Production and Operation Managements
Forecasting
Professor JIANG Zhibin
Dr. GENG Na
gengna@sjtu.edu.cn
13917048340
Department of Industrial Engineering & Logistics
Management
Shanghai Jiao Tong University
What is forecasting?
• Forecasting is the process of predicting the future;
What do you want to forecast?
• Your future
• Career
• Marriage
• House price
• Stock
• …
Why forecast?
How forecast??
Introduction(1)
Why forecast in a business factory?
All business planning is based on a forecast;
What a factory should forecast?
Factors affecting the future success of a firmSales of existing products
Customer demand patterns for new products;
Needs and availabilities of raw materials;
Changing skills of workers;
Interest rates;
Capacity requirements;
International policies;
Marketing and production make the most use of forecasting methods.
Marketing needs to forecast for both new products and existing
products;
Sales forecasts are used for production planning
Introduction(2)
Examples of benefiting from good forecasting and paying
price from poor one:
Detroit make slow respond to customer tastes in automobiles from
heavy gas guzzlers to smaller and more fuel efficient ones during 1960’s,
such that it suffered much when OPEC oil embargoing in late 1970 speed
up the trend of shifting to smaller cars.
 Compaq Computer became a market leader in the early 1980s by
properly predicating consumer demand for portable version of the IBM
PC;
 Ford Motor’s early success and later demise
•It predicated that customer would want a simpler, less expensive,
and easier to be maintained car, and developed its Model T car that
dominated the market;
•However, later, did not see that customer tired of the open Model T
design, and failed to forecast the customer’s desire for other designs
that almost caused the end of a firm that has monopolized the
industry only a few years ago.
Forecasting
•Contents
•The Time Horizon in Forecasting;
•Subjective Foresting Methods;
•Objective Forecasting Methods;
•Evaluating Forecast
•Notation Conventions;
•Methods for Forecasting Stationary Series;
•Trend-Based Methods;
•Methods for Seasonal Series;
The Time Horizon in Forecasting
Fig.2-1 Forecast Horizons in Operation Planning
The Time Horizon in Forecasting
•The Short-term forecasting is required for day-to-day planning;
•Measured usually in day or weeks;
•Required for inventory management, production plan, and
Fig.2-1planning,
Forecast Horizons
Operation
resource requirement
and shift in
scheduling
The Time Horizon in Forecasting
•The Intermediate term is measured in weeks or months;
•Typical intermediate term forecasting problems include sales
pattern of product families, requirements and availabilities of
workers, and resource
requirements.
Fig.2-1 Forecast
Horizons in Operation Planning
The Time Horizon in Forecasting
•The long term is measured in months or years;
•It is one part of the overall firm’s manufacturing strategy;
•Problems for long term forecasting include long term capacity
planning; long term sales patterns, and growth trend.
•One of example is long term planning of capacity.
Fig.2-1 Forecast Horizons in Operation
Classification of Forecasts
•Sales force composites;
Subjective-based
on human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
•Causal Models-the forecast
Objective-derived
from analysis of
data
for a phenomenon is some function
of some variables
•Time Series Methodsforecast of future values of some
economic or physical phenomenon
is derived from a collection of their
past observations
Classification of Forecasts
•Sales force composites;
Subjectivebased on
human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
•Sale force is in a good position to see changes in their
preferences;
•Numbers of the sale force submit sales estimates of the
products they sell in the next year;
•Sales manager aggregate individual estimates
Classification of Forecasts
•Sales force composites;
Subjectivebased on
human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
•It can signal the future trends and shifting preference
patterns;
•Survey and sampling plans must ensure statistically
unbiased resulting data and representative of the
customer base;
Classification of Forecasts
•Sales force composites;
Subjectivebased on
human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
•Expert’s opinion is the only source of information for
forecasting, when no past historic data, as with new products;
•The approach is to combine the opinions of experts to derive a
forecast;
•Two ways for the combination.
•One is to have individual responsible for preparing for the forecast interview the
executive directly and develop a forecast from the result of the interview;
•Another is to require the executive to meet as a group and come to consensus.
Classification of Forecasts
•Sales force composites;
Subjectivebased on
human
judgment
•Customer surveys
The personalities
of some group
members
overshadow others
•Jury of executive opinion;
•The Delphi method;
•Named for the Delphic oracle of ancient Greece who had
power to predicate the future;
•Based on collecting the opinion of experts like jury of
executive opinion;
•However, in different manner in which individual opinions are
combined in order to overcome some of the inherent
shortcoming of group dynamics;
Classification of Forecasts
•Sales force composites;
Subjectivebased on
human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
Procedures for the Delphi method:
•A group of experts express their opinions;
•The opinions are then compiled and a summary of results are returned to the
expert, with special attention to those significant different opinions;
•The experts are asked if they wish to reconsider their original opinions in light
of the group response;
•The process is repeated until an overall group consensus is reached;
Classification of Forecasts
•Sales force composites;
Subjective-based
on human
judgment
•Customer surveys
•Jury of executive opinion;
•The Delphi method;
•Causal Models-the forecast
Objective-derived
from analysis of
data
for a phenomenon is some function
of some variables
•Time Series Methodsforecast of future values of some
economic or physical phenomenon
is derived from a collection of their
past observations
Objective Forecasting Methods
Causal Model
•Let
Y-the phenomenon needed to be forecasted;( numbers of
house sales)
X1, X2, …, Xn (interest rate of mortgage )are variables
supposed to be related to Y
•Then, the general casual model is as follows:
Y=f(X1, X2, …, Xn).
•Econometric models are lineal casual models:
Y=0+ 1X1+ 2X2+…+ nXn,,
where i (i=1~n) are constants.
•The method of least squares is most commonly used for
finding estimators of these constants.
Objective Forecasting Methods
Causal Model
Assume we have the past data (xi, yi), i=1~n; and the the
causal model is simply as Y=a+bX. Define
n
g (a, b)   [ yi  (a  bxi )]2
i 1
as the sum of the squares of the distances from line a+bX
to data points yi. We may choose a and b to minimize g, by
n
letting
1 n
g
0
a
g
0
b
2  yi   a  bxi    0  a 
i 1
 y  bx   y  bx

n
i
i 1
i
n
n
  y   a  bx    x   0  b 
i 1
i
i
i
n
 x y  y x
i 1
n
i
i
i 1
n
2
x
 i  x  xi
i 1
i 1
i
Objective Forecasting Methods
Causal Model
n
g (a, b)   [ yi  (a  bxi )]2
i 1
g
0
a
a  y  bx
g
0
b
n
b
n
 x y  y x
i
i 1
n
i
x
2
i
i 1
i 1
n
 x  xi
i

i 1
n
n
i 1
n
i 1
n
n xi yi  ny  xi
n x  nx  xi
i 1
n
n
n
n
i
i
i
i
2
i
n
S xy  n xi yi   xi  yi ; S xx  n xi  ( xi ) 2
1 n
1 n
x   xi ; y   yi ;
n i
n i
2
i
i 1

S xy
S xx
Objective Forecasting Methods
Time Series Methods•The idea is that information can be inferred from the pattern of
past observations and can be used to forecast future values of
the series.
•Try to isolate the following patterns that arise most often.
Trend-the tendency of a time series, usually a stable growth
or decline, either linear (a line) or nonlinear (described as
nonlinear function, e. g. a quadratic or exponential curve)
Seasonality-Variation of a series related to seasonal changes
and repeated every season.
Cycles-Cyclic variation similar to seasonality, except that
the length and the magnitude may change, usually associated
with economic variation.
Randomness-No recognizable pattern to the data.
Objective Forecasting Methods
Fig. 2-2 Time Series Patterns
Evaluating Forecast
The forecast error et in period t is the difference between the
forecast value for that period and the actual demand for that
period.
et  Ft  Dt
The three measures for evaluating forecasting accuracy
during n period
1 n
1 n 2
MAD   | ei | MSE   ei
n i 1
n i 1
1 n
MAPE  [  | ei / Di |] 100
n i 1
•MAD: The mean absolute deviation, preferred method;
•MSE: The mean squared error;
•MAPE: The mean absolute percentage error (MAPE)
Evaluating Forecast
Example 2.1
Artel, a manufacturer of SRAMs (static random access memories), has
production plants in Austin, Texas, and Sacramento, California. The
managers of these plants are asked to forecast production yields
(measured in percent) one week ahead for their plants. Based on six
weekly forecasts, the firm’s management wishes to determine which
manager is more successful at predicting his plant’s yields. The results
of their predictions are given in the following table.
Week
P1
O1
|E1| |E1/O1|
P2
O2
|E2| |E2/O2|
1
92
88
4
0.0455
96
91
5
0.0549
2
87
88
1
0.0114
89
89
0
0.0000
3
95
97
2
0.0206
92
90
2
0.0222
4
90
83
7
0.0843
93
90
3
0.0333
5
88
91
3
0.0330
90
86
4
0.0465
6
93
93
0
0.0000
85
89
4
0.0449
Evaluating Forecast
Example 2.1
MAD1=2.83
MAD2=3.00
Plant 1 better 2
MSE1=13.17
MSE2=11.67
Plant 2 better 1
MAPE1=0.0325
MAPE2=0.0336
Plant 1 better 2
•Both MAD1 and MAPE1 are less than
MAD2 and MAPE2, however MSE1 is
larger than MSE2. ???
•MSE is more sensitive to one large error than is the MAD.
Plant 1 has got a large error 7.
Evaluating Forecast
•A desirable forecast should be unbiased. Mathematically,
E(ei)=0.
•The forecast error ei over time should fluctuate randomly above
and below zero.
Fig2-3 Forecast Errors Over Time
Notation Convention
•Define D1, D2, …, Dt, …, as the observed values of demand
during periods 1, 2, …, t, ….
•Assume if we are predicating demand for period t, we have
already observed Dt-1, …, but have no Dt.
•Define Ft as the forecast for period t that is made at the end
of period t-1;
Ft
D1
1
D2
2
D3
3
Dt-1
t-1
t
Notation Convention
Ft
D1
1
D2
2
D3
3
Dt-1
t-1
t
•The above is one-step-ahead forecast-they are made for
predicating the demand only in the next period.
•A time series forecast is actually obtained by weighting
the past data
m
Ft    t i 1 Dt i 1 for some set of weights  t 1 ,  t  2 , L
i 0
Methods of Forecasting Stationary Series
Stationary time series: each observation can be
represented by a constant plus a random fluctuation.
Dt     t
where
 = an unknown constant corresponding to mean of the series;
= the random error with mean zero and variation 2.
•Methods:
Moving average;
Exponential Smoothing
Simple
Holt
Winters
Methods of Forecasting Stationary Series
Moving Average-A moving average of order N is
simply the arithmetic average of the most recent N
observations (one-step-ahead), denoted as MA(N).
1
Ft 
N
N
D
t i
i 1
1
 ( Dt 1  Dt  2  L  Dt  N )
N
Ft
D1 D2
1
Dt-NN past data D
Dt-2 t-1
… …
2
3
t-1
t
Example 2.2
Quarterly data for the failures of certain aircraft engines
at a local military base during the last two yrs are 200,
250, 175, 186, 225, 285, 305, 190. Determine the onestep-ahead forecasts for period 4 through 8 using threeperiod moving averages, and one-step-ahead forecasts
for periods 7 and 8 using six-period moving averages
MA(3)4=(1/3)(175+250+200)=208 200, 250, 175, 186, 225, 285, 305, 190.
MA(3)5=(1/3)(186+175+250)=204
200, 250, 175, 186, 225, 285, 305, 190.
MA(6)7=(1/6)(285+225+186+175+250+200)=220
200, 250, 175, 186, 225, 285, 305, 190.
The final results are as shown in the table on Page 67
Example 2.2
Moving Average of Order 3
for Period 4 made at period 3
MA(3)4=(1/3)(175+250+200)=208
MA(3)5=(1/3)(186+175+250)=204
MA(6)7=(1/6)(285+225+186+175+250+200)=220
Question: How to obtain multiple-step-ahead forecast?
Ft = Ft+1 = Ft+2
D1
1
D2
Dt-N
… …
2
Dt-2
3
Dt-1
3SA
2SA
1SA
t-1
t
Methods of Forecasting Stationary Series
Only need to calculate
the difference between
1 N
1
Ft   Dt i  ( Dt 1  Dt  2  L  Dt  N ) the most recent
N i 1
N
demands and the
demand N period
ahead for updating the
forecast.
•Calculate Ft+1 based on Ft-simplify the calculation
1 N
1
Ft 1   Dt 1i  [ Dt  Dt 1  Dt 2  L  Dt 1 N  Dt  N  Dt  N ]
N i 1
N
N
1
1
 ( Dt  Dt  N   Dt i )  Ft  ( Dt  Dt  N )
N
N
i 1
Methods of Forecasting Stationary Series
Forecasting by MA for series with trend
Implication: the use of
simple moving averages
is not proper forecasting
method when there is a
trend in the series.
Forecasts lag
behind the
demand
Fig.2-4 Moving-Average Forecasts Lag Behind a Trend
Methods of Forecasting Stationary Series
Test: The demand of some product for the past six
week is known. Please forecast the demand in 7th week
using MA. Note that the more accurate forecast is
preferred.
Week
1
2
3
4
5
6
Demand
92
87
95
90
88
93
Methods of Forecasting Stationary Series
Answer: First, the forecasting errors are compared.
When N=3, MAD is smallest.
Week
1
2
3
4
5
6
Demand MA(2)
92
87
95
90
88
93
93
89
MAD
4.5
MA(3)
MA(4)
91
91
2.5
91
90
3
• Using MA(3) to predict the demand in period 7, the
answer is 90.
Methods of Forecasting Stationary Series
Exponential Smoothing-the current forecast is weighted
average of the last forecast and the last value of demand.
new forecast   (current observation of demand )  (1   )(Last forecast)
The forecast in any period t is
Ft   Dt 1  (1   ) Ft 1
the forecast in period t-1 minus
some fraction of the observed
forecast error in period t-1
where 0<1 is the smoothing constant, which determines the
relative weight placed on the last observation of demand,
while 1-  is weight placed on the last forecast.
Ft   Dt 1  (1   ) Ft 1  Ft 1   ( Ft 1  Dt 1 )  Ft 1   et 1
Methods of Forecasting Stationary Series
Exponential Smoothing-the current forecast is
weighted average of the last forecast and the last value
of demand.
Ft   Dt 1  (1   ) Ft 1
where 0<1 is the smoothing constant, which determines the
relative weight placed on the last observation of demand,
while 1-  is weight placed on the last forecast.
Ft   Dt 1  (1   ) Ft 1  Ft 1   ( Ft 1  Dt 1 )  Ft 1   et 1
Ft 1   Dt 2  (1   ) Ft 2

Ft   Dt 1   (1   ) Dt  2  (1   ) Ft  2  ...    (1   )i Dt i 1
2
i 0
 (1   )i
  0.1
The older of a past data, the
smaller of its contribution to
the forecast for a future
period.
Fig.2-5 Weights in Exponential Smoothing
Example 2.3
Consider Example 2.2, in which the observed number of failures
over a two yrs period are 200, 250, 175, 186, 225, 285, 305, 190.
We will now forecast using exponential smoothing. We assume
that the forecast for period 1 was 200, and suppose that =0.1
F2= ES(0.1)2= D1+(1- 1)F1=0.1200+(1-0.1)  200=200
F3= ES(0.1)3= D2+(1- 1)F2=0.1250+(1-0.1)  200=205
•Since ES requires that at each stage we need the previous
forecast, it is not obvious how to get the method started.
•We may assume that the initial forecast is equal to the initial
value of demand.
•However, this approach has a serious drawback?
Methods of Forecasting Stationary Series
Smaller  turns out a
stable forecast, while
larger  results in better
track of series
Fig.2-6 Exponential Smoothing for Different Values of Alpha
Methods of Forecasting Stationary Series
Comparing of ES and MA
Similarities
• Both methods are based on assumption that underlying demand
is stationary .
• Both methods depend on a single parameters.
• Both methods will lag behind a trend if one exits.
Differences
• MA is better than EA in that it needs only past N data, while
EA needs all the past data;
Trend –Based Methods
Two methods that account for a trend in the data:
regression analysis and Holt’s method.
•Regression Analysis
Let (x1, y1), (x2, y2), …, (xn, yn) are n paired data points for
the two variables X and Y; and
Assume that yi is the observed value of Y when xi is the
observed value of X.
It is believed that there is a relationship between X and Y as
follows
• Represents the predicated value of Y;
Ŷ  a  bX
• a and b are chosen to minimize the sum
of squared distance between regression
line and the data point
Trend –Based Methods
Two methods that account for a trend in the data:
regression analysis and Holt’s method.
•Regression Analysis
Let (x1, y1), (x2, y2), …, (xn, yn) are n paired data points for
the two variables X and Y; and
Assume that yi is the observed value of Y when xi is the
observed value of X.
It is believed that there is a relationship between X and Y as
follows
Ŷ  a  bX
Least square
method
b
S xy
S xx
; a  y  bx
Methods of Forecasting Trend Series
(i, Di)
Ŷ  a  bX
Fig 2-7 An Example of a Regression Line
Methods for Seasonal Series
A seasonal series is one that has a pattern that repeats every N
periods (at least 3).
Length of season-the
number of periods before
the pattern begins to
A season
repeat
Fig. 2-8 A Seasonal Demand Series
Methods for Seasonal Series
How to represent seasonality?
•Seasonal factor-A set of multipliers ct, 1 t N, ct=N;
•ct represents the average amount that the demand in tth period
of the season is above or below the average.
•For example: if c3=1.25 and c5=0.6, then the demand in the 3rd
period is 25 percent above the average demand; while demand
in the 5th period is 40 percent below the average demand.
Methods of Forecasting Stationary Seasonal Series
Seasonal Factors for Stationary Seasonal Series (No trend)
Compute the sample mean of all data(A minimum of two
seasons of date is required): m
Divide each observation by sample mean  the seasonal
factors of observed data for each period in each season:
SFi,j=Dij/m （Dij-the observed dada for period j in season i, total
H seasons)
Average the factors for the same periods within each season
the seasonal factor: SF  1 H SF
j
H

i 1
ij
Multiplying the sample mean
by a seasonal factor  the
forecast of demand in the
corresponding period of the season.
Methods of Forecasting Stationary Seasonal Series
Monday
Tuesday
Wednesday
Thursday
Friday
Wk1
16.2
12.2
14.2
17.3
22.5
Wk2
17.3
11.5
15
17.6
23.5
Wk3
14.6
13.1
13
16.9
21.9
Wk4
16.1
11.8
12.9
16.6
24.3
Monday 0.977169
Tuesday 0.739726
Wednesday 0.838661
Thursday 1.041096
Friday 1.403349
Avg=16.425
Wk1
Monday 0.986301
Tuesday 0.74277
Wednesday 0.864536
Thursday 1.053272
Friday 1.369863
Wk2
1.053272
0.700152
0.913242
1.071537
1.430746
Wk3
0.888889
0.797565
0.791476
1.028919
1.333333
Wk4
0.980213
0.718417
0.785388
1.010654
1.479452
16.425*0.977169=16.05
Monday
Tuesday
Wednesday
Thursday
Friday
16.05
12.15
13.775
17.1
23.05
Methods of Forecasting Trend Seasonal Series
A more complex time series: Trend + Seasonality
Seasonal Decomposition Using Moving Averages
•Deseaonalized- Get
seasonality away;
•Make forecast on
deseaonalized data;
•Get seasonality
back
Seasonal Decomposition Using Moving Averages
Example 2.7Suppose that original demand history of a certain item for the past
eight quarters is given by 10, 20, 26, 17, 12, 23, 30, 22. The graph
of this demand is shown in the following figure.
Methods of Forecasting Trend Seasonal Series
Procedures:
• Draw the demand curves and estimate the season
length N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
• Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
N=4
Fig. 2-9 Demand History for Example 2.7
Methods of Forecasting Trend Seasonal Series
Procedures:
 Draw the demand curves and estimate the season
length N;
 Computer the moving average MA(N);
 Centralize the moving averages;
 Get the centralized MA values back on period;
 Calculate seasonal factors, and make sure of ct=N.
 Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
 Forecast is made based on deseasonalized demand.
 Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
MA(4) CMA
20
26
17
18.25
12
18.75
23
19.50
30
20.50
22
21.75
BOCMA
Ratio
Factor
D. D.
Methods of Forecasting Trend Seasonal Series
Procedures:
• Draw the demand curves and estimate the season
length N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
• Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
MA(4) CMA
20
18.25
26
18.75
17
18.25
19.50
12
18.75
20.50
23
19.50
21.75
30
20.50
22
21.75
BOCMA
Ratio
Factor
D. D.
Since 18.25 is calculated by
moving demand of periods 1, 2,
3, and 4. The center of these
period is 2.5
Methods of Forecasting Trend Seasonal Series
Procedures:
• Draw the demand curves and estimate the season
length N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
MA(4) CMA
BOCMA
20
18.25
26
18.5
18.75
17
18.25
19.125
19.50
12
18.75
20.00
20.50
23
19.50
21.125
21.75
30
20.50
22
21.75
Ratio
Factor
D. D.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
MA(4) CMA
20
BOCMA
18.81
18.81
18.25
26
18.5
18.75
17
18.25
19.125
19.50
12
18.75
20.00
20.50
23
19.50
21.125
21.75
30
20.50
20.56
22
21.75
20.56
Ratio
Factor
D. D.
Methods of Forecasting Trend Seasonal Series
Seasonal Decomposition Using Moving AveragesExample 2.7
• Draw the demand curves and estimate the season length
N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
20
MA(4) CMA
10/18.81
BOCMA
18.81
Ratio
0.532
Factor
D. D.
0.566 0.558
18.81
1.063
1.076
1.061
18.5
1.405
1.434
1.415
19.125
0.888
0.979
0.966
20.00
0.6
21.125
1.089
18.25
26
18.75
17
18.25
19.50
12
18.75
(0.532+0.60)/2
20.50
23
19.50
21.75
30
20.50
20.56
1.463
22
21.75
20.56
1.070
Ratio- the demand over centered
MA
Modify factors:
0.5664/(0.566+1.076+1.434+0.979)
Methods of Forecasting Trend Seasonal Series
Seasonal Decomposition Using Moving AveragesExample 2.7
• Draw the demand curves and estimate the season length
N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Period
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
Demand
10
20
MA(4) CMA
10/0.588
BOCMA
18.81
Ratio
0.532
Factor
D. D.
0.566 0.588 17.92
18.81
1.063
1.076
1.061 18.85
18.5
1.405
1.434
1.415 18.39
19.125
0.888
0.979
0.966 17.60
20.00
0.6
21.50
21.125
1.089
21.68
18.25
26
18.75
17
18.25
19.50
12
18.75
20.50
23
19.50
21.75
30
20.50
20.56
1.463
21.22
22
21.75
20.56
1.070
22.77
Methods of Forecasting Trend Seasonal Series
Seasonal Decomposition Using Moving AveragesExample 2.7
• Draw the demand curves and estimate the season length
N;
• Computer the moving average MA(N);
• Centralize the moving averages;
• Get the centralized MA values back on period;
• Calculate seasonal factors, and make sure of ct=N.
• Divide each observation by the appropriate seasonal
factor to obtain the deseasonalized demand
Forecast is made based on deseasonalized demand.
• Final forecast is obtained by multiplying the forecast
(with no seasonality) with seasonal factors.
Methods of Forecasting Trend Seasonal Series
Forecast made on Deseasonalized demand by
MA
• MA(6) for period 9=20.52 (without seasonality);
• Forecast for period: 20.520.558=11.45 (with
seasonality)
D. D.
17.92
18.85
18.39
Q
17.60
How to forecast demand for period 10,
11, 12?
21.50
F10= MA(6) of 2-step-head=F9=20.52
21.22
F10×SF2=20.52× 1.061=21.77
22.77
21.68
Methods of Forecasting Trend Seasonal Series
• Forecast made on Deseasonalized demand by
regression
By regression analysis over D. D., obtain:
Dt=16.8+0.7092t
By substituting t=9 through 12, obtain forecasts
(without seasonality): 23.18, 23.89, 24.60 and 25.31;
By multiplying seasonal factors, obtain forecast in
the future periods 9 through 12: 12.93, 25.35, 34.81,
and 24.45.
Forecasting
Contents
•The Time Horizon in Forecasting;
•Subjective Foresting Methods;
•Objective Forecasting Methods;
•Evaluating Forecast
•Notation Conventions;
•Methods for Forecasting Stationary Series;
•Trend-Based Methods;
•Methods for Seasonal Series;
Homework for Chapter 2:
Q13, Q24, Q34
In two weeks
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