MGT3303 Michel Leseure Forecasting –Introduction to forecasting –Do you need a forecasting...
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Transcript of MGT3303 Michel Leseure Forecasting –Introduction to forecasting –Do you need a forecasting...
MGT3303Michel Leseure
Forecasting
– Introduction to forecasting– Do you need a forecasting system?– Forecasting models– Qualitative judgments in forecasting– Reading: Chapter 8
MGT3303Michel Leseure
Forecasting
• All operational systems operate in an environment of uncertainty
• Information is an asset - managing it a necessity
• “Reliable” information about the future is a source of competitive edge
• Forecasting supplements the intuitive feelings of managers and decision makers.
MGT3303Michel Leseure
The Uses of
Demand Forecasts
Users %
Budgets 86
Market planning 70
Production planning 59
Capital investment 57
Sales quota 44
Production scheduling 42
Product introduction 31
Others 10
Forecasting practices of Canadian FirmsInt. J. Production Economics70(2001) 163-174
MGT3303Michel Leseure
Forecasting in the hand tool industry (1997 survey)
• 84% of hand tool manufacturers (UK+US) use forecasting techniques
• Out of the manufacturers using forecasting techniques:– 0% think they are inaccurate and not
helpful– 38 % think they are inaccurate but helpful– 50% think they are somewhat accurate– 12% think they are accurate
MGT3303Michel Leseure
Forecasting « Laws »
• Forecasts are always wrong• Forecasts always change• The further into the future, the less reliable the
forecast. – (greatest uncertainty and potential for a large error
when there is still time to prepare)
• Forecasts for group statistics tend to be more accurate than forecasts for individuals (risk/uncertainty pooling concept)
• Learning not predicting
MGT3303Michel Leseure
Forecasting Error TrumpetWhen the start of the new season is
farthest off, We still have time to produce in anticipation of start of season
demand
We have the least accurate picture of what the demand will look like
Start of season
20%40%
+10%-10%
16 weeks26 weeks
Time
MGT3303Michel Leseure
Time scope in manufacturing forecasting
• Short-term forecasting: – planning and scheduling manufacturing
operations, purchasing, staffing - mostly quantitative
• Long-term forecasting: – planning for capital investment, facility
layout, job shop design, etc. - subjective and qualitative considerations
MGT3303Michel Leseure
Frequency of ForecastingFrequency of forecasting %
Daily 2
Weekly 7
Monthly 38
Quarterly 24
Semi-annual 8
Yearly 21
Total 100
Forecasting practices of Canadian FirmsInt. J. Production Economics70(2001) 163-174
MGT3303Michel Leseure
Do you need a forecasting system?
• Difficult to estimate all the benefits (or losses avoided)
• Not an excuse for not knowing the economics of a forecasting system
MGT3303Michel Leseure
Benefits of a forecasting system
• Cost of inventory• Loss of business because of stockout• Permanent loss of customers because of
stockout• Cost of obsolescence• Increase in the cost of production for
producing what is not in stock
MGT3303Michel Leseure
Computing the value of the benefits
• Sales = £800,000• Markup= 100%• Cost of inventory = 9% of Cost of Goods
Sold
MGT3303Michel Leseure
Computing the value of the benefits
• Inventory reduced by 5 days• Decrease in order cancellation: 1% of sales• Reduction of lost customers: 0.25% of sales• Reduction of obsolescence: 1% of sales• Reduction of product cost: 2%• How much can you invest in forecasting without
decreasing profits?
MGT3303Michel Leseure
Computing the value of the benefits
• Annual CGS: 800,000*0.5= £ 400,000• Product Cost of 5 days worth of inventory: £5,479• of which inventory costs: 9% = £493• Decrease in order cancellation: 1%=£4000• Reduction of lost customers: 0.25% of sales =
£1000• Reduction of obsolescence: 1% of sales = £4000• Reduction of product cost: 2% = £8,000• TOTAL = £17,493
MGT3303Michel Leseure
Forecasting System ExpendituresExpenditures
(thousand C$)No. of firms Median Product
0-50 69 25K 1725
50-100 16 75 1200
100-250 11 175 1925
250-1000 8 625 5000
>1000 6 1000 6000
Sum 110 15850
Mean = 15,850/110= 144 K
Forecasting practices of Canadian FirmsInt. J. Production Economics70(2001) 163-174
MGT3303Michel Leseure
Forecasting Techniques
MGT3303Michel Leseure
U n p re d ic ta b le
M o v in g A va ra g es
S im p le (N o T re n d)D o u b le (L in e a r T re n d)T rip le (C u rv ilin e a r T re n d )
E xp o ne n tia l S m oo th ing
T im e -S e ries M e th o ds
L in e a r T re ndQ u a d ra tic T re ndE xp o n e n tia l T re nd
S im p le R e g re ss ion
M u lt ip le R e g re ss ionE co n o m e tric M o d e lingL e a d in g In d ica to r A n a lys isD iffu s io n In d e xes
C a u sa l / E xp lan a to ry M e th o ds
Q u a n tita tive
D e lp h i T e ch n iq ueE xp e rt O p in ionF a c to r L is t in g M e th od
Q u a lita t ive
T yp e s o f Fo re ca s tingA p p roa ch e s & M eth o ds
MGT3303Michel Leseure
Overview of forecasting models
• Naïve models• Time series
– Moving average
– weighting past value
– The decomposition method
• Associative models– Correlation analysis
– Regression analysis
MGT3303Michel Leseure
Sales of saws for the Acme Tool
Company (1991-1996)
Year Quarter T Sales1991 1 1 500
2 2 3503 3 2504 4 400
1992 1 5 4502 6 3503 7 2004 8 300
1993 1 9 3502 10 2003 11 1504 12 400
1994 1 13 5502 14 3503 15 2504 16 550
1995 1 17 5502 18 4003 19 3504 20 600
1996 1 21 7502 22 5003 23 4004 24 650
Sales
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30
MGT3303Michel Leseure
Time series analysis
• Time series: – A time-ordered sequence of observations
taken at regular interval over a period of time
• Time series are analysed to discover past patterns of growth and change that can be used to predict future patterns and needs for business operations
MGT3303Michel Leseure
Naïve model
• The forecast for any period equals the previous period’s actual value
X Xt t 1 Example, for the Acme tool company,
X25= 650
MGT3303Michel Leseure
Jazzing-up the naïve model
• Incorporating a trend:
X X X Xt t t t 1 1( ) This model takes into account the
amount of change that occurred between the last two periods
X25=X24+(X24-X23)=650 + (650-400)=900
MGT3303Michel Leseure
Jazzing-up the naïve model
• Incorporating seasonal variations:
X Xt t 1 3
Visual inspection of the data indicates that seasonal variations seems to exist. Sales in the fourth quarter are typically larger than any of the other quarters
X25= X21= 750
MGT3303Michel Leseure
Moving Averages• Many possible extensions of the naïve model,
moving averages is one• Averages a number of recent actual values,
updated as new values become available
MAY
nn
ii
n
1
i: “age” of the data
n= number of periods in the moving average
Ai: actual value with age i
MGT3303Michel Leseure
Application to Acme Tools
• Forecast during the third quarter of 1996, with n=4
• Actual value = 650
• Forecast during the fourth quarter of 1996, with n=4
MA
MA
4
4
600 750 500 400
4562 5
.
MA
MA
4
4
750 500 400 650
4575
MGT3303Michel Leseure
Smoothing effect
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30
Sales
MA4
MGT3303Michel Leseure
Spreadsheet
Period Index
12 Months Moving Average
2 Months Moving Average
Error 12 Error 2
1 1082 1083 1104 1065 1086 1087 1058 1009 9710 9511 9512 9213 95 102.67 93.50 -7.67 1.5014 95 101.58 93.50 -6.58 1.5015 98 100.50 95.00 -2.50 3.0016 97 99.50 96.50 -2.50 0.5017 101 98.75 97.50 2.25 3.5018 104 98.17 99.00 5.83 5.0019 101 97.83 102.50 3.17 -1.5020 99 97.50 102.50 1.50 -3.5021 95 97.42 100.00 -2.42 -5.0022 95 97.25 97.00 -2.25 -2.0023 96 97.25 95.00 -1.25 1.0024 96 97.33 95.50 -1.33 0.5025 97 97.67 96.00 -0.67 1.0026 98 97.83 96.50 0.17 1.5027 94 98.08 97.50 -4.08 -3.5028 92 97.75 96.00 -5.75 -4.00
MGT3303Michel Leseure
Results
90
95
100
105
110
115
0 5 10 15 20 25 30
Index
12 Months MovingAverage
2 Months MovingAverage
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
1 4 7 10 13 16 19 22 25 28
Error 12
Error 2
MGT3303Michel Leseure
Using weighted averages
• Using weights in moving averages allows to give more or less importance to different periods
• An example is exponential smoothing, a procedure for continually revising an estimate in light of more recent experiences
• Adaptive filtering is a procedure which identifies the best set of weights for the actual data
MGT3303Michel Leseure
Exponential Smoothing
Form of Weighted Moving Average Weights Decline Exponentially Most Recent Data Weighted Most Each Smoothing Calculation or Forecast Depends On
All Previously Observed Values Used for Smoothing to provide an overall impression of
data over time & short-term Forecasting (one period into the future) Assumes No Trend
Requires Smoothing Coefficient () Subjectively Chosen Ranges from 0 to 1
MGT3303Michel Leseure
Exponential Smoothing
• Ft+1= Dt + (1- )Ft
– Ft+1: Forecast for period t+1
– Dt: Demand for period t
– Ft: Forecast for period t : smoothing constant
MGT3303Michel Leseure
Exponential Smoothing
90
92
94
96
98
100
102
104
106
108
110
112
0 5 10 15 20 25 30
Data
Smoothing (0.5)
MGT3303Michel Leseure
Choice of Alpha
90
92
94
96
98
100
102
104
106
108
110
112
0 5 10 15 20 25 30
Data
Smoothing (0.2)
Smoothing (0.4)
Smoothing (0.6)
Smoothing (0.8)
The greater is , the greater the reaction to the most recent demand.
MGT3303Michel Leseure
Adjusted Exponentially Smoothing
• Exponentional smoothing with a trend component
• AFt+1= Ft+1+Tt+1
• AF is the adjusted forecast• T is an exponentially smoothed trend
• Tt+1= (Ft+1 – Ft )+ (1- )Tt
• F is the normal forecast based on the smoothing constant
MGT3303Michel Leseure
Adjusted Exponentially Smoothing
-50000
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Actual
Regression
4-MAV
FIT
MGT3303Michel Leseure
The decomposition method
• The most widely used method to forecast time series
• Three components are found in annual time series: the trend, the cyclical variation, and irregular fluctuations
• In short-term time series (i.e. classified by quarters, months, weeks) an additional seasonal component is added
MGT3303Michel Leseure
The trend
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30
Sales
Trend
Y t 276 27 10 56. .• The long-term
component of a time series
• Underlies the growth (or decline) in the series
• usually assumed to be linear (regression analysis of Y(t)
• in the same unit than Y
MGT3303Michel Leseure
The cyclical component C
• Only for long term time series - scale of the economic cycles
• Compute C=Y/TS• Search for a published economic index
which is correlated with C (leading, coincident, lagging indicators)
• Use published forecasts of the indicator
MGT3303Michel Leseure
The seasonal component
• Important in manufacturing, where the model Y=TCSI is often reduced to Y=TSI
• S is usually a centered moving average• Computations of the seasonal indexes can
be long - the use of time serie and forecasting software is more appropriate
MGT3303Michel Leseure
Centered moving average
• A moving average positioned at the center of the data that were used to compute it
• Period index = actual/centered average
CenteredPeriod Y average Index
1 401 46 42.67 107.80413 42
MGT3303Michel Leseure
The irregular component: I
• what is leftover when dividing the actual values of Y by T, C and
• is plotted to identify any significant patterns (rare event, e.g. strike, etc.)
• usually, I=1.0 when forecasting
MGT3303Michel Leseure
A simple application
• Acme data, C=I=1.0 for all quarters
• Y=TS• T= 276.27 +10.56t
Results of SEASON procedure for variable SALESMultiplicative Model. Centered MA method. Period = 4.
Seasonal index Period (* 100) 1 134.133 2 87.481 3 64.285 4 114.102
MGT3303Michel Leseure
Time series Analysis with SPSS
G1. SALES
Date
3RD961ST96
3RD951ST95
3RD941ST94
3RD931ST93
3RD921ST92
3RD911ST91
800700600500
400
300
200
100
B1.Original series
E1.Mod. for extremes
with 0 final weight
MGT3303Michel Leseure
Measuring forecast error
• The mean squared error is the most common method
• Plotting out actual and forecasted points
MSEY F
n
i ii
n
( )2
1
MGT3303Michel Leseure
Associative forecasting models
• The fluctuations of the quantity to forecast (the independent variable Y)are “linked” to the fluctutations of a dependent variable X
• Time series trend analysis X=t• if there is a single X, regression analysis• if there are several X, multivariate
regression analysis
MGT3303Michel Leseure
Correlation Analysis
• The first step of associative forecasting models: finding and testing the correlation of Y with potential Xs
• The correlation measures the strength and direction of relationship between two variables
MGT3303Michel Leseure
Correlation Coefficient
• A correlation of +/-1 indicates a change in one variable is always matched by a change in the other, and indicates a strong linear relationship between the two variables
• r=0 indicates a poor correlation
rn xy x y
n x x n y y
( ) ( )( )
( ) ( ) ( ) ( )2 2 2 2
MGT3303Michel Leseure
Application - Correlation • r= -0.966• Good explanatory
power• U explains 96.6% of
sales variations• not necessarily
statistically significant
Period 1 2 3 4 5 6 7Unemployement 7.2 4 7.3 5.5 6.8 6 5.4Units Sold 20 41 17 35 25 31 38
Units Sold
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8
MGT3303Michel Leseure
Regression Analysis-Graphical
• If two variables are correlated, express their linear relationship
• Y= a+ bX y
x
a
dy
dx b=dy/dx
MGT3303Michel Leseure
Regression Analysis - least square method
• A computational method to fit the best line through a collection of points
• available on all spreadsheets• precise (?), convenient• but cannot detect outliers, noise in the
data, etc.• Always plot the data
MGT3303Michel Leseure
Subjective judgments in forecasting
• A wide variety of tools and techniques– example: Delphi technique
• problem of the availability of data• problem of the quality of data• these tools and techniques force
managers to a thorough analysis of their businesses -what counts
• supplement “gut feelings”
MGT3303Michel Leseure
Newer Methods
• Chaos theory• Expert systems• Genetic algorithms• Neural networks
MGT3303Michel Leseure
Suggested Homework
• Use excel• Solved problems p 376-377• Problem 8-1, p. 378• Problem 8-7, p. 380• Problem 8-14, p. 381• Case problem 8-1, p. 388