## A.1 Forecast Calculation Methods

Twelve methods of calculating forecasts are available. Most of these techniques administer for limited user regulate. For example, the weight inserted on current historical information or the date array of historical information provided in the calculations can be stated. The adhering to examples show the calculation procedure for each of the available forespreading approaches, offered an similar set of historical data.

You are watching: For every forecasting problem, there is one best forecasting technique.

The adhering to examples usage the exact same 2004 and 2005 sales information to create a 2006 sales foreactors. In addition to the forecast calculation, each example consists of a simulated 2005 foreactors for a three month holdout duration (processing alternative 19 = "3") which is then provided for percent of accuracy and suppose absolute deviation calculations (actual sales compared to simulated forecast).

## A.2 Forecast Performance Evaluation Criteria

Depfinishing on your selection of processing alternatives and on the fads and patterns existing in the sales information, some forecasting techniques will certainly percreate better than others for a offered historical data collection. A forespreading technique that is proper for one product may not be appropriate for one more product. It is likewise unmost likely that a forespreading strategy that offers great results at one stage of a product"s life cycle will certainly remajor correct throughout the entire life cycle.

You deserve to pick in between two techniques to evaluate the existing performance of the forecasting techniques. These are Average Absolute Deviation (MAD) and also Percent of Accuracy (POA). Both of these performance evaluation techniques require historic sales data for a user stated period of time. This period of time is dubbed a holdout duration or durations finest fit (PBF). The information in this duration is used as the basis for recommending which of the forespreading approaches to usage in making the next foreactors projection. This referral is certain to each product, and may change from one foreactors generation to the following. The two foreactors performance testimonial methods are demonstrated in the peras complying with the examples of the twelve forespreading methods.

## A.3 Method 1 - Specified Percent Over Last Year

This approach multiplies sales data from the previous year by a user stated factor; for example, 1.10 for a 10% rise, or 0.97 for a 3% decrease.

Required sales history: One year for calculating the foreactors plus the user specified number of time periods for evaluating forecast performance (handling option 19).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128147
February132117135
March115115132
April137125144
May122122140
June130137158
July141129148
August128140161
September118131151
October123114131141.45
November139119137159.85
December133137158152.95

### A.3.1 Forecast Calculation

User stated aspect (handling choice 1a) = 1.15 in this instance.

### A.3.2 Simulated Foreactors Calculation

October, 2004 sales = 123 * 1.15 = 141.45

November, 2004 sales = 139 * 1.15 = 159.85

December, 2004 sales = 133 * 1.15 = 152.95

### A.3.3 Percent of Accuracy Calculation

POA = (141.45 + 159.85 + 152.95) / (114 + 119 + 137) * 100 = 454.25 / 370 = 122.770

### A.3.4 Typical Absolute Deviation Calculation

MADVERTISEMENT = (|141.45 - 114| + |159.85 - 119| + |152.95 - 137|) / 3 = (27.45 + 40.85 + 15.95) / 3 = 84.25/3 = 28.08

## A.4 Method 2 - Calculated Percent Over Last Year

This strategy multiplies sales information from the previous year by a element calculated by the system.

Required sales history: One year for calculating the foreactors plus the user mentioned number of time durations for evaluating foreactors performance (handling alternative 19).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128120
February132117110
March115115108
April137125117
May122122114
June130137128
July141129121
August128140131
September118131123
October123114107127.13178
November139119111143.66925
December133137128137.4677

### A.4.1 Foreactors Calculation

Range of sales background to usage in calculating growth variable (processing option 2a) = 3 in this instance.

Sum the final three months of 2005: 114 + 119 + 137 = 370

Sum the exact same 3 months for the previous year: 123 + 139 + 133 = 395

The calculated aspect = 370/395 = 0.9367

Calculate the forecasts:

January, 2005 sales = 128 * 0.9367 = 119.8036 or about 120

February, 2005 sales = 117 * 0.9367 = 109.5939 or about 110

March, 2005 sales = 115 * 0.9367 = 107.7205 or about 108

### A.4.2 Simulated Foreactors Calculation

Sum the 3 months of 2005 before holdout duration (July, Aug, Sept):

129 + 140 + 131 = 400

Sum the exact same three months for the previous year:

141 + 128 + 118 = 387

The calculated aspect = 400/387 = 1.033591731

Calculate simulated forecast:

October, 2004 sales = 123 * 1.033591731 = 127.13178

November, 2004 sales = 139 * 1.033591731 = 143.66925

December, 2004 sales = 133 * 1.033591731 = 137.4677

### A.4.3 Percent of Accuracy Calculation

POA = (127.13178 + 143.66925 + 137.4677) / (114 + 119 + 137) * 100 = 408.26873 / 370 * 100 = 110.3429

### A.4.4 Median Absolute Deviation Calculation

MADVERTISEMENT = (|127.13178 - 114| + |143.66925 - 119| + |137.4677- 137|) / 3 = (13.13178+ 24.66925 + 0.4677)/3 = 12.75624

## A.5 Method 3 - Last year to This Year

This method copies sales data from the previous year to the next year.

Required sales history: One year for calculating the forecast plus the variety of time durations stated for evaluating forecast performance (handling alternative 19).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128128
February132117117
March115115115
April137125125
May122122122
June130137137
July141129129
August128140140
September118131131
October123114114123
November139119119139
December133137137133

### A.5.1 Forecast Calculation

January 2005 sales = January 2006 forecast = 128

February 2005 sales = February 2006 forecast = 117

March 2005 sales = March 2006 foreactors = 115

### A.5.2 Simulated Foreactors Calculation

October 2004 sales = 123

November 2004 sales = 139

December 2004 sales = 133

### A.5.3 Percent of Accuracy Calculation

POA = (123 + 139 + 133) / (114 + 119 + 137) * 100 = 395/370 * 100 = 106.7567

### A.5.4 Mean Absolute Deviation Calculation

MAD = (|123-114| + |139 - 119| + |133 - 137|) / 3 = (9 + 20 + 4)/3 = 11

## A.6 Method 4 - Moving Average

This method averperiods a user mentioned number of months (handling alternative 4a) to project the following months demand.

Required sales history: Twice the number of durations to be contained in the average (processing option 4a), plus variety of time periods for evaluating foreactors performance (handling option 19).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128123
February132117126
March115115129
April137125126
May122122127
June130137127
July141129127
August128140127
September118131127
October123114127133.3333
November139119127128.3333
December133137127121.3333

### A.6.1 Forecast Calculation

Number of durations to be contained in the average (handling alternative 4a) = 3 in this example

For each month of the forecast, average the previous 3 month"s information.

January forecast: 114 + 119 + 137 = 370, 370 / 3 = 123.333 or 123

February forecast: 119 + 137 + 123 = 379, 379 / 3 = 126.333 or 126

March forecast: 137 + 123 + 126 = 379, 386 / 3 = 128.667 or 129

### A.6.2 Simulated Foreactors Calculation

October 2005 sales = (129 + 140 + 131)/3 = 133.3333

November 2005 sales = (140 + 131 + 114)/3 = 128.3333

December 2005 sales = (131 + 114 + 119)/3 = 121.3333

### A.6.3 Percent of Accuracy Calculation

POA = (133.3333 + 128.3333 + 121.3333) / (114 + 119 + 137) * 100 = 103.513

### A.6.4 Typical Absolute Deviation Calculation

MADVERTISEMENT = (|133.3333 - 114| + |128.3333 - 119| + |121.3333 - 137|) / 3 = 14.7777

## A.7 Method 5 - Linear Approximation

Liclose to Approximation calculates a trend based upon two sales history data points.

Those two points define a straight trend line that is projected right into the future. Use this technique through caution, as long selection forecasts are leveraged by little changes in just 2 data points.

Required sales history: The number of durations to include in regression (handling option 5a), plus 1 plus the variety of time periods for evaluating forecast performance (processing choice 19).

Month2004 Sales2005 Sales2006 SalesSimulated 2005 Forecast
January125128149
February132117160
March115115172
April137125183
May122122195
June130137206
July141129218
August128140229
September118131241
October123114252132
November139119264101
December133137275113

### A.7.1 Forecast Calculation

Number of durations to incorporate in regression (processing choice 5a) = 3 in this example

For each month of the foreactors, include the increase or decrease during the specified periods before holdout period the previous period.

January forecast: (137 - 114)/2 + 137 = 148.5 or 149

February forecast: (137 - 114)/2 * 2 + 137 = 160

March forecast: (137 - 114)/2 * 3 + 137 = 171.5 or 172

### A.7.2 Simulated Foreactors Calculation

October 2004 sales = (131 - 129) / 2 + 131 = 132

November 2004 sales = (114 - 140) / 2 + 114 = 101

December 2004 sales = (119 - 131) /2 + 119 = 113

### A.7.3 Percent of Accuracy Calculation

POA = (132 + 101 + 113) / (114 + 119 + 137) * 100 = 93.5135

### A.7.4 Average Absolute Deviation Calculation

MAD = (|132 - 114| + |101 - 119| + |113 - 137|) / 3 = 20

## A.8 Method 6 - Leastern Square Regression

Liclose to Regression or Leastern Squares Regression (LSR) is the most popular approach for identifying a straight trfinish in historical sales information. The strategy calculates the worths for "a" and also "b" to be used in the formula: Y = a + bX. The equation explains a directly line where Y represents sales, and X represents time. Liclose to regression is sluggish to recognize milestones and step attribute shifts in demand. Linear regression fits a directly line to the data, even once the data is seasonal or would certainly better be described by a curve. When the sales history information follows a curve or has actually a strong seasonal pattern, forecast bias and also systematic errors take place.

Forecast specifications: n = identifies the durations of sales history that will certainly be supplied in calculating the worths for a and also b. For instance, specify n = 3 to use the background from October through December, 2005 as the basis for the calculations. When information is accessible a larger n (such as n = 24) would ordinarily be supplied. LSR will define a line for as few as 2 data points. For this example, a little worth for n (n = 3) was chosen to mitigate the manual calculations required to verify the results.

Required sales history: The variety of durations to incorporate in regression (handling alternative 6a) plus the variety of time durations for evaluating foreactors performance (processing option 19).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128146
February132117158
March115115169
April137125181
May122122192
June130137204
July141129215
August128140227
September118131238
October123114250135.333
November139119261102.333
December133137273109.333

### A.8.1 Forecast Calculation

Number of periods to include in regression (processing choice 6a) = 3 in this example

For each month of the foreactors, include the rise or decrease during the stated durations prior to holdout duration the previous period.

January forecast:

Average of the previous 3 months = (114 + 119 + 137)/3 = 123.3333

Synopsis of the previous 3 months with weight considered

= (114 * 1) + (119 * 2) + (137 * 3) = 763

Difference between the values

= 763 - 123.3333 * (1 + 2 + 3) = 23

Ratio = (1^2 + 2^2 + 3^2) - (1 + 2 + 3)/3^2 * 3 = 14 - 12 = 2

Value1 = Difference/Ratio = 23/2 = 11.5

Value2 = Median - value1 * ratio = 123.3333 - 11.5 * 2 = 100.3333

Forecast = (1 + n) * value1 + value2 = 4 * 11.5 + 100.3333 = 146.333 or 146

February forecast:

Forecast = 5 * 11.5 + 100.3333 = 157.8333 or 158

March forecast:

Forecast = 6 * 11.5 + 100.3333 = 169.3333 or 169

### A.8.2 Simulated Forecast Calculation

October 2004 sales:

Median of the previous 3 months

= (129 + 140 + 131)/3 = 133.3333

Synopsis of the previous three months through weight considered

= (129 * 1) + (140 * 2) + (131 * 3) = 802

Difference in between the values

= 802 - 133.3333 * (1 + 2 + 3) = 2

Ratio = (1^2 + 2^2 + 3^2) - (1 + 2 + 3)/3^2 * 3 = 14 - 12 = 2

Value1 = Difference/Ratio = 2/2 = 1

Value2 = Median - value1 * ratio = 133.3333 - 1 * 2 = 131.3333

Forecast = (1 + n) * value1 + value2 = 4 * 1 + 131.3333 = 135.3333

November 2004 sales

Median of the previous three months

= (140 + 131 + 114)/3 = 128.3333

Outline of the previous three months via weight considered

= (140 * 1) + (131 * 2) + (114 * 3) = 744

Difference in between the worths = 744 - 128.3333 * (1 + 2 + 3) = -25.9999

Value1 = Difference/Ratio = -25.9999/2 = -12.9999

Value2 = Average - value1 * ratio = 128.3333 - (-12.9999) * 2 = 154.3333

Foreactors = 4 * -12.9999 + 154.3333 = 102.3333

December 2004 sales

Average of the previous three months

= (131 + 114 + 119)/3 = 121.3333

Outline of the previous 3 months with weight considered

= (131 * 1) + (114 * 2) + (119 * 3) = 716

Difference between the values

= 716 - 121.3333 * (1 + 2 + 3) = -11.9999

Value1 = Difference/Ratio = -11.9999/2 = -5.9999

Value2 = Average - value1 * proportion = 121.3333 - (-5.9999) * 2 = 133.3333

Foreactors = 4 * (-5.9999) + 133.3333 = 109.3333

### A.8.3 Percent of Accuracy Calculation

POA = (135.33 + 102.33 + 109.33) / (114 + 119 + 137) * 100 = 93.78

### A.8.4 Average Absolute Deviation Calculation

MAD = (|135.33 - 114| + |102.33 - 119| + |109.33 - 137|) / 3 = 21.88

## A.9 Method 7 - Second Degree Approximation

Linear Regression determines worths for a and also b in the forecast formula Y = a + bX with the objective of fitting a straight line to the sales background data. 2nd Degree Approximation is equivalent. However before, this technique determines worths for a, b, and c in the foreactors formula Y = a + bX + cX2 with the objective of fitting a curve to the sales history information. This method might be helpful as soon as a product is in the change between stages of a life cycle. For example, once a brand-new product moves from advent to development steras, the sales trfinish might acceleprice. Since of the second order term, the forecast have the right to quickly method infinity or drop to zero (relying on whether coreliable c is positive or negative). As such, this strategy is useful just in the short term.

Forecast specifications: The formulae finds a, b, and also c to fit a curve to exactly three points. You specify n in the handling option 7a, the number of time durations of information to accumulate right into each of the three points. In this example n = 3. As such, actual sales information for April with June are combined into the initially suggest, Q1. July through September are included together to create Q2, and also October with December sum to Q3. The curve will be fitted to the three worths Q1, Q2, and Q3.

Required sales history: 3 * n periods for calculating the forecast plus the variety of time periods required for evaluating the foreactors performance (PBF).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January12512898
February13211798
March11511598
April13712557
May12212257
June13013757
July1411291
August1281401
September1181311
October123114136
November139119136
December133137136

### A.9.1 Forecast Calculation

Number of periods to incorporate (processing alternative 7a) = 3 in this example

Use the previous (3 * n) months in three-month blocks:

Q1(Apr - Jun) = 125 + 122 + 137 = 384

Q2(Jul - Sep) = 129 + 140 + 131 = 400

Q3(Oct - Dec) = 114 + 119 + 137 = 370

The next action entails calculating the three coefficients a, b, and c to be supplied in the forecasting formula Y = a + bX + cX^2

(1) Q1 = a + bX + cX^2 (where X = 1) = a + b + c

(2) Q2 = a + bX + cX^2 (wbelow X = 2) = a + 2b + 4c

(3) Q3 = a + bX + cX^2 (where X = 3) = a + 3b + 9c

Solve the 3 equations concurrently to find b, a, and also c:

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

(2) - (1) = Q2 - Q1 = b + 3c

b = (Q2 - Q1) - 3c

Substitute this equation for b right into equation (3)

(3) Q3 = a + 3<(Q2 - Q1) - 3c> + c

a = Q3 - 3(Q2 - Q1)

Finally, substitute these equations for a and b right into equation (1)

+ <(q2 - Q1) - 3c> + c = Q1

c = <(Q3 - Q2) + (Q1 - Q2)>/2

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

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

c = <(Q3 - Q2) + (Q1 - Q2)>/2 = <(370 - 400) + (384 - 400)>/2 = -23

b = (Q2 - Q1) - 3c = (400 - 384) - (3 * -23) = 85

Y = a + bX + cX^2 = 322 + 85*X + (-23)X^2

January thru March foreactors (X=4):

(322 + 340 - 368)/3 = 294/3 = 98 per period

April thru June foreactors (X=5):

(322 + 425 - 575)/3 = 57.333 or 57 per period

July thru September foreactors (X=6):

(322 + 510 - 828)/3 = 1.33 or 1 per period

October thru December (X=7)

(322 + 595 - 1127/3 = -70

### A.9.2 Simulated Forecast Calculation

October, November and December, 2004 sales:

Q1(Jan - Mar) = 360

Q2(Apr - Jun) = 384

Q3(Jul - Sep) = 400

a = 400 - 3(384 - 360) = 328

c = <(400 - 384) + (360 - 384)>/2 = -4

b = (384 - 360) - 3 * (-4) = 36

<328 + 36 * 4 + (-4) * 16>/3 = 136

### A.9.3 Percent of Accuracy Calculation

POA = (136 + 136 + 136) / (114 + 119 + 137) * 100 = 110.27

### A.9.4 Average Absolute Deviation Calculation

MADVERTISEMENT = (|136 - 114| + |136 - 119| + |136 - 137|) / 3 = 13.33

## A.10 Method 8 - Flexible Method

The Flexible Method (Percent Over n Months Prior) is similar to Method 1, Percent Over Last Year. Both techniques multiply sales information from a previous time duration by a user stated aspect, then task that result into the future. In the Percent Over Last Year strategy, the estimate is based upon data from the exact same time period in the previous year. The Flexible Method adds the capcapability to specify a time period various other than the exact same period last year to usage as the basis for the calculations.

Forecast specifications:

Multiplication element. For instance, specify 1.15 in the handling alternative 8b to increase the previous sales background information by 15%.

Base duration. For example, n = 3 will certainly cause the first forecast to be based upon sales information in October, 2005.

Minimum sales history: The user mentioned variety of durations ago to the base duration, plus the variety of time periods required for evaluating the foreactors performance (PBF).

Month2004 Sales2005 Sales2006 SalesSimulated 2005 Forecast
January125128131
February132117137
March115115158
April137125151
May122122157
June130137181
July141129173
August128140181
September118131208
October123114199148.35
November139119208161
December133137240150.65

### A.10.1 Foreactors Calculation

Number of durations prior (handling option 8a) = 3, and the percent over the previous period (processing option 8b) is 1.15 in this example

For each month of the foreactors, multiple the sales history n periods prior by the specified percent

January forecast: (114 * 1.15) = 131.1 or 131

February forecast: (119 * 1.15) = 136.85 or 137

March forecast: (137 * 1.15) = 157.55 or 158

### A.10.2 Simulated Forecast Calculation

October 2004 sales = 129 * 1.15 = 148.35

November 2004 sales = 140 * 1.15 = 161

December 2004 sales = 131 * 1.15 = 150.65

### A.10.3 Percent of Accuracy Calculation

POA = (148 + 161 + 151) / (114 + 119 + 137) * 100 = 124.32

### A.10.4 Average Absolute Deviation Calculation

MAD = (|148 - 114| + |161 - 119| + |151 - 137|) / 3 = 30

## A.11 Method 9 - Weighted Moving Average

The Weighted Moving Mean (WMA) approach is comparable to Method 4, Moving Median (MA). However before, with the Weighted Moving Typical you deserve to assign unequal weights to the historic information. The technique calculates a weighted average of current sales background to arrive at a estimate for the brief term. More recent information is commonly assigned a higher weight than older information, so this makes WMA more responsive to shifts in the level of sales. However before, foreactors prejudice and also systematic errors still execute take place as soon as the product sales background exhibits strong trfinish or seasonal fads. This method works much better for short array forecasts of mature commodities quite than for assets in the growth or obsolescence steras of the life cycle.

Foreactors specifications:

n = the number of periods of sales history to usage in the foreactors calculation. For example, specify n = 3 in the processing choice 9a to use the the majority of recent three periods as the basis for the projection right into the following time period. A big value for n (such as 12) requires more sales history. It results in a steady foreactors, however will be sluggish to identify shifts in the level of sales. On the various other hand also, a little worth for n (such as 3) will certainly respond quicker to shifts in the level of sales, however the forecast may fluctuate so widely that manufacturing deserve to not respond to the variations.

The weight assigned to each of the historic data durations. The assigned weights need to complete to 1.00. For instance, once n = 3, asauthorize weights of 0.6, 0.3, and also 0.1, through the the majority of current information receiving the best weight.

Minimum compelled sales history: n plus the number of time durations forced for evaluating the forecast performance (PBF).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128129
February132117131
March115115131
April137125131
May122122131
June130137131
July141129131
August128140131
September118131131
October123114131133.5
November139119131121.7
December133137131118.7

### A.11.1 Foreactors Calculation

Number of periods prior (handling alternative 9a) = 3, and also the weight for one, 2 and 3 periods prior (processing alternative 9b, 9c and 9d) are 0.6, 03, and 0.1 in this example.

January forecast: 137 * 0.6 + 119 * 0.3 + 114 * 0.1 = 129.3 or 129

February forecast: 129.3 * 0.6 + 137 * 0.3 + 119 * 0.1 = 130.58 or 131

March forecast: 131 * 0.6 + 129 * 0.3 + 137 * 0.1 = 130.748 or 131

### A.11.2 Simulated Forecast Calculation

October 2004 sales = 129 * 0.1 + 140 * 0.3 * 131 * 0.6 = 133.5

November 2004 sales = 140 * 0.1 + 131 * 0.3 + 114 * 0.6 = 121.7

December 2004 sales = 131 * 0.1 + 114 * 0.3 + 119 * 0.6 = 118.7

### A.11.3 Percent of Accuracy Calculation

POA = (133.5 + 121.7 + 118.7) / (114 + 119 + 137) * 100 = 101.05

### A.11.4 Average Absolute Deviation Calculation

MADVERTISEMENT = (|133.5 - 114| + |121.7 - 119| + |118.7 - 137|) / 3 = 13.5

## A.12 Method 10 - Liclose to Smoothing

This method is comparable to Method 9, Weighted Moving Typical (WMA). However before, instead of arbitrarily assigning weights to the historical information, a formula is provided to assign weights that decrease linearly and amount to 1.00. The technique then calculates a weighted average of recent sales background to arrive at a forecast for the short term.

As is true of all straight moving average forespreading techniques, forecast prejudice and methodical errors occur when the product sales history exhibits solid trend or seasonal trends. This technique works better for brief range forecasts of mature commodities quite than for assets in the growth or obsolescence stperiods of the life cycle.

Forecast specifications:

n = the variety of periods of sales history to usage in the foreactors calculation. This is stated in the handling choice 10a. For instance, specify n = 3 in the handling alternative 10b to usage the most recent 3 periods as the basis for the projection into the next time duration. The mechanism will immediately assign the weights to the historic information that decrease linearly and also amount to 1.00. For example, as soon as n = 3, the mechanism will asauthorize weights of 0.5, 0.3333, and also 0.1, through the many recent information receiving the greatest weight.

Minimum forced sales history: n plus the variety of time durations required for evaluating the forecast performance (PBF).

Month2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January125128
February132117127
March115115129
April137125130
May122122129
June130137129
July141129129
August128140129
September118131129
October123114129133.6666
November139119129124
December133137129119.3333

### A.12.1 Forecast Calculation

Number of durations to encompass in smoothing average (handling choice 10a) = 3 in this example

Ratio for one duration prior = 3/(n^2 + n)/2 = 3/(3^2 + 3)/2 = 3/6 = 0.5

Ratio for 2 durations prior = 2/(n^2 + n)/2 = 2/(3^2 + 3)/2 = 2/6 = 0.3333..

Ratio for 3 durations prior = 1/(n^2 + n)/2 = 1/(3^2 + 3)/2 = 1/6 = 0.1666..

January forecast: 137 * 0.5 + 119 * 1/3 + 114 * 1/6 = 127.16 or 127

February forecast: 127 * 0.5 + 137 * 1/3 * 119 * 1/6 = 129

March forecast: 129 * 0.5 + 127 * 1/3 * 137 * 1/6 = 129.666 or 130

### A.12.2 Simulated Forecast Calculation

October 2004 sales = 129 * 1/6 + 140 * 2/6 * 131 * 3/6 = 133.6666

November 2004 sales = 140 * 1/6 + 131 * 2/6 + 114 * 3/6 = 124

December 2004 sales = 131 * 1/6 + 114 * 2/6 + 119 * 3/6 = 119.3333

### A.12.3 Percent of Accuracy Calculation

POA = (133.6666 + 124 + 119.3333) / (114 + 119 + 137) * 100 = 101.891

### A.12.4 Typical Absolute Deviation Calculation

MADVERTISEMENT = (|133.6666 - 114| + |124 - 119| + |119.3333 - 137|) / 3 = 14.1111

## A.13 Method 11 - Exponential Smoothing

This strategy is similar to Method 10, Liclose to Smoothing. In Liclose to Smoothing the mechanism asindicators weights to the historical information that decrease livirtually. In exponential smoopoint, the device assigns weights that exponentially decay. The exponential smoopoint forecasting equation is:

Foreactors =a(Previous Actual Sales) + (1 -a) Previous Forecast

The foreactors is a weighted average of the actual sales from the previous period and the forecast from the previous duration. a is the weight used to the actual sales for the previous period. (1 -a) is the weight applied to the forecast for the previous duration. Valid worths for a selection from 0 to 1, and normally fall in between 0.1 and 0.4. The sum of the weights is 1.00. a+ (1 -a) = 1

You have to assign a value for the smoopoint constant, a. If you carry out not assign values for the smoopoint constant, the mechanism calculates an assumed value based upon the number of durations of sales history specified in the handling option 11a.

Foreactors specifications:

a = the smoopoint consistent used in calculating the smoothed average for the basic level or magnitude of sales. Valid values for a range from 0 to 1.

n = the selection of sales history information to encompass in the calculations. Usually one year of sales history information is adequate to estimate the basic level of sales. For this instance, a small value for n (n = 3) was chosen in order to alleviate the hands-on calculations required to verify the results. Exponential smoothing deserve to generate a forecast based on as little as one historic information suggest.

Minimum forced sales history: n plus the variety of time durations required for evaluating the foreactors performance (PBF).

Month2004 Sales2005 Sales2006 SalesSimulated 2005 Forecasts
January125128127
February132117127
March115115127
April137125127
May122122127
June130137127
July141129127
August128140127
September118131127
October123114127133.6666
November139119127124
December133137127119.3333

### A.13.1 Forecast Calculation

Number of periods to encompass in smoopoint average (processing alternative 11a) = 3, and also alpha variable (handling alternative 11b) = blank in this example

a aspect for the oldest sales data = 2/(1+1), or 1 as soon as alpha is specified

a element for the 2nd earliest sales information = 2/(1+2), or alpha when alpha is specified

a element for the 3rd earliest sales data = 2/(1+3), or alpha once alpha is specified

a variable for the many current sales data = 2/(1+n), or alpha when alpha is specified

November Sm. Avg. =a(October Actual) + (1 - a)October Sm. Avg. = 1 * 114 + 0 * 0 = 114

December Sm. Avg. =a(November Actual) + (1 - a)November Sm. Avg. = 2/3 * 119 + 1/3 * 114 = 117.3333

January Forecast =a(December Actual) + (1 - a)December Sm. Avg. = 2/4 * 137 + 2/4 * 117.3333 = 127.16665 or 127

February Forecast = January Forecast = 127

March Foreactors = January Foreactors = 127

### A.13.2 Simulated Foreactors Calculation

July, 2004 Sm. Avg. = 2/2 * 129 = 129

August Sm. Avg. = 2/3 * 140 + 1/3 * 129 = 136.3333

September Sm. Avg. = 2/4 * 131 + 2/4 * 136.3333 = 133.6666

October, 2004 sales = Sep Sm. Avg. = 133.6666

August, 2004 Sm. Avg. = 2/2 * 140 = 140

September Sm. Avg. = 2/3 * 131 + 1/3 * 140 = 134

October Sm. Avg. = 2/4 * 114 + 2/4 * 134 = 124

November, 2004 sales = Sep Sm. Avg. = 124

September 2004 Sm. Avg. = 2/2 * 131 = 131

October Sm. Avg. = 2/3 * 114 + 1/3 * 131 = 119.6666

November Sm. Avg. = 2/4 * 119 + 2/4 * 119.6666 = 119.3333

December 2004 sales = Sep Sm. Avg. = 119.3333

### A.13.3 Percent of Accuracy Calculation

POA = (133.6666 + 124 + 119.3333) / (114 + 119 + 137) * 100 = 101.891

### A.13.4 Typical Absolute Deviation Calculation

MADVERTISEMENT = (|133.6666 - 114| + |124 - 119| + |119.3333 - 137|) / 3 = 14.1111

## A.14 Method 12 - Exponential Smoothing with Trfinish and Seasonality

This technique is equivalent to Method 11, Exponential Smoopoint in that a smoothed average is calculated. However, Method 12 additionally contains a term in the forespreading equation to calculate a smoothed trfinish. The foreactors is composed of a smoothed averaged adjusted for a direct trend. When stated in the handling choice, the forecast is likewise readjusted for seasonality.

Foreactors specifications:

a = the smoothing consistent provided in calculating the smoothed average for the general level or magnitude of sales. Valid worths for alpha range from 0 to 1.

b = the smoothing constant provided in calculating the smoothed average for the trend component of the forecast. Valid worths for beta range from 0 to 1.

Whether a seasonal index is used to the forecast

Note:

a and b are independent of each other. They carry out not need to include to 1.0.

Minimum compelled sales history: 2 years plus the variety of time periods required for evaluating the forecast performance (PBF).

Method 12 uses 2 exponential smoothing equations and also one basic average to calculate a smoothed average, a smoothed trend, and a basic average seasonal variable.

### A.14.1 Foreactors Calculation

A) An significantly smoothed average

Figure A-1 Description of "Figure A-1 "

B) An significantly smoothed trend

Figure A-2 Description of "Figure A-2 "

C) A simple average seasonal index

Figure A-3 Description of "Figure A-3 "

When a is not stated in the processing choice, it is calculated.

When b is not mentioned in the handling choice, it is calculated.

Note:

A "t" is taken into consideration 6 when it is 6 or better.

The forecast is then calculated making use of the outcomes of the 3 equations:

D)

Figure A-4 Description of "Figure A-4 "

Where:

L is the length of seasonality (L=12 months or 52 weeks)

t is the present time period

m is the variety of time periods right into the future of the forecast

S is the multiplicative seasonal adjustment aspect indexed to the correct time periods

Month2003 Sales2004 Sales2005 Sales2006 ForecastSimulated 2005 Forecast
January115115116
February137125132
March122122123
April130137135
May141129137
June128140136
July118131127
August118123114121122.81
September121139119132133.14
October130133137139135.33
November15431514
December
Total

### A.14.2 Forecast Calculation

Alpha, and beta element (handling option 12a, and also 12b) = empty, and also seasonality (processing alternative 13c) is "1" in this example

DescriptionCalculation
January, 05 Seasonal Index, S1= (125 + 128)/(1543 + 1514) * 12

= 0.99313

January, 05 Smoothed Mean, A1= Jan, 05 Actual/Jan, 05 Seasonal Index

= 128/0.99313

= 128.885

January, 05 Smoothed Trfinish, T1= 0 insufficient information to calculate initially smoothed trend
February Seasonal Index, S2=(132 + 117)/(1543 + 1514) * 12

= 0.97742

February Smoothed Median, A2

= 122.7519

February Smoothed Trfinish, T2

= 2/3 * (122.7519 - 128.885) + 1/3 * 0

= -4.0887333

March Seasonal Index, S3= (115 + 115)/3057 * 12 = 0.90284
March Smoothed Average, A3= 2/4 * 115/0.90284 + 2/4 * <122.7519 + (-4.088733)> = 123.01950
March Smoothed Trend, T3= 2/4 (123.01950 - 122.7519) + 2/4 (-4.0888733) = -1.91063665
(Continued via December "06)
December "06 Seasonal Index, S12= (133 + 137)/3057 * 12 = 1.05986
December Smoothed Median, A12= (2/13)137/1.05986 + (11/13)(A11 + T11) = 19.8865 + 107.47247 = 127.35897

Calculation of Liclose to and also Seasonal Exponentially Smoothed Forecast

January "06 = (A12+T12)S1 = (127.35897 + 0.28814 * 1) * 0.99313 = 126.77 or 127

February "06 = (A12+T12)S2 = (127.35897 + 0.28814 * 2 ) * 0.9774 = 125.04 or 125

March "06 = (A12+T12)S3 = (127.35897 + 0.28814 * 3) * 0.902845 = 115.77 or 116

December "06 = (A12+T12)S12 = (127.35897 + 0.28814 * 12) * 1.059862 = 138.65 or 139

### A.14.3 Simulated Foreactors Calculation

DescriptionCalculation
October, 04 Seasonal Index, S1= (118 + 123)/(3056) * 12

= 0.94633

October, 04 Smoothed Median, A1=a * Oct, 04 Actual/Oct, 04 Seasonal Index

= 123/0.94633

= 129.9758

October, 04 Smoothed Trfinish, T1= 0 inadequate information to calculate initially smoothed trend
(Continued via September "05)
September, 05 Seasonal Index, S12= (118 + 131)/(3056) * 12

= 0.97774869

September, 05 Smoothed Average, A12= 2/13*131/0.97774869 + 11/13*(A11 + T11)

= 129.1410

September, 05 Smoothed Trend, T12= 2/7 * (129.141025630 - A11) + 5/7 * T11 = 0.6343542

October 2005 sales = (A12 + T12*1)S1 = (129.1410 + 0.6343542 * 1) * 0.94633 = 129.775379872 * 0.94633 = 122.81

November 2005 sales = (A12 + T12*2)S2 = (129.1410 + 0.6343542 * 2) * 1.02094236 = 133.14

December 2005 sales = (A12 + T12*3)S3 = (129.1410 + 0.6343542 * 3) * 1.032722508 = 135.33

### A.14.4 Percent of Accuracy Calculation

POA = (122.81 + 133.14 + 135.33) / (114 + 119 + 137) * 100 = 105.75

### A.14.5 Median Absolute Deviation Calculation

MADVERTISEMENT = (|122.81 - 114| + |133.14 - 119| + |135.33 - 137|) / 3 = 8.2

## A.15 Assessing the Forecasts

You can select forecasting techniques to generate as many kind of as twelve forecasts for each product. Each forespreading method will certainly more than likely develop a slightly different estimate. When thousands of commodities are forecast, it is imuseful to make a subjective decision about which of the forecasts to usage in your plans for each of the commodities.

The device instantly evaluates performance for each of the forecasting approaches that you select, and also for each of the products forecast. You deserve to select in between 2 performance criteria, Average Absolute Deviation (MAD) and also Percent of Accuracy (POA). MAD is a measure of forecast error. POA is a measure of forecast predisposition. Both of these performance evaluation methods need actual sales history information for a user stated duration of time. This period of recent history is called a "holdout period" or "durations finest fit" (PBF).

To measure the performance of a forespreading strategy, use the foreactors formulae to simulate a forecast for the historical holdout duration. Tbelow will normally be differences in between actual sales data and the simulated foreactors for the holdout duration.

When multiple foreactors techniques are selected, this very same process occurs for each strategy. Multiple forecasts are calculated for the holdout duration, and compared to the known sales background for that same duration of time. The forespreading technique creating the ideal match (best fit) between the forecast and also the actual sales throughout the holdout duration is recommended for use in your plans. This referral is specific to each product, and might readjust from one forecast generation to the next.

## A.16 Mean Absolute Deviation (MAD)

MAD is the intend (or average) of the absolute values (or magnitude) of the deviations (or errors) between actual and also foreactors information. MADVERTISEMENT is a measure of the average magnitude of errors to mean, offered a forecasting technique and also data history. Because absolute values are offered in the calculation, positive errors execute not cancel out negative errors. When comparing a number of forecasting approaches, the one via the smallest MADVERTISEMENT has shown to be the the majority of trusted for that product for that holdout duration. When the foreactors is unbiased and errors are normally distributed, tright here is a simple mathematical connection in between MADVERTISEMENT and also 2 various other widespread actions of distribution, typical deviation and Median Squared Error:

### A.16.1 Percent of Accuracy (POA)

Percent of Accuracy (POA) is a meacertain of forecast bias. When forecasts are repetitively as well high, inventories accumulate and inventory prices rise. When forecasts are repetitively two low, inventories are consumed and customer organization declines. A forecast that is 10 units also low, then 8 units as well high, then 2 systems as well high, would certainly be an unbiased foreactors. The positive error of 10 is canceled by negative errors of 8 and 2.

Error = Actual - Forecast

When a product deserve to be stored in inventory, and once the foreactors is unbiased, a small amount of safety and security stock deserve to be provided to buffer the errors. In this situation, it is not so important to remove foreactors errors as it is to generate unbiased forecasts. However in organization sectors, the over case would be viewed as three errors. The company would certainly be understaffed in the initially period, then overstaffed for the following two periods. In solutions, the magnitude of foreactors errors is typically more vital than is foreactors bias.

See more: Reasons Why Do The Wicked Prosper And The Righteous Suffer ?

Figure A-5 Description of "Figure A-5 "

Note:

The summation over the holdout period enables positive errors to cancel negative errors. When the full of actual sales exceeds the full of foreactors sales, the proportion is greater than 100%. Of course, it is impossible to be even more than 100% specific. When a forecast is unbiased, the POA ratio will be 100%. Therefore, it is even more preferable to be 95% exact than to be 110% accurate. The POA criteria select the forecasting strategy that has a POA ratio closest to 100%.