## Understanding Forecast Levels and Methods

You can generate both detail (single item) forecasts and summary (product line) forecasts that reflect product demand patterns. The system analyzes past sales to calculate forecasts by using 12 forecasting methods. The forecasts include detail information at the item level and higher level information about a branch or the company as a whole.

This chapter discusses:

- Forecast performance evaluation criteria.

- Forecasting methods.

- Forecast evaluations.

- Forecast management and demand patterns.

### Forecast Performance Evaluation Criteria

Depending on the selection of processing options and on trends and patterns in the sales data, some forecasting methods perform better than others for a given historical data set. A forecasting method that is appropriate for one product might not be appropriate for another product. You might find that a forecasting method that provides good results at one stage of a product life cycle remains appropriate throughout the entire life cycle.

You can select between two methods to evaluate the current performance of the forecasting methods:

- Percent of accuracy (POA).

- Mean absolute deviation (MAD).

Both of these performance evaluation methods require historical sales data for a period of time that you specify. This period of time is called a holdout period or period of best fit. The data in this period is used as the basis for recommending which forecasting method to use in making the next forecast projection. This recommendation is specific to each product and can change from one forecast generation to the next.

Best Fit

The system recommends the best fit forecast by applying the selected forecasting methods to past sales order history and comparing the forecast simulation to the actual history. When you generate a best fit forecast, the system compares actual sales order histories to forecasts for a specific time period and computes how accurately each different forecasting method predicted sales. Then the system recommends the most accurate forecast as the best fit. This graphic illustrates best fit forecasts:

Best fit forecast

The system uses this sequence of steps to determine the best fit:

1. Use each specified method to simulate a forecast for the holdout period.

2. Compare actual sales to the simulated forecasts for the holdout period.

3. Calculate the POA or the MAD to determine which forecasting method most closely matches the past actual sales.

   The system uses either POA or MAD, based on the processing options that you select.

4. Recommend a best fit forecast by the POA that is closest to 100 percent (over or under) or the MAD that is closest to zero.

### Forecasting Methods

JD Edwards EnterpriseOne Forecast Management uses 12 methods for quantitative forecasting and indicates which method provides the best fit for the forecasting situation.

This section discusses:

- Method 1: Percent Over Last Year.

- Method 2: Calculated Percent Over Last Year.

- Method 3: Last Year to This Year.

- Method 4: Moving Average.

- Method 5: Linear Approximation.

- Method 6: Least Squares Regression.

- Method 7: Second Degree Approximation.

- Method 8: Flexible Method.

- Method 9: Weighted Moving Average.

- Method 10: Linear Smoothing.

- Method 11: Exponential Smoothing.

- Method 12: Exponential Smoothing with Trend and Seasonality.

Specify the method that you want to use in the processing options for the Forecast Generation program (R34650). Most of these methods provide limited control. For example, the weight placed on recent historical data or the date range of historical data that is used in the calculations can be specified by you.

Note. The examples in the guide indicate the calculation procedure for each of the available forecasting methods, given an identical set of historical data.

The method examples in the guide use part or all of these data sets, which is historical data from the past two years. The forecast projection goes into next year.

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 (one year ago) | 128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137
2 (two years ago) | 125 | 123 | 115 | 137 | 122 | 130 | 141 | 128 | 118 | 123 | 139 | 133

This sales history data is stable with small seasonal increases in July and December. This pattern is characteristic of a mature product that might be approaching obsolescence.

#### Method 1: Percent Over Last Year

This method uses the Percent Over Last Year formula to multiply each forecast period by the specified percentage increase or decrease.

To forecast demand, this method requires the number of periods for the best fit plus one year of sales history. This method is useful to forecast demand for seasonal items with growth or decline.

Example: Method 1: Percent Over Last Year

The Percent Over Last Year formula multiplies sales data from the previous year by a factor you specify and then projects that result over the next year. This method might be useful in budgeting to simulate the affect of a specified growth rate or when sales history has a significant seasonal component.

Forecast specifications: Multiplication factor. For example, specify 110 in the processing option to increase the previous year's sales history data by 10 percent.

Required sales history: One year for calculating the forecast, plus the number of time periods that are required for evaluating the forecast performance (periods of best fit) that you specify.

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | 128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137

This table shows the forecast for next year, 110 Percent Over Last Year:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
141 | 129 | 127 | 138 | 134 | 151 | 154 | 142 | 144 | 125 | 131 | 151

January forecast equals 128 × 1.1 = 140.8 rounded to 141.

February forecast equals 117 × 1.1 = 128.7 rounded to 129.

March forecast equals 115 × 1.1 = 126.5 rounded to 127.

#### Method 2: Calculated Percent Over Last Year

This method uses the Calculated Percent Over Last Year formula to compare the past sales of specified periods to sales from the same periods of the previous year. The system determines a percentage increase or decrease, and then multiplies each period by the percentage to determine the forecast.

To forecast demand, this method requires the number of periods of sales order history plus one year of sales history. This method is useful to forecast short term demand for seasonal items with growth or decline.

Example: Method 2: Calculated Percent Over Last Year

The Calculated Percent Over Last Year formula multiplies sales data from the previous year by a factor that is calculated by the system, and then it projects that result for the next year. This method might be useful in projecting the affect of extending the recent growth rate for a product into the next year while preserving a seasonal pattern that is present in sales history.

Forecast specifications: Range of sales history to use in calculating the rate of growth. For example, specify n equals 4 in the processing option to compare sales history for the most recent four periods to those same four periods of the previous year. Use the calculated ratio to make the projection for the next year.

Required sales history: One year for calculating the forecast plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation, given n = 4:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | 128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137
2 | None | None | None | None | None | None | None | None | 118 | 123 | 139 | 133

Calculation of Percent Over Last Year, given n = 4.

Past year 2 equals 118 + 123 + 139 + 133 = 513.

Past year 1 equals 131 + 114 + 119 + 137 = 501.

ratio percent = (501/513) × 100 percent = 97.66 percent.

This table is the forecast for next year, 97.66 Percent Over Last Year:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
125 | 114 | 112 | 122 | 119 | 134 | 137 | 126 | 128 | 111 | 116 | 134

January forecast equals 128 × 0.9766 = 125.00 rounded to 125.

February forecast equals 117 × 0.9766 = 114.26 rounded to 114.

March forecast equals 115 × 0.9766 = 112.31 rounded to 112.

#### Method 3: Last Year to This Year

This method uses last year's sales for the next year's forecast.

To forecast demand, this method requires the number of periods best fit plus one year of sales order history. This method is useful to forecast demand for mature products with level demand or seasonal demand without a trend.

Example: Method 3: Last Year to This Year

The Last Year to This Year formula copies sales data from the previous year to the next year. This method might be useful in budgeting to simulate sales at the present level. The product is mature and has no trend over the long run, but a significant seasonal demand pattern might exist.

Forecast specifications: None.

Required sales history: One year for calculating the forecast plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | 128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137

This table is the forecast for next year, Last Year to This Year:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137

January forecast equals January of last year with a forecast value of 128.

February forecast equals February of last year with a forecast value of 117.

March forecast equals March of last year with a forecast value of 115.

#### Method 4: Moving Average

This method uses the Moving Average formula to average the specified number of periods to project the next period. You should recalculate it often (monthly, or at least quarterly) to reflect changing demand level.

To forecast demand, this method requires the number of periods best fit plus the number of periods of sales order history. This method is useful to forecast demand for mature products without a trend.

Example: Method 4: Moving Average

Moving Average (MA) is a popular method for averaging the results of recent sales history to determine a projection for the short term. The MA forecast method lags behind trends. Forecast bias and systematic errors occur when the product sales history exhibits strong trend or seasonal patterns. This method works better for short range forecasts of mature products than for products that are in the growth or obsolescence stages of the life cycle.

Forecast specifications: n equals the number of periods of sales history to use in the forecast calculation. For example, specify n = 4 in the processing option to use the most recent four periods as the basis for the projection into the next time period. A large value for n (such as 12) requires more sales history. It results in a stable forecast, but is slow to recognize shifts in the level of sales. Conversely, a small value for n (such as 3) is quicker to respond to shifts in the level of sales, but the forecast might fluctuate so widely that production cannot respond to the variations.

Required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

Calculation of Moving Average, given n = 4

(131 + 114 + 119 + 137) / 4 = 125.25 rounded to 125.

This table is the Moving Average forecast for next year, given n = 4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
125 | 124 | 126 | 128 | 126 | 126 | 127 | 127 | 126 | 126 | 126 | 126

January forecast equals (131 + 114 + 119 + 137) / 4 = 125.25 rounded to 125.

February forecast equals (114 + 119 + 137 + 125) / 4 = 123.75 rounded to 124.

March forecast equals (119 + 137 + 125 + 124) / 4 = 126.25 rounded to 126.

#### Method 5: Linear Approximation

This method uses the Linear Approximation formula to compute a trend from the number of periods of sales order history and to project this trend to the forecast. You should recalculate the trend monthly to detect changes in trends.

This method requires the number of periods of best fit plus the number of specified periods of sales order history. This method is useful to forecast demand for new products, or products with consistent positive or negative trends that are not due to seasonal fluctuations.

Example: Method 5: Linear Approximation

Linear Approximation calculates a trend that is based upon two sales history data points. Those two points define a straight trend line that is projected into the future. Use this method with caution because long range forecasts are leveraged by small changes in just two data points.

Forecast specifications: n equals the data point in sales history that is compared to the most recent data point to identify a trend. For example, specify n = 4 to use the difference between December (most recent data) and August (four periods before December) as the basis for calculating the trend.

Minimum required sales history: n plus 1 plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 129 | 131 | 114 | 119 | 137

Calculation of Linear Approximation, given n = 4

(137 – 129) / 4 = 2.0

This table is the Linear Approximation forecast for next year, given n = 4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
139 | 141 | 143 | 145 | 147 | 149 | 151 | 153 | 155 | 157 | 159 | 161

January forecast = December of past year 1 + (Trend) which equals 137 + (1 × 2) = 139.

February forecast = December of past year 1 + (Trend) which equals 137 + (2 × 2) = 141.

March forecast = December of past year 1 + (Trend) which equals 137 + (3 × 2) = 143.

#### Method 6: Least Squares Regression

The Least Squares Regression (LSR) method derives an equation describing a straight line relationship between the historical sales data and the passage of time. LSR fits a line to the selected range of data so that the sum of the squares of the differences between the actual sales data points and the regression line are minimized. The forecast is a projection of this straight line into the future.

This method requires sales data history for the period that is represented by the number of periods best fit plus the specified number of historical data periods. The minimum requirement is two historical data points. This method is useful to forecast demand when a linear trend is in the data.

Example: Method 6: Least Squares Regression

Linear Regression, or Least Squares Regression (LSR), is the most popular method for identifying a linear trend in historical sales data. The method calculates the values for a and b to be used in the formula:

Y = a + b X

This equation describes a straight line, where Y represents sales and X represents time. Linear regression is slow to recognize turning points and step function shifts in demand. Linear regression fits a straight line to the data, even when the data is seasonal or better described by a curve. When sales history data follows a curve or has a strong seasonal pattern, forecast bias and systematic errors occur.

Forecast specifications: n equals the periods of sales history that will be used in calculating the values for a and b. For example, specify n = 4 to use the history from September through December as the basis for the calculations. When data is available, a larger n (such as n = 24) would ordinarily be used. LSR defines a line for as few as two data points. For this example, a small value for n ( n = 4) was chosen to reduce the manual calculations that are required to verify the results.

Minimum required sales history: n periods plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

This table is the calculation of Linear Regression Coefficients, given n = 4:

Month and Year | X | Y | XY | X2
September | 1 | 131 | 131 | 1
October | 2 | 114 | 228 | 4
November | 3 | 119 | 357 | 9
December | 4 | 137 | 548 | 16
Totals (Σ) | ΣX = 10 | ΣY = 501 | ΣXY = 1264 | ΣX2 = 30

b = (nΣXY–ΣXΣY) / (nΣX2– (ΣX)2

b = [4 (1264) – (10×501)] / [4 (30) – (10)2

b = (5056 – 5010) / (120 – 100)

b= 46 / 20 = 2.3

a = (ΣY / n) – b (ΣX / n)

a = (501 / 4) – [(2.3)(10 / 4)] = 119.5

This table is the Linear Regression forecast for next year, given Y = 119.5 – 2.3 X, where X = 1 ≧ September of past year 1:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
131 | 133 | 136 | 138 | 140 | 143 | 145 | 147 | 149 | 152 | 154 | 156

January forecast equals 119.5 + (5 × 2.3) = 131.

February forecast equals 119.5 + (6 × 2.3) = 133.3 or 133.

March forecast equals 119.5 + (7 × 2.3) = 135.6 rounded to 136.

#### Method 7: Second Degree Approximation

To project the forecast, this method uses the Second Degree Approximation formula to plot a curve that is based on the number of periods of sales history.

This method requires the number of periods best fit plus the number of periods of sales order history times three. This method is not useful to forecast demand for a long-term period.

Example: Method 7: Second Degree Approximation

Linear Regression determines values for a and b in the forecast formula Y = a + b X with the objective of fitting a straight line to the sales history data. Second Degree Approximation is similar, but this method determines values for a, b, and c in the this forecast formula:

Y = a + b X + c X2

The objective of this method is to fit a curve to the sales history data. This method is useful when a product is in the transition between life cycle stages. For example, when a new product moves from introduction to growth stages, the sales trend might accelerate. Because of the second order term, the forecast can quickly approach infinity or drop to zero (depending on whether coefficient c is positive or negative). This method is useful only in the short term.

Forecast specifications: the formula find a, b, and c to fit a curve to exactly three points. You specify n, the number of time periods of data to accumulate into each of the three points. In this example, n = 3. Actual sales data for April through June is combined into the first point, Q1. July through September are added together to create Q2, and October through December sum to Q3. The curve is fitted to the three values Q1, Q2, and Q3.

Required sales history: 3 × n periods for calculating the forecast plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137

Q0 = (Jan) + (Feb) + (Mar)

Q1 = (Apr) + (May) + (Jun) which equals 125 + 122 + 137 = 384

Q2 = (Jul) + (Aug) + (Sep) which equals 140 + 129 + 131 = 400

Q3 = (Oct) + (Nov) + (Dec) which equals 114 + 119 + 137 = 370

The next step involves calculating the three coefficients a, b, and c to be used in the forecasting formula Y = a + b X + c X2 .

Q1, Q2, and Q3 are presented on the graphic, where time is plotted on the horizontal axis. Q1 represents total historical sales for April, May, and June and is plotted at X = 1; Q2 corresponds to July through September; Q3 corresponds to October through December; and Q4 represents January through March. This graphic illustrates the plotting of Q1, Q2, Q3, and Q4 for second degree approximation:

Plotting Q1, Q2, Q3, and Q4 for second degree approximation

Three equations describe the three points on the graph:

(1) Q1 = a + b X + c X2 where X = 1(Q1 = a + b + c)

(2) Q2 = a + b X + c X2 where X = 2(Q2 = a + 2b + 4c)

(3) Q3 = a + b X + c X2 where X = 3(Q3 = a + 3b + 9c)

Solve the three equations simultaneously to find b, a, and c:

1. Subtract equation 1 (1) from equation 2 (2) and solve for b:

   (2) – (1) = Q2 – Q1 = b + 3c

   b = (Q2 – Q1) – 3c

2. Substitute this equation for b into equation (3):

   (3) Q3 = a + 3[(Q2 – Q1) – 3c] + 9c a = Q3 – 3(Q2 – Q1)

3. Finally, substitute these equations for a and b into equation (1):

   (1)[Q3 – 3(Q2 – Q1)] + [(Q2 – Q1) – 3c] + c = Q1

   c = [(Q3 – Q2) + (Q1 – Q2)] / 2

The Second Degree Approximation method calculates a, b, and c as follows:

a = Q3 – 3(Q2 – Q1) = 370 – 3(400 – 384) = 370 – 3(16) = 322

b = (Q2 – Q1) –3c = (400 – 384) – (3 × –23) = 16 + 69 = 85

c = [(Q3 – Q2) + (Q1 – Q2)] / 2 = [(370 – 400) + (384 – 400)] / 2 = –23

This is a calculation of second degree approximation forecast:

Y =a+bX + cX 2 = 322 + 85X + (–23) (X2)

When X = 4, Q4 = 322 + 340 – 368 = 294. The forecast equals 294 / 3 = 98 per period.

When X = 5, Q5 = 322 + 425 – 575 = 172. The forecast equals 172 / 3 = 58.33 rounded to 57 per period.

When X = 6, Q6 = 322 + 510 – 828 = 4. The forecast equals 4 / 3 = 1.33 rounded to 1 per period.

This is the forecast for next year, Last Year to This Year:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
98 | 98 | 98 | 57 | 57 | 57 | 1 | 1 | 1 | NA | NA | NA

#### Method 8: Flexible Method

This method enables you to select the best fit number of periods of sales order history that starts n months before the forecast start date, and to apply a percentage increase or decrease multiplication factor with which to modify the forecast. This method is similar to Method 1, Percent Over Last Year, except that you can specify the number of periods that you use as the base.

Depending on what you select as n, this method requires periods best fit plus the number of periods of sales data that is indicated. This method is useful to forecast demand for a planned trend.

Example: Method 8: Flexible Method

The Flexible Method (Percent Over n Months Prior) is similar to Method 1, Percent Over Last Year. Both methods multiply sales data from a previous time period by a factor specified by you, and then project that result into the future. In the Percent Over Last Year method, the projection is based on data from the same time period in the previous year. You can also use the Flexible Method to specify a time period, other than the same period in the last year, to use as the basis for the calculations.

Forecast specifications:

- Multiplication factor. For example, specify 110 in the processing option to increase previous sales history data by 10 percent.

- Base period. For example, n = 4 causes the first forecast to be based on sales data in September of last year.

Minimum required sales history: the number of periods back to the base period plus the number of time periods that is required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

This is the forecast for next year, 110 percent Over n = 4 months prior:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
144 | 125 | 131 | 151 | 159 | 138 | 144 | 166 | 174 | 152 | 158 | 182

#### Method 9: Weighted Moving Average

The Weighted Moving Average formula is similar to Method 4, Moving Average formula, because it averages the previous month's sales history to project the next month's sales history. However, with this formula you can assign weights for each of the prior periods.

This method requires the number of weighted periods selected plus the number of periods best fit data. Similar to Moving Average, this method lags behind demand trends, so this method is not recommended for products with strong trends or seasonality. This method is useful to forecast demand for mature products with demand that is relatively level.

Example: Method 9: Weighted Moving Average

The Weighted Moving Average (WMA) method is similar to Method 4, Moving Average (MA). However, you can assign unequal weights to the historical data when using WMA. The method calculates a weighted average of recent sales history to arrive at a projection for the short term. More recent data is usually assigned a greater weight than older data, so WMA is more responsive to shifts in the level of sales. However, forecast bias and systematic errors occur when the product sales history exhibits strong trends or seasonal patterns. This method works better for short range forecasts of mature products than for products in the growth or obsolescence stages of the life cycle.

Forecast specifications:

- The number of periods of sales history (n) to use in the forecast calculation.

  For example, specify n = 4 in the processing option to use the most recent four periods as the basis for the projection into the next time period. A large value for n (such as 12) requires more sales history. Such a value results in a stable forecast, but it is slow to recognize shifts in the level of sales. Conversely, a small value for n (such as 3) responds more quickly to shifts in the level of sales, but the forecast might fluctuate so widely that production cannot respond to the variations.

- The weight that is assigned to each of the historical data periods.

  The assigned weights must total 1.00. For example, when n = 4, assign weights of 0.50, 0.25, 0.15, and 0.10 with the most recent data receiving the greatest weight.

Minimum required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

This is the calculation of Moving Average, given n = 4:

[(131 × 0.10) + (114 × 0.15) + (119 × 0.25) + (137 × 0.50)] / (0.10 + 0.15 + 0.25 + 0.50) = 128.45 rounded to 128

This is the Weighted Moving Average forecast for next year, given n = 4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
128 | 128 | 128 | 129 | 129 | 129 | 129 | 129 | 129 | 129 | 129 | 129

January forecast equals [(131 × 0.10) + (114 × 0.15) + (119 × 0.25) + (137 × 0.50)] / (0.10 + 0.15+ 0.25 + 0.50) = 128.45 rounded to 128.

February forecast equals [(114 × 0.10) + (119 × 0.15) + (137 × 0.25) + (128 × 0.50)] / 1 = 127.5 rounded to 128.

March forecast equals [(119 × 0.10) + (137 × 0.15) + (128 × 0.25) + (128 × 0.50)] / 1 = 128.45 rounded to 128.

#### Method 10: Linear Smoothing

This method calculates a weighted average of past sales data. In the calculation, this method uses the number of periods of sales order history (from 1 to 12) that is indicated in the processing option. The system uses a mathematical progression to weigh data in the range from the first (least weight) to the final (most weight). Then the system projects this information to each period in the forecast.

This method requires the month's best fit plus the sales order history for the number of periods that are specified in the processing option.

Example: Method 10: Linear Smoothing

This method is similar to Method 9, WMA. However, instead of arbitrarily assigning weights to the historical data, a formula is used to assign weights that decline linearly and sum to 1.00. The method then calculates a weighted average of recent sales history to arrive at a projection for the short term. Like all linear moving average forecasting techniques, forecast bias and systematic errors occur when the product sales history exhibits strong trend or seasonal patterns. This method works better for short range forecasts of mature products than for products in the growth or obsolescence stages of the life cycle.

Forecast specifications:

n equals the number of periods of sales history to use in the forecast calculation. For example, specify n equals 4 in the processing option to use the most recent four periods as the basis for the projection into the next time period. The system automatically assigns the weights to the historical data that decline linearly and sum to 1.00. For example, when n equals 4, the system assigns weights of 0.4, 0.3, 0.2, and 0.1, with the most recent data receiving the greatest weight.

Minimum required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

Here are the Calculation of Weights, given n = 4:

(n2 + n) / 2 = (16 + 4) / 2 = 10

Month | Weight
September | 1 / 10
October | 2 / 10
November | 3 / 10
December | 4 / 10
Total Weight | 10 / 10

This is the calculation of Moving Average, given n = 4:

[(131 * 0.1) + (114 * 0.2) + (119 * 0.3) + (137 * 0.4)] / (0.1 + 0.0.2 + 0.3 + 0.4) = 126.4 rounded to 126.

This table is the Linear Smoothing forecast for next year, given n = 4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
126 | 127 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128

#### Method 11: Exponential Smoothing

This method calculates a smoothed average, which becomes an estimate representing the general level of sales over the selected historical data periods.

This method requires sales data history for the time period that is represented by the number of periods best fit plus the number of historical data periods that are specified. The minimum requirement is two historical data periods. This method is useful to forecast demand when no linear trend is in the data.

Example: Method 11: Exponential Smoothing

This method is similar to Method 10, Linear Smoothing. In Linear Smoothing, the system assigns weights that decline linearly to the historical data. In Exponential Smoothing, the system assigns weights that exponentially decay. The equation for Exponential Smoothing forecasting is:

Forecast = α (Previous Actual Sales) + (1 – α) (Previous Forecast)

The forecast is a weighted average of the actual sales from the previous period and the forecast from the previous period. Alpha is the weight that is applied to the actual sales for the previous period. (1 – α) is the weight that is applied to the forecast for the previous period. Values for alpha range from 0 to 1 and usually fall between 0.1 and 0.4. The sum of the weights is 1.00 (α + (1 – α) = 1).

You should assign a value for the smoothing constant, alpha. If you do not assign a value for the smoothing constant, the system calculates an assumed value that is based on the number of periods of sales history that is specified in the processing option.

Forecast specifications:

- α equals the smoothing constant that is used to calculate the smoothed average for the general level or magnitude of sales.

  Values for alpha range from 0 to 1.

- n equals the range of sales history data to include in the calculations.

  Generally, one year of sales history data is sufficient to estimate the general level of sales. For this example, a small value for n (n = 4) was chosen to reduce the manual calculations that are required to verify the results. Exponential Smoothing can generate a forecast that is based on as little as one historical data point.

Minimum required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | None | 131 | 114 | 119 | 137

This table is the calculation of Exponential Smoothing, given n = 4, α = 0.3:

Month | Calculation
October Smoothed Average* | = September Actual = α (September Actual) + (1 –α) September Smoothed Average = 1 * (131) + (0) (0) = 131
November Smoothed Average | = 0.3 (October Actual) + (1 – 0.3) October Smoothed Average = 0.3 (114) + 0.7 (131) = 125.9 rounded to 126
December Smoothed Average | = 0.3 (November Actual) + 0.7 (November Smoothed Average) = 0.3 (119) + 0.7 (126) = 123.9 or 124
January Forecast | = 0.3 (December Actual) + 0.7 (December Smoothed Average) = 0.3 (137) + 0.7 (124) = 127.9 or 128
February Forecast | = January Forecast
March Forecast | = January Forecast

* Exponential Smoothing is initialized by setting the first smoothed average equal to the first specified actual sales data point. In effect, α = 1.0 for the first iteration. For subsequent calculations, alpha is set to the value that is specified in the processing option.

This table is the Exponential Smoothing forecast for next year, given α = 0.3, n = 4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128 | 128

#### Method 12: Exponential Smoothing with Trend and Seasonality

This method calculates a trend, a seasonal index, and an exponentially smoothed average from the sales order history. The system then applies a projection of the trend to the forecast and adjusts for the seasonal index.

This method requires the number of periods best fit plus two years of sales data, and is useful for items that have both trend and seasonality in the forecast. You can enter the alpha and beta factor, or have the system calculate them. Alpha and beta factors are the smoothing constant that the system uses to calculate the smoothed average for the general level or magnitude of sales (alpha) and the trend component of the forecast (beta).

Example: Method 12: Exponential Smoothing with Trend and Seasonality

This method is similar to Method 11, Exponential Smoothing, in that a smoothed average is calculated. However, Method 12 also includes a term in the forecasting equation to calculate a smoothed trend. The forecast is composed of a smoothed average that is adjusted for a linear trend. When specified in the processing option, the forecast is also adjusted for seasonality.

Forecast specifications:

- Alpha equals the smoothing constant that is used in calculating the smoothed average for the general level or magnitude of sales.

  Values for alpha range from 0 to 1.

- Beta equals the smoothing constant that is used in calculating the smoothed average for the trend component of the forecast.

  Values for beta range from 0 to 1.

- Whether a seasonal index is applied to the forecast.

  Note. Alpha and beta are independent of one another. They do not have to sum to 1.0.

Minimum required sales history: One year plus the number of time periods that are required to evaluate the forecast performance (periods of best fit). When two or more years of historical data is available, the system uses two years of data in the calculations.

Method 12 uses two Exponential Smoothing equations and one simple average to calculate a smoothed average, a smoothed trend, and a simple average seasonal index.

An exponentially smoothed average:

An exponentially smoothed trend:

A simple average seasonal index:

The forecast is then calculated by using the results of the three equations:

where:

- L is the length of seasonality (L equals 12 months or 52 weeks).

- t is the current time period.

- m is the number of time periods into the future of the forecast.

- S is the multiplicative seasonal adjustment factor that is indexed to the appropriate time period.

  This table lists history used in the forecast calculation:

  Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Total
  1 | 128 | 117 | 115 | 125 | 122 | 137 | 140 | 129 | 131 | 114 | 119 | 137 | 1514
  2 | 125 | 123 | 115 | 137 | 122 | 130 | 141 | 128 | 118 | 123 | 139 | 133 | 1534

  Calculation of Linear and Seasonal Exponential Smoothing, given alpha = 0.3, beta = 0.4

Initializing the Process:

January of past year 1 Seasonal Index, S1 =

S1 = (125 + 128 / 1534 + 1514) × 12 = 0.083005 × 12 = 0.9961

January of past year 1 Smoothed Average*, A1 =

A1 = (January of past year 1 Actual) / (January Seasonal Index)

A1 = 128 / 0.9960

A1 = 128.51

January of past year 1 Smoothed Trend*, T1 =

T1 = 0 insufficient information to calculate first smoothed trend

February of past year 1 Seasonal Index, S2 =

S2 = (123 + 117 / 1534 + 1514) × 12 = 0.07874 × 12 = 0.9449

February of past year 1 Smoothed Average, A2 =

A2 = α(D2 / S2 ) + (1 – α) (A1 + T1 )

A2 = 0.3(117 / 0.9449) + (1 – 0.3) (128.51 + 0) = 127.10

February of past year 1 Smoothed Trend, T2 =

March of past year 1 Seasonal Index, S3 =

S3 = (115 + 115 / 1534 + 1514) × 12 = 0.07546 × 12=0.9055

March of past year 1 Smoothed Average, A3 =

A3 = α(D3/ S3) + (1 – α)(A2+ T2)

A3 = 0.3(115 / 0.9055) + (1– 0.3)(127.10 – 0.56) = 126.68

March of past year 1 Smoothed Trend, T3 =

T3 = β(A3 – A2) + (1 – β)T2

T3 = 0.4(126.68 – 127.10) + (1 – 0.4) x – 0.56 = – 0.50

(Continue through December of past year 1)

December of past year 1 Seasonal Index, S12 =

S12 = (133 + 137 / 1534 + 1514) × 12 = 0.08858 × 12 = 1.0630

December of past year 1 Smoothed Average, A12 =

A12 = α (D12/S12) + (1 – α)( A11 + T11)

A12 = 0.3 (137/1.0630 ) + ( 1 – 0.3)( 124.64 – 1.121 ) = 125.13)

December of past year 1 Smoothed Trend, T12 =

T12 = β (A 12 – A11) + (1 – β)T11

T12 = 0.4 (125.13 – 124.64) + ( 1 – 0.4) x – 1.121 = – 0.477

Calculation of linear and seasonal exponentially smoothed forecast is calculated as follows:

F t + m = (At + Tt m )St – L + m

* Calculations for Exponential Smoothing with Trend and Seasonality are initialized by setting the first smoothed average equal to the deseasonalized first actual sales data. The trend is initialized at zero for the first iteration. For subsequent calculations, alpha and beta are set to the values that are specified in the processing options.

This table indicates the Exponential Smoothing with Trend and Seasonality forecast for next year, where alpha = 0.3, beta = 0.4:

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
124.16 | 117.33 | 112.01 | 127.10 | 117.91 | 128.52 | 134.73 | 122.74 | 118.45 | 121.77 | 121.77 | 126.92

### Forecast Evaluations

This section provides an overview of Forecast Evaluations and discusses:

- MAD

- POA

You can select forecasting methods to generate as many as 12 forecasts for each product. Each forecasting method might create a slightly different projection. When thousands of products are forecast, a subjective decision is impractical regarding which forecast to use in the plans for each product.

The system automatically evaluates performance for each forecasting method that you select and for each product that you forecast. You can select between two performance criteria: MAD and POA. MAD is a measure of forecast error. POA is a measure of forecast bias. Both of these performance evaluation techniques require actual sales history data for a period of time specified by you. The period of recent history used for evaluation is called a holdout period or period of best fit.

To measure the performance of a forecasting method, the system:

- Uses the forecast formulas to simulate a forecast for the historical holdout period.

- Makes a comparison between the actual sales data and the simulated forecast for the holdout period.

When you select multiple forecast methods, this same process occurs for each method. Multiple forecasts are calculated for the holdout period and compared to the known sales history for that same period of time. The forecasting method that produces the best match (best fit) between the forecast and the actual sales during the holdout period is recommended for use in the plans. This recommendation is specific to each product and might change each time that you generate a forecast.

#### Mean Absolute Deviation

Mean Absolute Deviation (MAD) is the mean (or average) of the absolute values (or magnitude) of the deviations (or errors) between actual and forecast data. MAD is a measure of the average magnitude of errors to expect, given a forecasting method and data history. Because absolute values are used in the calculation, positive errors do not cancel out negative errors. When comparing several forecasting methods, the one with the smallest MAD is the most reliable for that product for that holdout period. When the forecast is unbiased and errors are normally distributed, a simple mathematical relationship exists between MAD and two other common measures of distribution, which are standard deviation and Mean Squared Error. For example:

- MAD = (Σ│(Actual) – (Forecast)│)n

- Standard Deviation, (σ) ≅ 1.25 MAD

- Mean Squared Error ≅ –σ2

This example indicates the calculation of MAD for two of the forecasting methods. This example assumes that you have specified in the processing option that the holdout period length (periods of best fit) is equal to five periods.

Method 1: Last Year to This Year

This table is history used in the calculation of MAD, given Periods of Best Fit = 5:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
2 | None | None | None | None | None | None | None | 128 | 118 | 123 | 139 | 133

This table is the 110 Percent Over Last Year forecast for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 141 | 130 | 135 | 153 | 146

This table is the Actual Sales History for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 129 | 131 | 114 | 119 | 137

This table is the Absolute Value of Errors, (Actual) – (Forecast):

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 12 | 1 | 21 | 34 | 9

Mean Absolute Deviation = (12 + 1 + 21 + 34 + 9) / 5 = 15.4

Method 4: Moving Average, n = 4

This table is history used in the Calculation of MAD, given Periods of Best Fit = 5, n = 4:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | 125 | 122 | 137 | 140 | None | None | None | None | None

This is the Moving Average calculation for the Holdout Period, given n = 4:

Calculation | Month
(125 + 122 + 137 + 140) / 4 = 131 | August
(122 + 137 + 140 + 129) / 4 = 132 | September
(137 + 140 + 129 + 131) / 4 = 134.25 or 134 | October
(140 + 129 + 131 + 114) / 4 = 128.5 or 129 | November
(129 + 131 + 114 + 119) / 4 = 123.25 or 123 | December

This table is the results of the Moving Forecast Average calculation:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 131 | 132 | 134 | 129 | 123

This table is the Actual Sales History for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 129 | 131 | 114 | 119 | 137

This table is the Absolute Value of Errors (Actual – Forecast):

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 2 | 1 | 20 | 10 | 14

Mean Absolute Deviation equals (2 + 1 + 20 + 10 + 14) / 5 = 9.4.

Based on these two choices, the Moving Average, n = 4 method is recommended because it has the smaller MAD, 9.4, for the given holdout period.

#### Percent of Accuracy

Percent of Accuracy (POA) is a measure of forecast bias. When forecasts are consistently too high, inventories accumulate and inventory costs rise. When forecasts are consistently too low, inventories are consumed and customer service declines. A forecast that is 10 units too low, then 8 units too high, then 2 units too high is an unbiased forecast. The positive error of 10 is canceled by negative errors of 8 and 2.

(Error) = (Actual) – (Forecast)

When a product can be stored in inventory, and when the forecast is unbiased, a small amount of safety stock can be used to buffer the errors. In this situation, eliminating forecast errors is not as important as generating unbiased forecasts. However, in service industries, the previous situation is viewed as three errors. The service is understaffed in the first period, and then overstaffed for the next two periods. In services, the magnitude of forecast errors is usually more important than is forecast bias.

POA = [(ΣActual sales during holdout period) / (ΣForecast sales during holdout period)] × 100 percent

The summation over the holdout period enables positive errors to cancel negative errors. When the total of actual sales exceeds the total of forecast sales, the ratio is greater than 100 percent. Of course, the forecast cannot be more than 100 percent accurate. When a forecast is unbiased, the POA ratio is 100 percent. A 95 percent accuracy rate is more desirable than a 110 percent accurate rate. The POA criterion selects the forecasting method that has a POA ratio that is closest to 100 percent.

This example indicates the calculation of POA for two forecasting methods. This example assumes that you have specified in the processing option that the holdout period length (periods of best fit) is equal to five periods.

Method 1: Last Year to This Year

This table is history used in the calculation of MAD, given Periods of Best Fit = 5:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
2 | None | None | None | None | None | None | None | 128 | 118 | 123 | 139 | 133

This table is the 110 Percent Over Last Year forecast for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 141 | 130 | 135 | 153 | 146

This table is the Actual Sales History for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 129 | 131 | 114 | 119 | 137

Sum of Actuals equals (129 + 131 + 114 + 119 + 137) = 630.

Sum of Forecasts equals (141 + 130 + 135 + 153 + 146) = 705.

POA ratio equals (630 / 705) × 100 percent = 89.36 percent.

Method 4: Moving Average, n = 4

This table is history used in the Calculation of MAD, given Periods of Best Fit = 5, n = 4:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | 125 | 122 | 137 | 140 | None | None | None | None | None

This is the Moving Average forecast for the Holdout Period, Given n = 4:

Calculation | Month
(125 + 122 + 137 + 140) / 4 = 131 | August
(122 + 137 + 140 + 129) / 4 = 132 | September
(137 + 140 + 129 + 131) / 4 = 134.25 or 134 | October
(140 + 129 + 131 + 114) / 4 = 128.5 or 129 | November
(129 + 131 + 114 + 119) / 4 = 123.25 or 123 | December

This table is the results of the Moving Forecast Average:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 131 | 132 | 134 | 129 | 123

This table is the Actual Sales History for the Holdout Period:

Past Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec
1 | None | None | None | None | None | None | None | 129 | 131 | 114 | 119 | 137

Sum of Actuals equals (129 + 131 + 114 + 119 + 137) = 630.

Sum of Forecasts equals (131 + 132 + 134 + 129 + 123) = 649.

POA ratio equals (630 / 649) * 100 percent = 97.07 percent.

Based on these two choices, the Moving Average, n = 4 method is recommended because it has POA closest to 100 percent for the given holdout period.

### Forecast Management and Demand Patterns

JD Edwards EnterpriseOne Forecast Management uses sales order history to predict future demand. This section discusses:

- Six typical demand patterns.

- Forecast accuracy.

- Forecast considerations.

- Forecasting process.

Forecast methods available in JD Edwards EnterpriseOne Forecast Management are tailored for these demand patterns.

#### Six Typical Demand Patterns

This graphic illustrates the six typical demand patterns:

Charting six typical demand patterns

You can forecast the independent demand of information for which you have past data:

- Samples

- Promotional items

- Customer orders

- Service parts

- Interplant demands

You can also forecast demand for manufacturing strategy types by using the manufacturing environments in which they are produced:

This table presents manufacturing strategies:

Manufacturing Strategy | Description
Make-to-stock | The manufacture of end items that meet the customer demand, which occurs after the product is completed.
Assemble-to-order | The manufacture of subassemblies that meet customer option selections.
Make-to-order | The manufacture of raw materials and components that are stocked to reduce leadtime.

#### Forecast Accuracy

These statistical laws govern forecast accuracy:

- A long term forecast is less accurate than a short term forecast because the further into the future you project the forecast, the more variables can affect the forecast.

- A forecast for a product family tends to be more accurate than a forecast for individual members of the product family.

  Some errors cancel each other as the forecasts for individual items summarize into the group, thus creating a more accurate forecast.

#### Forecast Considerations

You should not rely exclusively on past data to forecast future demands. These circumstances might affect the business, and require you to review and modify the forecast:

- New products that have no past data.

- Plans for future sales promotion.

- Changes in national and international politics.

- New laws and government regulations.

- Weather changes and natural disasters.

- Innovations from competition.

- Economic changes.

You can use long term trend analysis to influence the design of the forecasts:

- Market surveys.

- Leading economic indicators.

#### Forecasting Process

You use the Refresh Actuals program (R3465) to copy data from the Sales Order History File table (F42119), the Sales Order Detail File table (F4211), or both, into either the Forecast File table (F3460) or the Forecast Summary File table (F3400), depending on the kind of forecast that you plan to generate.