-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
1/44
Demand Forecasting
in a Supply Chain
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
2/44
Chapter 7
Demand Forecasting
in a Supply Chain
Supply Chain Management
(3rd Edition)
7-2
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
3/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
4/44
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, newproduction introduction
Finance: plant/equipment investment, budgetaryplanning
Personnel: workforce planning, hiring, layoffs
All of these decisions are interrelated
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
5/44
Characteristics of Forecasts
Forecasts are always wrong. Should include
expected value and measure of error.
Long-term forecasts are less accurate thanshort-term forecasts (forecast horizon is
important)
Aggregate forecasts are more accurate thandisaggregate forecasts
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
6/44
Forecasting Methods
Qualitative: primarily subjective; rely on judgmentand opinion
Time Series: use historical demand only
Static Adaptive
Causal: use the relationship between demand andsome other factor to develop forecast
Simulation Imitate consumer choices that give rise to demand Can combine time series and causal methods
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
7/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
8/44
Time Series Forecasting
Q uarter D em and D tII, 1998 8000
III, 1998 13000
IV , 1998 23000
I, 1999 34000
II, 1999 10000
III, 1999 18000
IV , 1999 23000
I, 2000 38000
II, 2000 12000
III, 2000 13000IV , 2000 32000
I, 2001 41000
Forecast demand for the
next four quarters.
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
9/44
Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
97,
297,
397,
498,
198,2
98,3
98,
499,
199,2
99,3
99,
400,
1
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
10/44
Forecasting Methods
Static
Adaptive
Moving average Simple exponential smoothing
Holts model (with trend)
W
inters model (w
ith trend and seasonality)
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
11/44
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 forecastingtechnique
Establish performance and error measures forthe forecast
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
12/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
13/44
Static Methods
Assume a mixed model:
Systematic component = (level + trend)(seasonal factor)
Ft+l= [L + (t + l)T]St+l
= forecast in period tfor 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
14/44
Static Methods
Estimating level and trend
Estimating seasonal factors
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
15/44
Estimating Level and Trend
Before estimating level and trend, demanddata must be deseasonalized
Deseasonalized demand = demand that would
have been observed in the absence ofseasonal fluctuations
Periodicity (p)
the number of periods after which the seasonalcycle repeats itself
for demand at Tahoe Salt (Table 1, Figure 1) p = 4
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
16/44
Time Series Forecasting
(Table 1)Quarter Dem and D tII, 1998 8000
III, 1998 13000
IV, 1998 23000
I, 1999 34000
II, 1999 10000
III, 1999 18000
IV, 1999 23000
I, 2000 38000
II, 2000 12000
III, 2000 13000
IV, 2000 32000
I, 2001 41000
Forecast demand for the
next four quarters.
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
17/44
Time Series Forecasting
(Figure 1)
0
10,000
20,000
30,000
40,000
50,000
97,
297,
397,
498,
198,2
98,3
98,
499,
199,2
99,3
99,
400,
1
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
18/44
Estimating Level and Trend
Before estimating level and trend, demanddata must be deseasonalized
Deseasonalized demand = demand that would
have been observed in the absence ofseasonal fluctuations
Periodicity (p)
the number of periods after which the seasonalcycle repeats itself
for demand at Tahoe Salt (Table 1, Figure 1) p = 4
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
19/44
Deseasonalizing Demand
[Dt-(p/2) + Dt+(p/2) + 7 2Di] / 2p forp evenDt = (sum is from i = t+1-(p/2) to t+1+(p/2))
7 Di / p forpodd(sum is from i = t-(p/2) to t+(p/2)), p/2 truncated to lower integer
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
20/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
21/44
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 usingdeseasonalized demand as the dependent variable andperiod as the independent variable (can be done in
Excel)In the example, L = 18,439 and T = 524
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
22/44
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
Deman Dt
Dt-bar
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
23/44
Estimating Seasonal Factors
Use the previous equation to calculatedeseasonalized demand for each period
St= D
t/ D
t= 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
24/44
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 = 10000/210596 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
25/44
Estimating Seasonal Factors
The overall seasonal factor for a season is then obtained byaveraging all of the factors for a season
If there are r seasonal cycles, for all periods of the form pt+i,1
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
26/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
27/44
Adaptive Forecasting
The estimates of level, trend, and seasonalityare 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 exponentialsmoothing (Winters model)
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
28/44
Basic Formula for
Adaptive Forecasting
Ft+1 = (Lt+ lT)St+1 = forecast for period t+lin 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
29/44
General Steps in
Adaptive Forecasting
Initialize: Compute initial estimates of level (L0), trend(T0), and seasonal factors (S1,,Sp). This is done as instatic 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
30/44
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 levelLt = (Dt + Dt-1 + + Dt-N+1) / N
Ft+1 = Lt and Ft+n = LtAfter observing the demand for period t+1, revise the estimates asfollows:
Lt+1 = (Dt+1 + Dt + + Dt-N+2) / NFt+2 = Lt+1
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
31/44
Moving Average Example
From Tahoe Salt example (Table 7.1)
At the end of period 4, what is the forecast demand for periods 5through 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
32/44
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 allhistorical data
L0 = [Sum(i=1 to n)Di]/nCurrent forecast for all future periods is equal to the currentestimate of the level and is given as follows:
Ft+1 = Ltand Ft+n = LtAfter observing demand Dt+1, revise the estimate of the level:
Lt+1 = EDt+1 + (1-E)LtLt+1 = Sum(n=0 to t+1)[E(1-E)
nDt+1-n ]
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
33/44
Simple Exponential Smoothing
ExampleFrom 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 = 8000Forecast error for period 1, E1, is as follows:
E1 = F1 - D1 = 22083 - 8000 = 14083
Assuming E = 0.1, revised estimate of level for period 1:
L1 = ED1 + (1-E)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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
34/44
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
35/44
Trend-Corrected Exponential
Smoothing (Holts Model)After observing demand for period t, revise the estimates for level and
trend as follows:
Lt+1 = EDt+1 + (1-E)(Lt + Tt)
Tt+1 =F(Lt+1 - Lt) + (1-F)Tt
E = smoothing constant for levelF = smoothing constant for trend
Example: Tahoe Salt demand data. Forecast demand for period 1 usingHolts model (trend corrected exponential smoothing)
Using linear regression,
L0 = 12015 (linear intercept)
T0 = 1549 (linear slope)
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
36/44
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 = 5564Assume E = 0.1,F = 0.2
L1 = ED1 + (1-E)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008
T1 =F(L1 - L0) + (1-F)T0 = (0.2)(13008 - 12015) + (0.8)(1549)
= 1438
F2 = L1 + T1 = 13008 + 1438 = 14446
F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
37/44
Trend- and Seasonality-Corrected
Exponential Smoothing Appropriate when the systematic component of
demand is assumed to have a level, trend, and seasonalfactor
Systematic component = (level+trend)(seasonal factor)
Assume periodicity p
Obtain initial estimates of level (L0), trend (T0), seasonalfactors (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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
38/44
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 = E(Dt+1/St+1) + (1-E)(Lt+Tt)
Tt+1 =F(Lt+1 - Lt) + (1-F)TtSt+p+1 = K(Dt+1/Lt+1) + (1-K)St+1
E = smoothing constant for levelF = smoothing constant for trend
K = smoothing constant for seasonal factor
Example: Tahoe Salt data. Forecast demand for period 1 using Wintersmodel.
Initial estimates of level, trend, and seasonal factors are obtained as inthe static forecasting case
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
39/44
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 E = 0.1,F=0.2, K=0.1; revise estimates for level and trend forperiod 1 and for seasonal factor for period 5
L1 = E(D1/S1)+(1-E)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769
T1 =F(L1-L0)+(1-F)T0 = (0.2)(18769-18439)+(0.8)(524) = 485
S5 = K(D1/L1)+(1-K)S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47
F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
40/44
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
W = 1.25MAD
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
41/44
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- oroverestimates 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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
42/44
7-42
Forecasting Demand at Tahoe Salt
Moving average
Simple exponential smoothing
Trend-corrected exponential smoothing Trend- and seasonality-corrected
exponential smoothing
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
43/44
7-43
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
-
8/6/2019 Supply Chain Management-L6a-Demand Forecasting
44/44
7-44
Summary of Learning Objectives
What are the roles of forecasting for anenterprise and a supply chain?
What are the components of a demandforecast?
How is demand forecast given historical datausing time series methodologies?
How is a demand forecast analyzed to estimateforecast error?