitude of the forecast error will depend greatly on industry, product complexity and market dynamics. Forecast errors by themselves reflect not just the quality of the forecast, but also the volatility of the business dynamics.

Analysis of Univariate Forecast Errors Purpose In this process, you improve the accuracy of your univariate forecasts by monitoring predefined tolerance thresholds for the standard errors, and by adjusting the forecast model where any of these thresholds are exceeded.

Prerequisites You have installed the Alert Monitor.

Process Flow 1. In the univariate forecast profile, set which forecast error measurements you want to be calculated. 2. In the diagnostic group which you enter in the univariate profile, specify the upper limits of the forecast error measurements. 3. In the Alert Monitor, create a forecast alert profile. Alert profiles are used to display specific alerts to specific users. They do not affect whether or not alerts are created.

4. In interactive demand planning (for mass processing, see * below), assign the alert profile you created in step 3 by choosing Edit → Assign alert profile. If desired, select Forecast deletes old alerts automatically. 5. Run the forecast in the statistical forecast view. The forecast errors that you set in the univariate profile are calculated automatically. You can view them on the Forecast errors tabstrip of the statistical forecast view. To compare the forecast errors with those of other models, look at the different forecast versions by choosing Settings  Forecast comparison. 6. 7. 8. 9. 10. 11.

From the workspace toolbar, choose Alerts on/off . Check the alerts to see if any forecast errors have exceeded their predefined upper limits. Make any necessary adjustments to the univariate forecast model. Run the forecast again. Study the alerts to see if the adjustments you made in step 8 have corrected the problem. If necessary, repeat steps 8 through 10.

* If you are forecasting in the background, continue as follows at step 4. 4. 5. 6. 7. 8. 9.

Specify in the mass processing activity that alerts are to be created. Run the forecast in the background as a mass processing job. Open the Alert Monitor by choosing Supply Chain Monitoring  Alert Monitor from the SAP Easy Access menu. Check the alerts. If necessary, make adjustments to the univariate forecast profile or use a different profile. Repeat steps 5 through 8 as often as necessary.

Forecast Accuracy Measurements Definition Univariate forecasting allows you to measure the forecast error in six ways:      

Mean absolute deviation (MAD) Error total (ET) Mean absolute percentage error (MAPE) Mean square error (MSE) Square root of the mean squared error (RMSE) Mean percentage error (MPE)

The system calculates the forecast errors by comparing the differences between the actual values and the ex-post values.

Use Use the forecast error measurements to help you evaluate the accuracy of the forecast. You select them in the Univariate forecast profile. To set upper limits for the forecast error measurements, use the Diagnostic group in the Univariate forecast profile; when a limit has been exceeded, the system issues an alert. You can also select the forecast error measurements on the demand planning desktop, under the Errors tab of the Forecast view.

MAD (Mean Absolute Deviation) Indicator The mean absolute deviation gives the mean average difference between the forecasted value and the historical value in the ex-post forecast.

Mean Absolute Deviation (MAD) for Ex-Post Forecast

Key to MAD Formula

Mean Absolute Deviation for Forecast Initialization

Procedure If you wish the mean absolute deviation (MAD) to be displayed in the Forecast errors tab, set this indicator.

Error Total

Key to Error Total Formula

Mean Absolute Percent Error (MAPE) Definition Is the mean absolute percentage error between the forecasted value and the historical value in the ex-post forecast.

Key to MAPE Formula

Procedure If you wish the mean absolute percentage error (MAPE) to be displayed in the Forecast errors tab, set this indicator

MPE (Mean Percentage Error) Indicator MPE Is the mean percentage error between the forecasted value and the historical value in the ex-post forecast.

Key to MPE Formula

Procedure If you wish the mean percentage error (MPE) to be displayed in the Forecast errors tab, set this indicator.

MSE (Mean Square Error) Indicator Is the mean square error between the forecasted value and the historical value in the ex-post forecast.

Key to MSE Formula

Procedure If you wish the mean square error (MSE) to be displayed in the Forecast errors tab, set this indicator.

RMSE (Root of the Mean Square Error) Indicator Definition Is the root mean square error between the forecasted value and the historical value in the ex-post forecast.

Key to RMSE Formula

Procedure If you wish the root mean square error (RMSE) to be displayed in the Forecast errors tab, set this indicator.