6323
Demand ESI Forecasting in a Supply Chain
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
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
3
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
4
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
5
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, 2006
III, 2006
IV, 2006
I, 2007
II, 2007
III, 2007
IV, 2007
I, 2008
II, 2008
III, 2008
IV, 2008
I, 2009
Demand Dt
8000
13000
23000
34000
10000
18000
23000
38000
12000
13000
32000
41000
Forecast demand for the
next four quarters.
Time Series Forecasting
60,000
40,000
20,000
0
7
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Forecasting Methods
Static
Adaptive
Moving average
Simple exponential smoothing
Holts model (with trend)
Winters 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]S t+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
Time Series Forecasting (Table 7.1)
Quarter, Year Demand Dt
II, 1
8000
III, 1
13000
IV, 1
23000
I, 2
34000
II, 2
10000
III, 2
18000
IV, 2
23000
I, 3
38000
II, 3
12000
III, 3
13000
IV, 3
32000
I, 4
41000
Forecast demand for the
next four quarters.
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14
Time Series Forecasting (Figure 7.1)
50,000
40,000
30,000
20,000
10,000
0
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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
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Deseasonalizing Demand
Dt =
[Dt-(p/2) + Dt+(p/2) + Sum 2Di] / 2p for p even
(sum is from i = t+1-(p/2) to t-1+(p/2))
Sum 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
Ft = L + t T
where Ft = deseasonalized demand forecast 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
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Deseasonalized Demand-(Dt-bar)
Figure 7.3 Deseasonalized Demand for Tahoe Salt
45,000
40,000
35,000
Demand
30,000
25,000
20,000
15,000
10,000
5,000
0
0
2
4
6
8
10
Period, t
Demand
Dt
Deseasonalized Demand
12
14
20
Demand
Forecasted Deseasonalized Demand
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
Dt
Ft-bar
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 / Ft = seasonal factor for period t
In the example,
F2 = 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
Dt
8000
13000
23000
34000
10000
18000
23000
38000
12000
13000
32000
41000
Ft-bar S-bar
18963 0.42 = 8000/18963
19487 0.67 = 13000/19487
20011 1.15 = 23000/20011
20535 1.66 = 34000/20535
21059 0.47 = 10000/21059
21583 0.83 = 18000/21583
22107 1.04 = 23000/22107
22631 1.68 = 38000/22631
23155 0.52 = 12000/23155
23679 0.55 = 13000/23679
24203 1.32 = 32000/24203
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 p t+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
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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
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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 (Holts model)
Trend- and seasonality-corrected exponential smoothing
(Winters model)
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Basic for Formula 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
1. Initialize: Compute initial estimates of level (L0), trend (T0), and
seasonal factors (S1,,Sp). This is done as in static forecasting.
2. Forecast: Forecast demand for period t+1 using the general
equation
3. Estimate error: Compute error Et+1 = Ft+1- Dt+1
4. 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
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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 4period 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 = 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 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 a = 0.1, revised estimate of level for period 1:
L1 = aD1 + (1-a)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 (Holts 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 (Holts Model)
After observing demand for period t, revise the estimates for level and trend as
follows:
Lt+1 = aDt+1 + (1-a)(Lt + Tt)
Tt+1 = b(Lt+1 - Lt) + (1-b)Tt
a = smoothing constant for level
b = smoothing constant for trend
Example: Tahoe Salt demand data. Forecast demand for period 1 using Holts
model (trend corrected exponential smoothing)
Using linear regression,
L0 = 12015 (linear intercept)
T0 = 1549 (linear slope)
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Holts 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) = 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 = 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 Winters 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 trend for 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 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
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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
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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?