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


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.


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


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


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


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


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


Frequency of ForecastingFrequency of forecasting %

Daily 2

Weekly 7

Monthly 38

Quarterly 24

Semi-annual 8

Yearly 21

Total 100



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


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


Computing the value of the benefits

• Sales = £800,000• Markup= 100%• Cost of inventory = 9% of Cost of Goods

Sold



• 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?



• 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


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 Techniques


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


Overview of forecasting models

• Naïve models• Time series

– Moving average

– weighting past value

– The decomposition method

• Associative models– Correlation analysis

– Regression analysis


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


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


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


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


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


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


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


Smoothing effect

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30

Sales

MA4


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


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


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


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



• Ft+1= Dt + (1- )Ft

– Ft+1: Forecast for period t+1

– Dt: Demand for period t

– Ft: Forecast for period t : smoothing constant



90

92

94

96

98

100

102

104

106

108

110

112

0 5 10 15 20 25 30

Data

Smoothing (0.5)


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.


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Regression Analysis-Graphical

• If two variables are correlated, express their linear relationship

• Y= a+ bX y

x

a

dy

dx b=dy/dx


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


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”


Newer Methods

• Chaos theory• Expert systems• Genetic algorithms• Neural networks


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

MGT3303 Michel Leseure Forecasting –Introduction to forecasting –Do you need a forecasting...

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