scm report on demand forecasting
TRANSCRIPT
© 2007 Pearson Education
Chapter 7Demand Forecasting
in a Supply Chain
Supply Chain Management(3rd Edition)
7-1
© 2007 Pearson Education 7-2
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 7-3
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
© 2007 Pearson Education 7-4
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
© 2007 Pearson Education 7-5
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
© 2007 Pearson Education 7-6
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
© 2007 Pearson Education 7-7
Time Series ForecastingQuarter Demand Dt
II, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2000 38000II, 2000 12000III, 2000 13000IV, 2000 32000I, 2001 41000
Forecast demand for thenext four quarters.
© 2007 Pearson Education 7-8
Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
97,2
97,3
97,4
98,1
98,2
98,3
98,4
99,1
99,2
99,3
99,4
00,1
© 2007 Pearson Education 7-9
Forecasting Methods
Static Adaptive
– Moving average
– Simple exponential smoothing
– Holt’s model (with trend)
– Winter’s model (with trend and seasonality)
© 2007 Pearson Education 7-10
Basic Approach toDemand 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 7-11
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 7-12
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
© 2007 Pearson Education 7-13
Static Methods
Estimating level and trend Estimating seasonal factors
© 2007 Pearson Education 7-14
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 7-15
Time Series Forecasting (Table 7.1)
Quarter Demand Dt
II, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2000 38000II, 2000 12000III, 2000 13000IV, 2000 32000I, 2001 41000
Forecast demand for thenext four quarters.
© 2007 Pearson Education 7-16
Time Series Forecasting(Figure 7.1)
0
10,000
20,000
30,000
40,000
50,000
97,2
97,3
97,4
98,1
98,2
98,3
98,4
99,1
99,2
99,3
99,4
00,1
© 2007 Pearson Education 7-17
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 7-18
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
© 2007 Pearson Education 7-19
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
© 2007 Pearson Education 7-20
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 7-21
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
Dem
an
d
Dt
Dt-bar
© 2007 Pearson Education 7-22
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
© 2007 Pearson Education 7-23
Estimating Seasonal Factors (Fig. 7.4)
t Dt Dt-bar S-bar1 8000 18963 0.42 = 8000/189632 13000 19487 0.67 = 13000/194873 23000 20011 1.15 = 23000/200114 34000 20535 1.66 = 34000/205355 10000 21059 0.47 = 10000/210596 18000 21583 0.83 = 18000/215837 23000 22107 1.04 = 23000/221078 38000 22631 1.68 = 38000/226319 12000 23155 0.52 = 12000/23155
10 13000 23679 0.55 = 13000/2367911 32000 24203 1.32 = 32000/2420312 41000 24727 1.66 = 41000/24727
© 2007 Pearson Education 7-24
Estimating Seasonal FactorsThe 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 7-25
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 7-26
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 7-27
Basic Formula forAdaptive 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 7-28
General Steps inAdaptive 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 7-29
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
© 2007 Pearson Education 7-30
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
© 2007 Pearson Education 7-31
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 ]
© 2007 Pearson Education 7-32
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
© 2007 Pearson Education 7-33
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
© 2007 Pearson Education 7-34
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)
© 2007 Pearson Education 7-35
Holt’s Model Example (continued)
Forecast for period 1:F1 = L0 + T0 = 12015 + 1549 = 13564Observed demand for period 1 = D1 = 8000E1 = F1 - D1 = 13564 - 8000 = 5564Assume = 0.1, = 0.2L1 = D1 + (1-)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008T1 = (L1 - L0) + (1-)T0 = (0.2)(13008 - 12015) + (0.8)(1549) = 1438F2 = L1 + T1 = 13008 + 1438 = 14446F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760
© 2007 Pearson Education 7-36
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
© 2007 Pearson Education 7-37
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
© 2007 Pearson Education 7-38
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
© 2007 Pearson Education 7-39
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
= 1.25MAD
© 2007 Pearson Education 7-40
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 7-41
Forecasting Demand at Tahoe Salt
Moving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential
smoothing
© 2007 Pearson Education 7-42
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 7-43
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?