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<ManualTopic ID="/baanerp/cp/onlinemanual/000110" xml:lang="en">
	<Header>
		<Title xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40">Forecast method: exponential smoothing</Title>
		<Keyword><Level1>Forecast method: exponential smoothing</Level1>
		</Keyword>
	</Header>
	<GeneralSection><Paragraph>SSA ERP calculates the demand forecast according to the <GUIRef href="/baanerp/cp/domains/rpd.fcmd#es" role="enum">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="formfield">Automatic Update of Forecast Parameters</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfd" role="formfield">Smoothing Factor for Demand</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smft" role="formfield">Smoothing Factor for Trend</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfs" role="formfield">Smoothing Factor for Season</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfe" role="formfield">Smoothing Factor for Forecast Error</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.trsi" role="formfield">Tracking Signal for Demand Forecast</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.ctsi" role="formfield">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="formfield">Automatic Update of Forecast Parameters</GUIRef> check box is selected, SSA ERP first recomputes the smoothing factors for the exponential smoothing method. Using an iterative process, with step sizes of 0.2 and subsequently 0.05, SSA ERP 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, SSA ERP 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><Paragraph UserLevel="Novice" UserType="Taskuser">AV(t) = FD(t) + a (AD(t) - FD(t))</Paragraph>
			</Formula>
			<Paragraph>With a constant seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">AV(t) = (FD(t) + a (AD(t) - FD(t))) - SF(t)</Paragraph>
			</Formula>
			<Paragraph>With a progressive seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">AV(t) = (FD(t) + a (AD(t) - FD(t))) / SF(t)</Paragraph>
			</Formula>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>AV(t)</TD>
						<TD>season-adjusted average demand for period t</TD>
					</TR>
					<TR><TD>FD(t)</TD>
						<TD>demand forecast for period t</TD>
					</TR>
					<TR><TD>AD(t)</TD>
						<TD>actual demand for period t (*)</TD>
					</TR>
					<TR><TD>SF(t)</TD>
						<TD>seasonal factor for period t</TD>
					</TR>
					<TR><TD>a</TD>
						<TD><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfd" role="formfield">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><Paragraph UserLevel="Novice" UserType="Taskuser">TF(t) = TF(t-1) + b ((AV(t)-AV(t-1)) - TF(t-1))</Paragraph>
			</Formula>
			<Paragraph>With a progressive trend influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">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"><TBODY><TR><TD>TF(t)</TD>
						<TD>trend factor for period t</TD>
					</TR>
					<TR><TD>AV(t)</TD>
						<TD>season-adjusted average demand for period t</TD>
					</TR>
					<TR><TD>b</TD>
						<TD><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smft" role="formfield">Smoothing Factor for Trend</GUIRef> field</TD>
					</TR>
				</TBODY>
			</TABLE>
		</GeneralSection>
		<GeneralSection><SectionTitle>Seasonal factor</SectionTitle>
			<Paragraph>With a constant seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">SF(t+L) = SF(t) + g ((AD(t) - AV(t)) - SF(t))</Paragraph>
			</Formula>
			<Paragraph>With a progressive seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">SF(t+L) = SF(t) + g ((AD(t) / AV(t)) - SF(t))</Paragraph>
			</Formula>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>SF(t)</TD>
						<TD>seasonal factor for period t</TD>
					</TR>
					<TR><TD>AD(t)</TD>
						<TD>actual demand for period t (*)</TD>
					</TR>
					<TR><TD>AV(t)</TD>
						<TD>season-adjusted average demand for period t</TD>
					</TR>
					<TR><TD>L</TD>
						<TD>season length in periods</TD>
					</TR>
					<TR><TD>g</TD>
						<TD><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfs" role="formfield">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><Paragraph UserLevel="Novice" UserType="Taskuser">FD(t+1) =	 AV(t)</Paragraph>
			</Formula>
			<Paragraph>With a linear trend influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">FD(t+1) = FD(t+1) + TF(t)</Paragraph>
			</Formula>
			<Paragraph>With a progressive trend influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">FD(t+1) = FD(t+1) * TF(t)</Paragraph>
			</Formula>
			<Paragraph>With a constant seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">FD(t+1) = FD(t+1) + SF(t+1)</Paragraph>
			</Formula>
			<Paragraph>With a progressive seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">FD(t+1) = FD(t+1) * SF(t+1)</Paragraph>
			</Formula>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>AV(t)</TD>
						<TD>season-adjusted average demand for period t</TD>
					</TR>
					<TR><TD>TF(t)</TD>
						<TD>trend factor for period t</TD>
					</TR>
					<TR><TD>SF(t+1)</TD>
						<TD>seasonal factor for period t+1</TD>
					</TR>
					<TR><TD>FD(t+1)</TD>
						<TD>demand forecast for period t+1</TD>
					</TR>
				</TBODY>
			</TABLE>
		</GeneralSection>
		<GeneralSection><SectionTitle>Mean forecast error</SectionTitle>
			<Figure><HTML:IMG SRC="../images/nt_flow_110.gif" width="792" height="108" xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40"/></Figure>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>AD(t)</TD>
						<TD>actual demand for period t</TD>
					</TR>
					<TR><TD>FD(t)</TD>
						<TD>demand forecast for period t</TD>
					</TR>
					<TR><TD>AE(t)</TD>
						<TD>mean absolute deviation (MAD) for period t</TD>
					</TR>
					<TR><TD>SE(t)</TD>
						<TD>mean forecast error (SER) for period t</TD>
					</TR>
					<TR><TD>abs(FD(t)-AD(t))</TD>
						<TD>absolute value of (FD(t)-AD(t))</TD>
					</TR>
					<TR><TD>e</TD>
						<TD><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.smfe" role="formfield">Smoothing Factor for Forecast Error</GUIRef> field</TD>
					</TR>
				</TBODY>
			</TABLE>
			<Paragraph>The tracking signal is calculated as follows:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser"> TS(t) = abs(SE(t)/AE(t)) </Paragraph>
			</Formula>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>TS(t)</TD>
						<TD>tracking signal</TD>
					</TR>
					<TR><TD>SE(t)</TD>
						<TD>mean forecast error (SER) for period t</TD>
					</TR>
					<TR><TD>AE(t)</TD>
						<TD>mean absolute deviation (MAD) for period t</TD>
					</TR>
					<TR><TD>abs(SE(t)/AE(t))</TD>
						<TD>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="formfield">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="formfield">Critical Tracking Signal</GUIRef> field, SSA ERP 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>
