global supply chain management lecture 5.pptx
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Supply Chain Management: Strategy,Planning, Operations (3/e)
Sunil Chopra & Peter Meindl
Chapter 7
Lecture 5Demand Forecasting in a Supply Chain
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Role of Forecasting in a Supply
Chain
The basis for all strategic and planning decisionsin a supply chain
Used for both push and pull processes
Examples: Production: scheduling, inventory, aggregate
planning
Marketing: sales force allocation, promotions, newproduction introduction
Finance: plant/equipment investment, budgetaryplanning
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 short-
term forecasts (forecast horizon is important) Aggregate forecasts are more accurate than
disaggregate forecasts
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Forecasting Methods
Qualitative: primarily subjective; rely on judgmentand opinion
Time Series: use historical demand only
Static Adaptive
Causal: use the relationship between demandand 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 ForecastingQuarter Demand Dt
II, 1998 8000
III, 1998 13000
IV, 1998 23000
I, 1999 34000II, 1999 10000
III, 1999 18000
IV, 1999 23000
I, 2000 38000II, 2000 12000
III, 2000 13000
IV, 2000 32000
I, 2001 41000
Forecast demand fo r th
next four quarters.
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Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
9 7 , 2
9 7 , 3
9 7 , 4
9 8 , 1
9 8 , 2
9 8 , 3
9 8 , 4
9 9 , 1
9 9 , 2
9 9 , 3
9 9 , 4
0 0 , 1
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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
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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
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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 seasonalfluctuations
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
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Time Series Forecasting
(Table 7.1)
Quarter Demand Dt
II, 1998 8000
III, 1998 13000
IV, 1998 23000
I, 1999 34000II, 1999 10000
III, 1999 18000
IV, 1999 23000
I, 2000 38000II, 2000 12000
III, 2000 13000
IV, 2000 32000
I, 2001 41000
Forecast demand fo r th
next four quarters.
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Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
9 7 , 2
9 7 , 3
9 7 , 4
9 8 , 1
9 8 , 2
9 8 , 3
9 8 , 4
9 9 , 1
9 9 , 2
9 9 , 3
9 9 , 4
0 0 , 1
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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 seasonalfluctuations
Periodicity ( p)
the number of periods after which the seasonal
cycle repeats itself
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Deseasonalizing Demand
[Dt-(p/2) + Dt+(p/2) + S 2Di] / 2p for p even
Dt = (sum is from i = t+1-(p/2) to t+1+(p/2))
S 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 + t T
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 donein Excel)
In the example, L = 18,439 and T = 524
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Time Series of Demand
(Figure 7.3)
0
10000
20000
30000
40000
50000
1 2 3 4 5 6 7 8 9 10 11 12
Period
D e m a n d
Dt
Dt-bar
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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 arecalculated in the same manner
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Estimating Seasonal Factors
(Fig. 7.4)
t Dt Dt-bar S-bar
1 8000 18963 0.42 = 8000/18963
2 13000 19487 0.67 = 13000/19487
3 23000 20011 1.15 = 23000/20011
4 34000 20535 1.66 = 34000/20535
5 10000 21059 0.47 = 10000/21059
6 18000 21583 0.83 = 18000/21583
7 23000 22107 1.04 = 23000/22107
8 38000 22631 1.68 = 38000/22631
9 12000 23155 0.52 = 12000/23155
10 13000 23679 0.55 = 13000/23679
11 32000 24203 1.32 = 32000/24203
12 41000 24727 1.66 = 41000/24727
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Estimating Seasonal Factors
The overall seasonal factor for a “season” is then obtainedby 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) S jp+i ]/r In the example, there are 3 seasonal cycles in the dataand p=4, so
S1 = (0.42+0.47+0.52)/3 = 0.47
S2 = (0.67+0.83+0.55)/3 = 0.68S3 = (1.15+1.04+1.32)/3 = 1.17
S4 = (1.66+1.68+1.66)/3 = 1.67
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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) = 11868F14 = (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
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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)
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Basic Formula for
Adaptive Forecasting
Ft+1 = (Lt + l T)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
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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 thegeneral 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 theerror Et +1 in the forecast
Repeat steps 2, 3, and 4 for each subsequent period
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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 Nperiods (the N-period moving average)
Current forecast for all future periods is the same and is basedon 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 periods5 through 8 using a 4-period moving average?
L4 = (D4+D3+D2+D1)/4 = (34000+23000+13000+8000)/4 =
19500F5 = 19500 = F6 = F7 = F8
Observe demand in period 5 to be D5 = 10000
Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 =
9500Revise estimate of level in period 5:
L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 =20000
F6 = L5 = 2000029
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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 = aDt+1 + (1-a)Lt
Lt+1 = Sum(n=0 to t+1)[a(1-a)nDt+1-n ]
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Simple Exponential Smoothing
Example
From Tahoe Salt data, forecast demand for period 1 usingexponential 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 = 8000Forecast error for period 1, E1, is as follows:
E1 = F1 - D1 = 22083 - 8000 = 14083
Assuming a = 0.1, revised estimate of level for period 1:
L1 = aD1 + (1-a)L0 = (0.1)(8000) + (0.9)(22083) = 20675
F2 = L1 = 20675Note 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 leveland trend in the systematic component of demand but noseasonality
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 asfollows:
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 leveland trend as follows:
Lt+1 = aDt+1 + (1-a)(Lt + Tt)
Tt+1 = b(Lt+1 - Lt) + (1-b)Tt
a = smoothing constant for levelb = smoothing constant for trend
Example: Tahoe Salt demand data. Forecast demand for period 1using 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 a = 0.1, b = 0.2
L1 = aD1 + (1-a)(L0+T0) = (0.1)(8000) + (0.9)(13564) =13008
T1 = b(L1 - L0) + (1-b)T0 = (0.2)(13008 - 12015) +(0.8)(1549)
= 1438
F2 = L1 + T1 = 13008 + 1438 = 14446
F5 = L1 + 4T1 = 13008 + (4)(1438) = 1876034
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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 staticforecasting
In period t, the forecast for future periods is given by:
Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + nTt)St+n 35
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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 = a(Dt+1/St+1) + (1-a)(Lt+Tt)
Tt+1 = b(Lt+1 - Lt) + (1-b)Tt
St+p+1 = g(Dt+1/Lt+1) + (1-g)St+1
a = smoothing constant for level
b = smoothing constant for trend
g = 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 a = 0.1, b=0.2, g=0.1; revise estimates for level and trendfor period 1 and for seasonal factor for period 5
L1 = a(D1/S1)+(1-a)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769
T1 = b(L1-L0)+(1-b)T0 = (0.2)(18769-18439)+(0.8)(524) = 485
S5 = g(D1/L1)+(1-g)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)[Et2])/n
Absolute deviation = At = |Et|
Mean absolute deviation (MAD)
MADn = (Sum(t=1 to n)[At])/n
s = 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 0biasn = 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
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Forecasting Demand at Tahoe
Salt
Moving average
Simple exponential smoothing
Trend-corrected exponential smoothing
Trend- and seasonality-corrected exponentialsmoothing
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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
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