Supply Chain Management
(3rd Edition)
Chapter 7
Demand Forecasting
in a Supply Chain
© 2007 Pearson Education
7-1
Outline
 The
role of forecasting in a supply chain
 Characteristics of forecasts
 Components of forecasts and forecasting methods
 Basic approach to demand forecasting
 Time series forecasting methods
 Measures of forecast error
 Forecasting demand at Tahoe Salt
 Forecasting in practice
© 2007 Pearson Education
7-2
Role of Forecasting
in a Supply Chain
 The
basis for all strategic and planning decisions
in a supply chain
 Used for both push and pull processes
 Examples:
– Production: scheduling, inventory, aggregate planning
– Marketing: sales force allocation, promotions, new
production introduction
– Finance: plant/equipment investment, budgetary
planning
– Personnel: workforce planning, hiring, layoffs
 All
of these decisions are interrelated
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Characteristics of Forecasts
 Forecasts
are always wrong. Should include
expected value and measure of error.
 Long-term forecasts are less accurate than shortterm forecasts (forecast horizon is important)
 Aggregate forecasts are more accurate than
disaggregate forecasts
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Forecasting Methods
 Qualitative:
primarily subjective; rely on
judgment and opinion
 Time Series: use historical demand only
– Static
– Adaptive
 Causal:
use the relationship between demand and
some other factor to develop forecast
 Simulation
– Imitate consumer choices that give rise to demand
– Can combine time series and causal methods
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Components of an Observation
Observed demand (O) =
Systematic component (S) + Random component (R)
Level (current deseasonalized demand)
Trend (growth or decline in demand)
Seasonality (predictable seasonal fluctuation)
• Systematic component: Expected value of demand
• Random component: The part of the forecast that
deviates from the systematic component
• Forecast error: difference between forecast and actual demand
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Time Series Forecasting
Quarter
II, 1998
III, 1998
IV, 1998
I, 1999
II, 1999
III, 1999
IV, 1999
I, 2000
II, 2000
III, 2000
IV, 2000
I, 2001
© 2007 Pearson Education
Demand Dt
8000
13000
23000
34000
10000
18000
23000
38000
12000
13000
32000
41000
Forecast demand for the
next four quarters.
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Time Series Forecasting
50,000
40,000
30,000
20,000
10,000
0
© 2007 Pearson Education
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Forecasting Methods
 Static
 Adaptive
–
–
–
–
Moving average
Simple exponential smoothing
Holt’s model (with trend)
Winter’s model (with trend and seasonality)
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Basic Approach to
Demand Forecasting
 Understand
the objectives of forecasting
 Integrate demand planning and forecasting
 Identify major factors that influence the demand
forecast
 Understand and identify customer segments
 Determine the appropriate forecasting technique
 Establish performance and error measures for the
forecast
© 2007 Pearson Education
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Time Series
Forecasting Methods
 Goal
is to predict systematic component of demand
– Multiplicative: (level)(trend)(seasonal factor)
– Additive: level + trend + seasonal factor
– Mixed: (level + trend)(seasonal factor)
 Static
methods
 Adaptive forecasting
© 2007 Pearson Education
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Static Methods
 Assume
a mixed model:
Systematic component = (level + trend)(seasonal factor)
Ft+l = [L + (t + l)T]St+l
= forecast in period t for demand in period t + l
L = estimate of level for period 0
T = estimate of trend
St = estimate of seasonal factor for period t
Dt = actual demand in period t
Ft = forecast of demand in period t
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Static Methods
 Estimating
level and trend
 Estimating seasonal factors
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Estimating Level and Trend
 Before
estimating level and trend, demand data
must be deseasonalized
 Deseasonalized demand = demand that would
have been observed in the absence of seasonal
fluctuations
 Periodicity (p)
– the number of periods after which the seasonal cycle
repeats itself
– for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4
© 2007 Pearson Education
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Time Series Forecasting
(Table 7.1)
Quarter
II, 1998
III, 1998
IV, 1998
I, 1999
II, 1999
III, 1999
IV, 1999
I, 2000
II, 2000
III, 2000
IV, 2000
I, 2001
© 2007 Pearson Education
Demand Dt
8000
13000
23000
34000
10000
18000
23000
38000
12000
13000
32000
41000
Forecast demand for the
next four quarters.
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Time Series Forecasting
(Figure 7.1)
50,000
40,000
30,000
20,000
10,000
0
© 2007 Pearson Education
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Estimating Level and Trend
 Before
estimating level and trend, demand data
must be deseasonalized
 Deseasonalized demand = demand that would
have been observed in the absence of seasonal
fluctuations
 Periodicity (p)
– the number of periods after which the seasonal cycle
repeats itself
– for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4
© 2007 Pearson Education
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Deseasonalizing Demand
[Dt-(p/2) + Dt+(p/2) +  2Di] / 2p for p even
Dt =
(sum is from i = t+1-(p/2) to t+1+(p/2))
 Di / p for p odd
(sum is from i = t-(p/2) to t+(p/2)), p/2 truncated to lower integer
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Deseasonalizing Demand
For the example, p = 4 is even
For t = 3:
D3 = {D1 + D5 + Sum(i=2 to 4) [2Di]}/8
= {8000+10000+[(2)(13000)+(2)(23000)+(2)(34000)]}/8
= 19750
D4 = {D2 + D6 + Sum(i=3 to 5) [2Di]}/8
= {13000+18000+[(2)(23000)+(2)(34000)+(2)(10000)]/8
= 20625
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Deseasonalizing Demand
Then include trend
Dt = L + tT
where Dt = deseasonalized demand in period t
L = level (deseasonalized demand at period 0)
T = trend (rate of growth of deseasonalized demand)
Trend is determined by linear regression using
deseasonalized demand as the dependent variable and
period as the independent variable (can be done in
Excel)
In the example, L = 18,439 and T = 524
© 2007 Pearson Education
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Time Series of Demand
(Figure 7.3)
50000
Demand
40000
30000
Dt
20000
Dt-bar
10000
0
1 2 3 4 5 6 7 8 9 10 11 12
Period
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Estimating Seasonal Factors
Use the previous equation to calculate deseasonalized
demand for each period
St = Dt / Dt = seasonal factor for period t
In the example,
D2 = 18439 + (524)(2) = 19487
D2 = 13000
S2 = 13000/19487 = 0.67
The seasonal factors for the other periods are
calculated in the same manner
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Estimating Seasonal Factors
(Fig. 7.4)
t
1
2
3
4
5
6
7
8
9
10
11
12
© 2007 Pearson Education
Dt Dt-bar S-bar
8000 18963 0.42 = 8000/18963
13000 19487 0.67 = 13000/19487
23000 20011 1.15 = 23000/20011
34000 20535 1.66 = 34000/20535
10000 21059 0.47 = 10000/21059
18000 21583 0.83 = 18000/21583
23000 22107 1.04 = 23000/22107
38000 22631 1.68 = 38000/22631
12000 23155 0.52 = 12000/23155
13000 23679 0.55 = 13000/23679
32000 24203 1.32 = 32000/24203
41000 24727 1.66 = 41000/24727
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Estimating Seasonal Factors
The overall seasonal factor for a “season” is then obtained
by averaging all of the factors for a “season”
If there are r seasonal cycles, for all periods of the form
pt+i, 1<i<p, the seasonal factor for season i is
Si = [Sum(j=0 to r-1) Sjp+i]/r
In the example, there are 3 seasonal cycles in the data and
p=4, so
S1 = (0.42+0.47+0.52)/3 = 0.47
S2 = (0.67+0.83+0.55)/3 = 0.68
S3 = (1.15+1.04+1.32)/3 = 1.17
S4 = (1.66+1.68+1.66)/3 = 1.67
© 2007 Pearson Education
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Estimating the Forecast
Using the original equation, we can forecast the next
four periods of demand:
F13 = (L+13T)S1 = [18439+(13)(524)](0.47) = 11868
F14 = (L+14T)S2 = [18439+(14)(524)](0.68) = 17527
F15 = (L+15T)S3 = [18439+(15)(524)](1.17) = 30770
F16 = (L+16T)S4 = [18439+(16)(524)](1.67) = 44794
© 2007 Pearson Education
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Adaptive Forecasting
 The
estimates of level, trend, and seasonality are
adjusted after each demand observation
 General steps in adaptive forecasting
 Moving average
 Simple exponential smoothing
 Trend-corrected exponential smoothing (Holt’s
model)
 Trend- and seasonality-corrected exponential
smoothing (Winter’s model)
© 2007 Pearson Education
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Basic Formula for
Adaptive Forecasting
Ft+1 = (Lt + lT)St+1 = forecast for period t+l in period t
Lt = Estimate of level at the end of period t
Tt = Estimate of trend at the end of period t
St = Estimate of seasonal factor for period t
Ft = Forecast of demand for period t (made period t-1 or
earlier)
Dt = Actual demand observed in period t
Et = Forecast error in period t
At = Absolute deviation for period t = |Et|
MAD = Mean Absolute Deviation = average value of At
© 2007 Pearson Education
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General Steps in
Adaptive Forecasting
 Initialize:
Compute initial estimates of level (L0), trend
(T0), and seasonal factors (S1,…,Sp). This is done as in
static forecasting.
 Forecast:
Forecast demand for period t+1 using the
general equation
 Estimate error: Compute error Et+1 = Ft+1- Dt+1
 Modify
estimates: Modify the estimates of level (Lt+1),
trend (Tt+1), and seasonal factor (St+p+1), given the error
Et+1 in the forecast
 Repeat
steps 2, 3, and 4 for each subsequent period
© 2007 Pearson Education
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Moving Average




Used when demand has no observable trend or seasonality
Systematic component of demand = level
The level in period t is the average demand over the last N
periods (the N-period moving average)
Current forecast for all future periods is the same and is based
on the current estimate of the level
Lt = (Dt + Dt-1 + … + Dt-N+1) / N
Ft+1 = Lt and Ft+n = Lt
After observing the demand for period t+1, revise the
estimates as follows:
Lt+1 = (Dt+1 + Dt + … + Dt-N+2) / N
Ft+2 = Lt+1
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Moving Average Example
From Tahoe Salt example (Table 7.1)
At the end of period 4, what is the forecast demand for periods 5
through 8 using a 4-period moving average?
L4 = (D4+D3+D2+D1)/4 = (34000+23000+13000+8000)/4 = 19500
F5 = 19500 = F6 = F7 = F8
Observe demand in period 5 to be D5 = 10000
Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 = 9500
Revise estimate of level in period 5:
L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 =
20000
F6 = L5 = 20000
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Simple Exponential Smoothing



Used when demand has no observable trend or seasonality
Systematic component of demand = level
Initial estimate of level, L0, assumed to be the average of all
historical data
L0 = [Sum(i=1 to n)Di]/n
Current forecast for all future periods is equal to the current
estimate of the level and is given as follows:
Ft+1 = Lt and Ft+n = Lt
After observing demand Dt+1, revise the estimate of the level:
Lt+1 = Dt+1 + (1-)Lt
Lt+1 = Sum(n=0 to t+1)[(1-)nDt+1-n ]
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Simple Exponential Smoothing
Example
From Tahoe Salt data, forecast demand for period 1 using
exponential smoothing
L0 = average of all 12 periods of data
= Sum(i=1 to 12)[Di]/12 = 22083
F1 = L0 = 22083
Observed demand for period 1 = D1 = 8000
Forecast error for period 1, E1, is as follows:
E1 = F1 - D1 = 22083 - 8000 = 14083
Assuming  = 0.1, revised estimate of level for period 1:
L1 = D1 + (1-)L0 = (0.1)(8000) + (0.9)(22083) = 20675
F2 = L1 = 20675
Note that the estimate of level for period 1 is lower than in period 0
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Trend-Corrected Exponential
Smoothing (Holt’s Model)


Appropriate when the demand is assumed to have a level and
trend in the systematic component of demand but no seasonality
Obtain initial estimate of level and trend by running a linear
regression of the following form:
Dt = at + b
T0 = a
L0 = b
In period t, the forecast for future periods is expressed as
follows:
Ft+1 = Lt + Tt
Ft+n = Lt + nTt
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Trend-Corrected Exponential
Smoothing (Holt’s Model)
After observing demand for period t, revise the estimates for level
and trend as follows:
Lt+1 = Dt+1 + (1-)(Lt + Tt)
Tt+1 = (Lt+1 - Lt) + (1-)Tt
 = smoothing constant for level
 = smoothing constant for trend
Example: Tahoe Salt demand data. Forecast demand for period 1
using Holt’s model (trend corrected exponential smoothing)
Using linear regression,
L0 = 12015 (linear intercept)
T0 = 1549 (linear slope)
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Holt’s Model Example (continued)
Forecast for period 1:
F1 = L0 + T0 = 12015 + 1549 = 13564
Observed demand for period 1 = D1 = 8000
E1 = F1 - D1 = 13564 - 8000 = 5564
Assume  = 0.1,  = 0.2
L1 = D1 + (1-)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008
T1 = (L1 - L0) + (1-)T0 = (0.2)(13008 - 12015) + (0.8)(1549)
= 1438
F2 = L1 + T1 = 13008 + 1438 = 14446
F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760
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Trend- and Seasonality-Corrected
Exponential Smoothing
 Appropriate
when the systematic component of
demand is assumed to have a level, trend, and seasonal
factor
 Systematic component = (level+trend)(seasonal factor)
 Assume periodicity p
 Obtain initial estimates of level (L0), trend (T0),
seasonal factors (S1,…,Sp) using procedure for static
forecasting
 In
period t, the forecast for future periods is given by:
Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + nTt)St+n
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Trend- and Seasonality-Corrected
Exponential Smoothing (continued)
After observing demand for period t+1, revise estimates for level,
trend, and seasonal factors as follows:
Lt+1 = (Dt+1/St+1) + (1-)(Lt+Tt)
Tt+1 = (Lt+1 - Lt) + (1-)Tt
St+p+1 = (Dt+1/Lt+1) + (1-)St+1
 = smoothing constant for level
 = smoothing constant for trend
 = smoothing constant for seasonal factor
Example: Tahoe Salt data. Forecast demand for period 1 using
Winter’s model.
Initial estimates of level, trend, and seasonal factors are obtained
as in the static forecasting case
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Trend- and Seasonality-Corrected
Exponential Smoothing Example (continued)
L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.67
F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913
The observed demand for period 1 = D1 = 8000
Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913
Assume  = 0.1, =0.2, =0.1; revise estimates for level and trend
for period 1 and for seasonal factor for period 5
L1 = (D1/S1)+(1-)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769
T1 = (L1-L0)+(1-)T0 = (0.2)(18769-18439)+(0.8)(524) = 485
S5 = (D1/L1)+(1-)S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47
F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093
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Measures of Forecast Error
 Forecast

error = Et = Ft - Dt
Mean squared error (MSE)
MSEn = (Sum(t=1 to n)[Et ])/n
2
Absolute deviation = At = |Et|
 Mean absolute deviation (MAD)
MADn = (Sum(t=1 to n)[At])/n

=1.25MAD
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Measures of Forecast Error

Mean absolute percentage error (MAPE)
MAPEn = (Sum(t=1 to n)[|Et/ Dt|100])/n
Bias
 Shows whether the forecast consistently under- or
overestimates demand; should fluctuate around 0
biasn = Sum(t=1 to n)[Et]

Tracking signal
 Should be within the range of +6
 Otherwise, possibly use a new forecasting method
TSt = bias / MADt

© 2007 Pearson Education
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Forecasting Demand at Tahoe Salt
 Moving
average
 Simple exponential smoothing
 Trend-corrected exponential smoothing
 Trend- and seasonality-corrected exponential
smoothing
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Forecasting in Practice
 Collaborate
in building forecasts
 The value of data depends on where you are in the
supply chain
 Be sure to distinguish between demand and sales
© 2007 Pearson Education
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Summary of Learning Objectives
 What
are the roles of forecasting for an enterprise and
a supply chain?
 What are the components of a demand forecast?
 How is demand forecast given historical data using
time series methodologies?
 How is a demand forecast analyzed to estimate
forecast error?
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