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<ManualTopic ID="/baanerp/cp/onlinemanual/000110" xml:lang="en">
   <Header>
      <Title>Forecast method: exponential smoothing</Title>
      <Keyword type="header" order="d1e202882">
         <Level1>Forecast method: exponential smoothing</Level1>
      </Keyword>
   </Header>
   <GeneralSection>
      <Paragraph>ERP Enterprise calculates the
      demand forecast according to the <GUIRef href="/baanerp/cp/domains/rpd.fcmd#es" role="option">Exponential Smoothing</GUIRef> forecast method as follows:</Paragraph>
      <List>
         <ListIntro>The relevant parameters for this forecast method are:</ListIntro>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="manual">Automatic Update of Forecast Parameters</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfd" role="manual">Smoothing Factor for Demand</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smft" role="manual">Smoothing Factor for Trend</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfs" role="manual">Smoothing Factor for Season</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfe" role="manual">Smoothing Factor for Forecast Error</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.trsi" role="manual">Tracking Signal for Demand Forecast</GUIRef>
         </ListItem>
         <ListItem> 
            <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.ctsi" role="manual">Critical Tracking Signal</GUIRef>
         </ListItem>
      </List>
      <Paragraph>You can maintain these
      parameters in the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000" role="session">Plan Items - Forecast Settings (cpdsp1110m000)</GUIRef> session.</Paragraph>
      <Paragraph>If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="manual">Automatic Update of Forecast Parameters</GUIRef> check box is selected, ERP Enterprise first recomputes the
      smoothing factors for the exponential smoothing method. Using an iterative
      process, with step sizes of 0.2 and subsequently 0.05, ERP Enterprise produces an
      optimum combination of smoothing factors for the demand, the season, and the
      trend. This combination gives the smallest mean absolute deviation (MAD).</Paragraph>
      <Paragraph>Next, ERP Enterprise calculates
      a demand forecast starting from the first period with demand history to the
      last forecast period via the exponential smoothing method.</Paragraph>
      <Paragraph>The various variables
      for the demand forecast are computed as follows:</Paragraph>
      <GeneralSection>
         <SectionTitle>Average demand</SectionTitle>
         <Paragraph>Without seasonal
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>AV(t) = FD(t) + a (AD(t) - FD(t))</Paragraph>
         </Formula>
         <Paragraph>With a constant
        seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>AV(t) = (FD(t) + a (AD(t) - FD(t))) - SF(t)</Paragraph>
         </Formula>
         <Paragraph>With a progressive seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>AV(t) = (FD(t) + a (AD(t) - FD(t))) / SF(t)</Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="5">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">AV(t)</TD>
                  <TD rowspan="1" colspan="1">season-adjusted average
              demand for period t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">FD(t)</TD>
                  <TD rowspan="1" colspan="1">demand forecast for period
              t</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">AD(t)</TD>
                  <TD rowspan="1" colspan="1">actual demand for period t
              (*)</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">SF(t)</TD>
                  <TD rowspan="1" colspan="1">seasonal factor for period
              t</TD>
               </TR>
               <TR no="5" isLast="true">
                  <TD rowspan="1" colspan="1">a</TD>
                  <TD rowspan="1" colspan="1">
                     <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfd" role="manual">Smoothing Factor for Demand</GUIRef> field</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>(*) For the current
        period and later periods, the forecast demand is taken as the actual demand.</Paragraph>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Trend factor</SectionTitle>
         <Paragraph>With a linear trend
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TF(t) = TF(t-1) + b ((AV(t)-AV(t-1)) - TF(t-1))</Paragraph>
         </Formula>
         <Paragraph>With a progressive
        trend influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>TF(t) = TF(t-1) + b (1.0 + ((AV(t)-AV(t-1))/AV(t)) - TF(t-1))</Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="3">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">TF(t)</TD>
                  <TD rowspan="1" colspan="1">trend factor for period
              t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">AV(t)</TD>
                  <TD rowspan="1" colspan="1">season-adjusted average demand for period
              t</TD>
               </TR>
               <TR no="3" isLast="true">
                  <TD rowspan="1" colspan="1">b</TD>
                  <TD rowspan="1" colspan="1">
                     <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smft" role="manual">Smoothing Factor for Trend</GUIRef> field</TD>
               </TR>
            </TBODY>
         </TABLE>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Seasonal factor</SectionTitle>
         <Paragraph>With a constant
        seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>SF(t+L) = SF(t) + g ((AD(t) - AV(t)) - SF(t))</Paragraph>
         </Formula>
         <Paragraph>With a progressive
        seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>SF(t+L) = SF(t) + g ((AD(t) / AV(t)) - SF(t))</Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="5">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">SF(t)</TD>
                  <TD rowspan="1" colspan="1">seasonal factor for period
              t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">AD(t)</TD>
                  <TD rowspan="1" colspan="1">actual demand for period t
              (*)</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">AV(t)</TD>
                  <TD rowspan="1" colspan="1">season-adjusted average demand for period
              t</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">L</TD>
                  <TD rowspan="1" colspan="1">season length in periods</TD>
               </TR>
               <TR no="5" isLast="true">
                  <TD rowspan="1" colspan="1">g</TD>
                  <TD rowspan="1" colspan="1">
                     <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfs" role="manual">Smoothing Factor for Season</GUIRef> field</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>(*) For the current
        period and later periods, the forecast demand is taken as the actual demand.</Paragraph>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Demand forecast</SectionTitle>
         <Paragraph>Without trend
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>FD(t+1) =	 AV(t)</Paragraph>
         </Formula>
         <Paragraph>With a linear trend
        influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>FD(t+1) = FD(t+1) + TF(t)</Paragraph>
         </Formula>
         <Paragraph>With a progressive trend influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>FD(t+1) = FD(t+1) * TF(t)</Paragraph>
         </Formula>
         <Paragraph>With a constant seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>FD(t+1) = FD(t+1) + SF(t+1)</Paragraph>
         </Formula>
         <Paragraph>With a progressive seasonal influence:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph>FD(t+1) = FD(t+1) * SF(t+1)</Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="4">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">AV(t)</TD>
                  <TD rowspan="1" colspan="1">season-adjusted average
              demand for period t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">TF(t)</TD>
                  <TD rowspan="1" colspan="1">trend factor for period
              t</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">SF(t+1)</TD>
                  <TD rowspan="1" colspan="1">seasonal factor for period
              t+1</TD>
               </TR>
               <TR no="4" isLast="true">
                  <TD rowspan="1" colspan="1">FD(t+1)</TD>
                  <TD rowspan="1" colspan="1">demand forecast for period
              t+1</TD>
               </TR>
            </TBODY>
         </TABLE>
      </GeneralSection>
      <GeneralSection>
         <SectionTitle>Mean forecast error</SectionTitle>
         <Figure space-and-orientation="indented-estimated">
            <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" width="792" height="108"
                      SRC="../images/nt_flow_110.gif"
                      alt="[...]"/>
         </Figure>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="6">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">AD(t)</TD>
                  <TD rowspan="1" colspan="1">actual demand for period
              t</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">FD(t)</TD>
                  <TD rowspan="1" colspan="1">demand forecast for period
              t</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">AE(t)</TD>
                  <TD rowspan="1" colspan="1">mean absolute deviation (MAD) for period
              t</TD>
               </TR>
               <TR no="4" isLast="false">
                  <TD rowspan="1" colspan="1">SE(t)</TD>
                  <TD rowspan="1" colspan="1">mean forecast error (SER) for period
              t</TD>
               </TR>
               <TR no="5" isLast="false">
                  <TD rowspan="1" colspan="1">abs(FD(t)-AD(t))</TD>
                  <TD rowspan="1" colspan="1">absolute value of
              (FD(t)-AD(t))</TD>
               </TR>
               <TR no="6" isLast="true">
                  <TD rowspan="1" colspan="1">e</TD>
                  <TD rowspan="1" colspan="1">
                     <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfe" role="manual">Smoothing Factor for Forecast Error</GUIRef> field</TD>
               </TR>
            </TBODY>
         </TABLE>
         <Paragraph>The tracking signal is
        calculated as follows:</Paragraph>
         <Formula space-and-orientation="indented-estimated">
            <Paragraph> TS(t) = abs(SE(t)/AE(t)) </Paragraph>
         </Formula>
         <Paragraph>Where:</Paragraph>
         <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
            <TBODY noTR="4">
               <TR no="1" isLast="false">
                  <TD rowspan="1" colspan="1">TS(t)</TD>
                  <TD rowspan="1" colspan="1">tracking
              signal</TD>
               </TR>
               <TR no="2" isLast="false">
                  <TD rowspan="1" colspan="1">SE(t)</TD>
                  <TD rowspan="1" colspan="1">mean forecast error (SER) for period
              t</TD>
               </TR>
               <TR no="3" isLast="false">
                  <TD rowspan="1" colspan="1">AE(t)</TD>
                  <TD rowspan="1" colspan="1">mean absolute deviation (MAD) for period
              t</TD>
               </TR>
               <TR no="4" isLast="true">
                  <TD rowspan="1" colspan="1">abs(SE(t)/AE(t))</TD>
                  <TD rowspan="1" colspan="1">absolute value of
              (SE(t)/AE(t))</TD>
               </TR>
            </TBODY>
         </TABLE>
      </GeneralSection>
      <Note>
         <SectionTitle>Note</SectionTitle>
         <Paragraph>If the forecast demand
        (FD) is always greater than the actual demand (AD), the value of (SE(t)/AE(t))
        is 1. If the forecast demand (FD) is always less than the actual demand, the
        value of (SE(t)/AE(t)) is -1. The tracking signal is a number between 0 and 1.
        The tracking signal indicates whether the forecast demand is systematically
        above or below the actual demand.</Paragraph>
         <Paragraph>If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.trsi" role="manual">Tracking Signal for Demand Forecast</GUIRef> check box is selected, the smoothing factor for the demand is
        dependent on the forecast error.</Paragraph>
         <Paragraph>If the tracking signal
        is greater than the value of the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.ctsi" role="manual">Critical Tracking Signal</GUIRef> field, ERP Enterprise makes the smoothing factor for the demand equal
        to the tracking signal.</Paragraph>
      </Note>
   </GeneralSection>
   <RelatedTopics>
      <SectionTitle>Related topics</SectionTitle>
      <RelTopic>
         <Link href="/baanerp/cp/onlinemanual/000079" role="manual">Algorithm for demand forecasting</Link>
      </RelTopic>
      <RelTopic>
         <Link href="/baanerp/cp/onlinemanual/000321" role="manual">Forecasting methods</Link>
      </RelTopic>
   </RelatedTopics>
</ManualTopic>