Forecasting: Basics
Supply Chain Management
Fall, 2004
Dr. Lu
Note 5
1
Outline
‹
‹
‹
‹
‹
‹
‹
Principals of demand forecasting
Time series method
Isolating the trend
Seasonal variation
Performance evaluation
A complete example
Conclusion
2
Four Module in SCM
‹
Demand Forecasting
– How to reduce the forecast error
‹
Managing the material flow
– Manage the inventory…
‹
Coordination
– To make sure the whole chain share the same objective
‹
Value of information and information technology
– Value of information sharing, early marketing signal
3
Forecasting: Importance
‹ Initial
‹
‹
step for making any decision
Good forecasting can reduce the uncertainty of the demand
Bad forecasting either leads to the lots of inventory or out of
stock
– Nike has a lot of inventory for one kind of product while out of stock
for the other product
‹
The better forecast can reduce the operating cost while
providing better service for the customer
4
Forecasting
‹ Forecasting
– For any given information, how to reduce the uncertainty in
demand
‹ Some
innovation: VMI, early market signal, postpone
– How to get more information so that the demand
uncertainty can be reduced
5
Philosophy of Forecasting
‹
The past can tell the future in some way
– The demand will not change rapidly in a short period
– Read Nike’s recent story of forecasting
‹
New information is very important
– When the demand changes rapidly, new information or expert opinion
should be combined together with the history data to get a better
forecast
‹
Trend is very important
– Trend detecting techniques will be addressed
‹
Long term forecast is almost impossible
– We focus on short term forecasting
6
Nike: Future Results Not Guaranteed
(2003)
‹
IT'S BEEN MORE than two years since Nike Chairman
Phil Knight owned up to the sneaker giant's disastrous
$400 million experiment with demand forecasting
software. The headlines are well known: Nike went live
with its much-vaunted i2 system in June 2000, and nine
months later, its executives acknowledged that they would
be taking a major inventory write-off because the forecasts
from the automated system had been so inaccurate. With
that announcement in February 2001, Nike's stock value
plummeted, along with its reputation as an innovative user
of technology.
7
Nike: Future Results Not Guaranteed
(2003)
‹
Relying exclusively on the automated projections, Nike
ended up ordering $90 million worth of shoes, such as the
Air Garnett II, that turned out to be very poor sellers. The
company also came up with an $80 million to $100 million
shortfall on popular models, such as the Air Force One.
Nike isn't the only company with a forecasting horror story.
Corporate America is littered with companies that invested
heavily in demand software but have little or nothing to
show for it. Goodyear, for example, implemented a demand
forecasting system in mid-2000 but hasn't shown significant
improvement in managing its inventory, and last year the tire
company lost more money than the year before.
‹
In 2002 alone, companies spent $19 billion on demand
‹
forecasting software and other supply chain solutions,
according to IDC (a sister company to CIO's publisher).
8
Past Can predict the Future?
‹
‹
From hard experience, a growing number of CIOs now
realize that computer systems alone are incapable of
producing accurate forecasts.
Software can't predict the future, particularly sudden,
unexpected shifts in economic or market conditions. Nor
can it exercise the kind of rational analysis or judgement
that human beings excel at. Hence, demand forecasting
technology is inherently limited, and companies such as
Nike and Cisco that rely on it without an institutionalized
set of human checks and balances will invariably end up in
trouble
9
Past Can predict the Future?
‹
‹
Even if a demand forecasting system had 100 percent accurate
information, there is another problem: The past can't predict the future.
Computer-generated forecasts use historical data to make assumptions
about what will happen, but there is no way for them to anticipate
major market changes.
Belvedere International, which is based in Ontario, Canada, makes
skin-care products. When SARS broke out in Toronto, Belvedere sold
more than a year's worth of its One Step hand disinfectant in a month.
No forecasting system could have predicted that. Belvedere has kept
its assembly line running 16 hours a day, six days a week—modifying
production of other goods in the process—just to keep pace with
demand. "It's no different from forecasting the weather," says Gene
Alvarez, Meta Group's vice president of technology re-search services.
"Once in a while something the model couldn't figure out catches them
off guard. Same thing happens with consumer taste and demand."
10
Nike
‹
In the end, the demand forecasting failure at Nike and other companies
can be laid squarely on the shoulders of executives who put too much
faith in technology. Court records in the lawsuits by shareholders
against Nike reveal that executives for the sneaker company didn't
even hold meetings to review and discuss the computerized forecasts
that turned out to be so disastrously wrong. In other words, Nike
management neglected to put in place a high-level process of human
checks and balances for the computerized forecast. While that
negligence actually enabled Nike executives to successfully argue that
they were initially unaware of the flawed forecast that was generating
such a huge inventory glut, it was a Pyrrhic victory. The company still
lost $180 million in sneaker sales and a third of its stock market value.
11
Global Crossing
‹
‹
‹
‹
Global Crossing is a major telecommunications company that provides
computer networking services worldwide. It maintains a large
backbone and offers transit and peering links , VPN and VoIP , mainly to
large customers as it is a tier 1 carrier . It rode the wave of the 1990s to
incredibly high market values, only to go bankrupt a few years later. Its
stock price hit a high of US $64 per share, and would eventually plunge to
below $1.
Reach Global Services Ltd. (Backbone owned by Telstra and PCCW )
In January 2002, the company declared chapter 11 bankruptcy, making it
the fourth largest insolvency in United States history. By December 2003 ,
the company completed its restructuring and emerged from bankruptcy,
after Singapore Technologies Telemedia bought a two-thirds stake in the
business.
The ratio of demand and supply for the whole industry is less than 2.7%
12
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
‹ Aggregate
forecasts are more accurate than
disaggregate forecasts
13
Initial Step of Forecasting
‹
‹
The more information you have, the better forecast can be
made
The following factors should be known
–
–
–
–
–
‹
Past demand
Market planning like promotions
State of economy
Planned price discounts
Actions from your competitors and more…
Example
– Cisco: duplicate orders
14
CISCO SYSTEMS, INC
‹ CISCO
is the worldwide leader in networking for
the Internet. Cisco Internet Protocol (IP)-based
networking solutions are the foundation of the
Internet and most corporate, education, and
government networks around the world. Cisco
provides the broadest line of solutions for
transporting data, voice, and video within
buildings, across campuses, or around the world.
‹ Cisco was founded in 1984 by a group of
computer scientists from Stanford University
15
Cisco
CONSOLIDATED STATEMENTS OF
OPERATIONS DATA
‹ (In millions, except per-share amounts)
‹ Years Ended July 28, 2001 July 29, 2000 July 31,
1999
‹ Net sales $22,293 $18,928 $12,173
‹ Income (loss) before provision for taxes $ (874) $
4,343 $ 3,203
‹ Net income (loss) $ (1,014) $ 2,668 $ 2,023
‹ Net income (loss) per share—diluted $ (0.14) $
0.36 $ 0.26
16
‹
Forecasting Methods
‹
Subjective Forecasting Methods
– subjective, human judgment
– Sales force composites, customer survey, jury of executive
opinion, delphi method
‹
Objective Methods: Statistics method
– Causal models: assume demand forecast is highly correlated with
certain factors
– Time series and more
– Bayisan update model and others …
‹
Objective Methods: Models from economy method
– Discrete choice model (will not be discussed in this class)
17
Phases of Supply Chain Decisions
Regression: Casual Method
Strategy
(Design)
Planning
Operation
Forecast
Time Series Method
Forecast
Actual
Demand
18
Time Series Forecasting
Historical Data
Di
i=1,2,…,t
Forecast
Time Series Model
Ft+u
u=1,2,…
19
Components of an observation
Observed demand (O) =
Systematic component + Random component (R)
Trend (growth or decline in demand)
Seasonality (predictable seasonal fluctuation)
Filter out the random component (noise) and estimate
the systematic component !
20
Trend and Seasonality
Trend(1)
demand
demand
stationary series
time
time
demand
demand
seasonality + trend
time
Trend(2)
time
21
Elements of a Time Series
‹ Additive
model: Observed demand=Trend +
Seasonal +Random
‹ Multiplicative model: Observed demand=Trend *
Seasonal +Random
‹ Forecasting is to identify the system term
– Which are trend and seasonal terms
– The observed demand minus system term should be
pure random (with mean zero symmetry)
22
Steps in Forecasting
‹ Preliminary
handling
– Filtering, moving average
‹ Identifying
the trend term
– Regression
– Curve fitting
‹ De-seasonalized
the demand data if exist
‹ Evaluate the forecast
23
Warm-up: Parameter Estimation
‹ Suppose
demand i.i.d. random variable with Normal
distribution, how to do forecast?
‹ Forecast becomes estimation, how to estimate the
parameters
1 t
Lt =
‹ Model
∑ Di
Ft +τ
‹
‹
N i = t − N +1
= Lt ,
τ = 1,2,...
All the data will be used to estimate the demand
How to estimate the standard deviation?
24
Parameter Estimation
‹ Assumptions
-
No trend
Equal weight to all the N observations
‹ Model
1 t
Lt =
Di
∑
N i = t − N +1
Ft +τ = L t ,
τ = 1,2,...
25
Moving Average
‹ Assumptions
-
No trend
Equal weight to all the N observations
‹ Model
‹ Decision
1 t
Lt =
Di
∑
N i = t − N +1
Ft +τ = L t ,
τ = 1,2,...
:N
26
Isolating the Trend: Moving Average
‹ Example
– Quarterly data for the demand of certain product is as
following: 200, 250, 175, 186, 225, 285, 305 and 190.
Determine the one-period ahead forecast for the next
quarter F4, F5,…, F8 by using three-period moving and
6-period moving?
27
Moving Average
‹ Multiple
period ahead: Ft,t+i=Ft+1
– The reason is, we assume the demand is stationary
‹ Example
– Quarterly data for the demand of certain product is as
following: 200, 250, 175, 186, 225, 285, 305 and 190.
Determine the forecast for the next quarter F4, F5,…, F8
by using three-period moving and 6-period moving?
28
Formula for Moving Average
Ft 1  Ft 
‹
1
N
Dt  Dt N 
Show me
29
Moving average lags behind the trend
‹ Example
– Suppose the demand has a linear increasing trend:
2,4,6,8,…, 24, consider the one-step ahead MA(3) and
MA(6) for this series
MA(3)
MA(6)
30
Isolating the Trend: Moving Average
‹ When
N is 2k+1, k=0,1,2,…
– The moving average is written in the center of the
values averaged
‹ Example
– 170, 120, 105, 156, 189, 107, 167, 205
– 3-point moving average?
– 5-point moving average?
31
Demand
Moving Average
250
200
150
100
50
0
Series1
Series2
Series3
1 2 3 4 5 6 7 8
Time
32
Isolating the Trend: Centred Moving Average
‹ When
N is 2k, the moving average will not
correspondence to a point, we can use centered
moving average
– Do moving average first
– Do average of every pair of moving average
‹ Example
– 170, 120, 105, 156, 189, 107, 167, 205
– 4-point moving average?
33
Decisions About N
‹ Bigger
N leads to smoother data, however
decreases the number of values obtained
‹ When there is obvious seasonality, N is the length
of the seasons
‹ Summary
for moving average
– Can be used to forecast the demand with no trend
– Can be used to identify the trend by providing more
smoothed data
34
Forecasting: Exponential Smoothing
‹
‹
New Forecast= α(current observation of the demand)+
(1- α)(Last forecast)
Ft 1  Dt  1   Ft , 0    1
Ft , t i  Ft 1 , i  1, 2, . . .
‹
Example
– Quarterly data for the demand of certain product is as following:
200, 250, 175, 186, 225, 285, 305 and 190. Determine the
forecast for the next quarter F4, F5,…, F8 by using exponential
smoothing for α =0.1, 0.3 ?
F1  200
35
Exponential Smoothing
Demnad
400
300
Series1
200
Series2
100
Series3
0
1 2 3 4 5 6 7 8
Time
36
200
200
200
250
200
200
175
205
215
186
202
203
225
200.4
197.9
285
202.86
206.03
305
211.074
229.721
190
220.4666
252.3047
37
Exponential Smoothing
New Forecast= α(current observation of the demand)+
(1-\ α) (Last forecast)
Ft  Ft1   Ft1  D t1 
‹
– Some kind of feedback: if the previous forecast is greater than
the demand, then reduce the forecast, otherwise, increase
forecast
– F_t=F_{t-1}- α e_{t-1}.
‹
Ft   i0 1   i Dt i1
38
Comparision of Moving average and Exponential Smoothing
‹ Similarities
– Both methods are more appropriate for the stationary
demand
– Both dependents on one parameter
– Both methods will lag behind a trend if one exists
‹ Difference
– The exponential smoothing is a weighted average of all
the past data while the moving average is a weighted
average of last N period demand
39
Isolating the Trend: Exponential Smoothing
value = α(current observation of the
demand)+ (1- α)(Smoothed data in the last period)
‹
St=αDt + (1-α) St-1
‹ Example
‹ Smoothed
– Quarterly data for the demand of certain product is as
following: 200, 250, 175, 186, 225, 285, 305 and 190.
Determine the smoothed demand by using exponential
smoothing for α =0.1, 0.3 ?
40
Isolating the Trend: Exponential Smoothing
St=αDt + (1-α) St-1
‹ A low α produces a more smoothing set of trend
elements and a high α is more sensitive to the
changes in the trend.
‹
– Compromise is needed and usually α should be around
0.1 to 0.3.
41
350
300
250
Series1
200
Series2
150
Series3
100
50
0
1
2
3
4
5
6
7
8
42
200
200
200
250
205
215
175
202
203
186
200.4
197.9
225
202.86
206.03
285
211.074
229.721
305
220.4666
252.3047
190
217.4199
233.6133
43
Summary
‹ We
present the basic ideas about demand
forecasting
‹ Two methods are presented for demand
forecasting
– Moving average and exponential smoothing
– Both the methods are lag behind the trend and so they
are proper for the stationary demand
‹ Those
two methods can be used to detect the trend
44
Outline
‹ Identifying
the trend: Regression
‹ Holt’s method
‹ Identify the seasonal factor
‹ Winter’s method
45
Isolating the Trend
‹
Regression method
n
Sxy  n  iDi 
i1
Sxx 
b 
a 
nn  1 
2
n 2 n  1 2n  1 
Sxy
Sxx
 ni1 Di
n
6

demand
– Linear regression
n
 Di
i1

n 2 n  1  2
4
time
n  1b
2
y t  a  bt
46
Formula for Linear Regerssion
n
Sxy  n  iDi 
i1
Sxx 
b 
a 
nn  1
2
n 2 n  12n  1
Sxy
Sxx
 ni1 Di
n
6

n
 Di
i1

n 2 n  1 2
4
n  1 b
2
47
Isolating Trend: Regression
‹ Example:
Using the first five observation to
estimate the demand in period 6, 7 and 8
–
–
–
–
–
200, 250, 175, 186, 225, 285, 305, 190
Sxy
Sxx
a and b
Dt=?
48
The case of observation is 5
Sxy  5200  250  2  175  3  186  4  225  5
 5  6  2200  250  175  186  225
 70
Sxx  25  6  11  25  36  50
6
4
b  Sxy / Sxx   70  1. 4
50
200  250  175  186  225
a
 1. 4 5  1  211. 4
5
2
Dt  211. 4  1. 4t
49
The case of observation is 6
Sxy  6200  250  2  175  3  186  4  225  5  285  6
 7  6  2200  250  175  186  225  285

Sxx  36  7  13  36  49 
6
4
b  Sxy / Sxx 
a 
200  250  175  186  225  285
b61 
6
2
Dt  a  bt  ?
50
Isolating Trend: Holt’s Method
St  Dt  1  St 1  Gt 1 
Gt  St  St 1   1   Gt 1
Ft , t i  St  iGt
‹
Example
– 200, 250, 175, 186, 225, 285, 305, 190
51
Solution
S0  200, G0  10,   0. 1,   0. 1
S1  D1  1  S0  G0   0. 1  200  0. 9  200  10  209
G1  S1  S0   1  G0   0. 1  209  200  0. 9  10  9. 9
S2  D2  1  S1  G1   0. 1  250  0. 9  209  9. 9  222
G2  S2  S1   1   G1   0. 1  222  209   0. 9  9. 9  10. 2
S3  D3  1   S2  G2   0. 1  175  0. 9  222  10. 2   226. 5
G3  S3  S2   1  G2   0. 1  226. 5  222  0. 9  10. 2  9. 6
F3,4  S3  1  G3  226. 5  9. 6  236. 1
F3,5  S3  2  G3  226. 5  2  9. 6  245. 7
52
Seasonal Variation: Additive Model
‹
Dt=Tt+Ct +Rt
– Dt is actual demand in period t , while Tt and Ct are trend and
seasonal variation in period t , Rt is the random term.
‹
‹
‹
‹
‹
Ct=Dt-Tt
Group the into different group according to seasonality
Computing the seasonal factor for each season by
averaging the season factors
The forecast = Trend +Season
Examples
– 35, 15, 42, 36, 19, 44, 22, 47, 45, 26, 52
– 120, 132, 106, 98, 88, 94, 119, 125, 99, 98,86, 90, 110, 119, 102,
89, 79,88,107, 114, 92, 88, 75, 80
53
35
15
30.66667
-15.6667
42
31
11
36
32.33333
3.666667
19
33
-14
44
34.66667
9.333333
41
35.66667
5.333333
22
36.66667
-14.6667
47
38
9
45
39.33333
5.666667
26
41
-15
52
S1=
-14.83
S2=
9.777778
S3=
4.888889
54
60
50
40
30
20
10
0
-10
1 2 3 4 5 6 7 8 9 10 11 12
-20
55
Forecast for the next three periods
T 13  43, T 14  44, T 15  45
F13  T 13  S13  T 13  S1  43  4. 89  47. 89
F14  T 14  S14  T 13  S2  44  14. 83  29. 17
F15  T 15  S15  T 15  S3  45  9. 78  54. 78
56
150
100
Series1
50
Series2
Series3
0
1
4
7 10 13 16 19 22
-50
57
Forecast for the Next 6 Periods
T 25  90. 6, T 26  89. 8, T 27  89. 1
T 28  88. 3, T 29  87. 5, T 30  86. 8
C1  12. 45, C2  20. 42, C3  0. 5
C4  6. 97, C5  16. 78, C6  9. 56
F25  T 25  C25  T 25  C1  90. 6  12. 45  103
F26  T 26  C26  T 26  C2  110
F27  T 27  C27  T 27  C3  88. 6
F28  T 28  C28  T 28  C4  81. 33
F29  T 29  C29  T 29  C5  70. 72
F30  T 30  C30  T 30  C6  77. 24
58
Seasonal Variation: Multiplicative Model
‹
Dt=Tt*Ct +Rt
– Dt is actual demand in period t , while Tt and Ct are trend and
seasonal variation in period t
‹
‹
‹
‹
‹
Ct=Dt/Tt
Group the into different group according to seasonality
Computing the seasonal factor for each season by
averaging the season factors
The forecast = Trend *Season
Example
– 120, 100, 121, 138, 120, 142, 160, 138, 163, 184, 162, 182, 208,
175, 206
59
250
200
150
100
50
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
60
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13
61
120
100
113.6667
0.879765
121
119.6667
1.011142
138
126.3333
1.092348
120
133.3333
0.9
142
140.6667
1.009479
160
146.6667
1.090909
138
153.6667
0.898048
163
161.6667
1.008247
184
169.6667
1.084479
162
176
0.920455
182
184
0.98913
208
188.3333
1.104425
175
196.3333
0.891341
206
0.897922
c2
1.0045
c3
1.09304
c1
62
Forecast for Next 3 Periods
T 16  203, T 17  210, T 18  217
C1  1. 09, C2  0. 898, C3  1. 005
F16  T 16  C16  T 16  C1  203  1. 09  221
F17  T 17  C17  T 17  C2  210  0. 898  189
F18  T 18  C18  T 18  C3  217  1. 005  218
63
Winter’s Seasonal Variation
‹ Dt=(L+Gt)ct+et
–
–
–
–
L is the base signal or intercept at time zero;
G is the slope of trend
et is error term that cannot be forecasted
The length of the season is N and summation of ci =N
‹ St=αDt/ct-N+(1-
α)(St-1 +Gt-1)
‹ Gt=β(St -St-1 )+ (1- β) Gt-1
‹ ct= γ Dt/St+(1- γ)ct-N
‹ Ft,t+i=(St+ i* Gt )ct+i-N
64
Winter’s Seasonal Variation: Example
‹ 10,
20, 26, 17, 12, 23, 30, 22
35
30
25
20
Series1
15
10
5
0
1
2
3
4
5
6
7
8
65
Initial Data and Initial Forecast
C5  0. 59, C6  1. 11, C7  1. 38, C8  0. 92
G8  0. 875, S8  23. 06
F8,9  S8  G9 C94  S8  G8 C5
 23. 06  0. 875   0. 59  14. 12
F8,10  S8  2  G8 C6  27. 54
F8,11  S8  3  G8 C7  35. 44
F8,12  S8  4  G8 C8  24. 38
66
Updating the Parameter and Forecast
C5  0. 59, C6  1. 11, C7  1. 38, C8  0. 92
G8  0. 875, S8  23. 06
  0. 2,   0. 1,   0. 1
D9  16
S9  D9 / c5   1  S8  G8   24. 57,
G9  S9  S8   1  G8  0. 9385,
C9  D9 / S9   1   C5  0. 5961
F9,10  S9  G9 C6  28. 3144
F9,11  S9  2G9 C7  36. 4969
67
Updating and Forecast
C5  0. 59, C6  1. 11, C7  1. 38, C8  0. 92
G8  0. 875, S8  23. 06
  0. 2,   0. 1,   0. 1
D9  16, S9  24. 57, G9  0. 9385, C9  0. 5961
D10  33, S10  26. 35, G10  1. 0227, C10  1. 124
D11  34, S11  26. 83, G11  0. 9678, C11  1. 369
D12  26, S12  27. 89, G12  0. 977, C12  0. 9212
68
Finding Initial Data
‹ Moving
Average to get trend
‹ Finding the ratio of the observed demand to the
data obtained after moving average to find the
seasonal factor
‹ Regression over the data to get trend
‹ Regression over the trend data (obtained after the
smoothing) to get the trend
69
Finding Initial Data
n
Sxy  n  x i y i 
i1
n
Sxx  n  x 2i 
i1
b 
a
Sxy
Sxx
 ni1 y i
n
y t  a  bt
b
n
n
 xi
 yi
i1
i1
i
2
n
 xi
i1
in1 x i
n
70
n  4, 3, 18. 5 , 4, 19. 125 , 5, 20, 6, 21. 125 
c1  0. 60255, c2  1. 09339, c3  1. 41139, c4  0. 89267,
n
Sxy  n  x i yi 
i1
n
n
 xi
 yi
i1
i1
 4  3  18. 5  4  19. 125  5  20  6  21. 125
 3  4  5  6   18. 5  19. 125  20  21. 125 
 4  358. 75  18  78. 75  17. 5
n
Sxx  n  x 2i 
i1
n
2
 xi
i1
 4  86  324  20
Sxy
 0. 875
Sxx
 ni1 yi
 in1 x i
a
b
 78. 75  0. 875  4. 5  15. 75
n
n
4
b 
y t  a  bt  15. 75  0. 875t
71
Finding Initial Parameter: Updating
C3  0. 59, C2  1. 11, C1  1. 38, C0  0. 92
G8  0. 875, S8  15. 75
  0. 2,   0. 1,   0. 1
D1  10
S9  D1 / c3   1  S0  G0   ?
G1  S1  S0   1   G0  ?,
C1  D1 / S1   1  C3  ?
72
Random Term
‹ If
the residue of the forecast error is pure random,
then we are done; otherwise, we have to use other
method to process the residue terms.
– One of such example will be given later as ARMA
model especially AR(1) model
– Remember, always that the residue term should be
examined
73
Forecast Performance Evaluation
‹ et=Ft-Dt
‹ MAD=(1/n)*(|e1|+|e2|+…+|en|)
‹ MSE=(1/n)*(e12+e22+…+en2)
or
‹ MSE=(1/(n-1))*(e12+e22+…+en2)
74
Summary
‹ Isolating
–
–
–
–
trend
Moving average and central moving average
Simple exponential smoothing
Regression
Holt’s model (with trend)
‹ Seasonal
variation
‹ Winter’s model (with trend and seasonality)
75