CHAPTER 2 FORECASTING. LEARNING OBJECTIVES Define forecasting, forecasts approaches Understand the...

CHAPTER 2CHAPTER 2

FORECASTINGFORECASTING

LEARNING OBJECTIVESLEARNING OBJECTIVES

Define forecasting, forecasts approaches

Understand the three time horizons

Describe, Explain and Apply the naïve, moving average, exponential smoothing, and trend method

Compute the measures of forecast accuracy

Apply a tracking signal

Forecasting?Forecasting?Forecast

a statement about the future value of a variable of interest.

Forecasting

the art and science of predicting future events.

Forecasts

Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing Operations Product / service design

Uses of ForecastsAccounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

Operations Schedules, MRP, workloads

Product/service design

New products and services

I see that you willget an A this semester.

Elements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

lWritten

Easy

to u

se

Forecasting Time Horizons

Short-range forecastMedium-range forecastLong-range forecast

Distinguishing Differences

Medium/long range- more comprehensive issues and support management decisions regarding planning and products, plants and processes

Short-term- employs different methodologies than longer-term

Short-term- more accurate than longer-term forecasts

Influence of Product Life Cycle

Best period to Best period to increase market increase market shareshare

R&D engineering is R&D engineering is criticalcritical

Practical to change Practical to change price or quality price or quality imageimage

Strengthen nicheStrengthen niche

Poor time to Poor time to change image, change image, price, or qualityprice, or quality

Competitive costs Competitive costs become criticalbecome criticalDefend market Defend market positionposition

Cost control Cost control criticalcritical

Introduction Growth Maturity Decline

Co

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y S

tra

teg

y/Is

sue

sC

om

pa

ny

Str

ate

gy/

Issu

es

Internet search enginesInternet search engines

SalesSales

Xbox 360Xbox 360

Drive-through Drive-through restaurantsrestaurants

CD-ROMsCD-ROMs

3 1/2” 3 1/2” Floppy Floppy disksdisks

LCD & plasma TVsLCD & plasma TVsAnalog TVsAnalog TVs

iPodsiPods

Types of Forecasts

Economic forecasts Technological forecasts Demand forecasts

Seven Steps in Forecasting

Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the

forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results

Forecasting Approaches

Qualitative

Quantitative

Qualitative Approaches

Jury of executive opinionDelphi methodSales force compositeConsumer market survey

Quantitative Approaches

Naïve approach Moving average Exponential smoothing Trend projection Linear regression

Time-Series Time-Series ModelsModels

Time Series Forecasting

Set of evenly spaced numerical data Obtained by observing response variable

at regular time periods

Forecast based only on past values, no other variables important Assumes that factors influencing past and

present will continue influence in future

Time Series Components

Trend

Seasonal

Cycles

Random

Components of DemandD

eman

d f

or

pro

du

ct o

r se

rvic

e

| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation

Trend Component

Overall upward or downward patternChanges due to population, technology,

age, culture, etc.Typically several years duration

Seasonal Component

Regular pattern of up and down fluctuations

Due to weather, customs, etcOccurs within a single year

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

Cycles Component

Repeating up and down movementsAffected by business cycle, political,

and economic factorsMultiple years duration

00 55 1010 1515 2020

Random Component

Erratic, unsystematic, Due to random variation or unforeseen

eventsShort duration and

non-repeating

MM TT WW TT FF

Naive Approach

Assumes demand in next period is the same as demand in most recent period

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

Moving Average Method

Use a number of historical actual data values to generate a forecast

An average of the n most recent periods

Useful if can assume that market demand will stay fairly steady over time

∑∑ demand in previous n demand in previous n periodsperiods

nn

Moving average =Moving average =

Moving Average Example

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33

(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33

Graph of Moving Average

| | | | | | | | | | | |

JJ FF MM AA MM JJ JJ AA SS OO NN DD

Sh

ed S

ales

Sh

ed S

ales

30 30 –28 28 –26 26 –24 24 –22 22 –20 20 –18 18 –16 16 –14 14 –12 12 –10 10 –

Actual Actual SalesSales

Moving Moving Average Average ForecastForecast

Weighted Moving Average

Used when trend or pattern is presentWeights based on experience and intuition

WeightedWeightedmoving averagemoving average ==

∑∑ ((weight for period nweight for period n)) x x ((demand in period ndemand in period n))

∑∑ weightsweights

Weighted Moving Average Example

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month Weighted3-Month WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period

3 Last month2 Two months ago1 Three months ago

6 Sum of weights

Potential Problems With Moving Average

Increasing n smooths the forecast but makes it less sensitive to changes

Do not forecast trends wellRequire extensive historical data

Moving Average And Weighted Moving Average

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

Sa

les

de

man

dS

ale

s d

em

and

| | | | | | | | | | | |


Actual Actual salessales

Moving Moving averageaverage

Weighted Weighted moving moving averageaverage

Exponential Smoothing Weighted averaging method based on

previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedbackWeights decline exponentially Most recent data weighted most

Involves little record keeping of past data Requires smoothing constant ()

Ranges from 0 to 1Subjectively chosen

Exponential Smoothing

New forecast =New forecast = Last period’s forecastLast period’s forecast+ + ((Last period’s actual demand Last period’s actual demand

– – Last period’s forecastLast period’s forecast))

FFtt = F = Ft t – 1– 1 + + ((AAt t – 1– 1 - - F Ft t – 1– 1))

wherewhere FFtt == new forecastnew forecast

FFt t – 1– 1 == previous forecastprevious forecast

== smoothing (or weighting) smoothing (or weighting) constant constant (0 ≤ (0 ≤ ≤ 1) ≤ 1)

Exponential Smoothing Example

Predicted demand Predicted demand = 142= 142 Ford Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20

New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

= 142 + 2.2= 142 + 2.2

= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars

Selecting of Smoothing Constant

Chose high values of Chose high values of when actual when actual demand display an increasing (or demand display an increasing (or decreasing) trenddecreasing) trend

Chose low values of Chose low values of when demand is when demand is relatively stable without any trendrelatively stable without any trend

Exponential Smoothing with Trend Adjustment

When a trend is present, exponential When a trend is present, exponential smoothing must be modifiedsmoothing must be modified

Forecast Forecast including including ((FITFITtt)) = = trendtrend

ExponentiallyExponentially ExponentiallyExponentiallysmoothed smoothed ((FFtt)) + + ((TTtt)) smoothedsmoothedforecastforecast trendtrend

FFtt = = ((AAtt - 1 - 1) + (1 - ) + (1 - )()(FFtt - 1 - 1 + + TTtt - 1 - 1))

TTtt = = ((FFtt - - FFtt - 1 - 1) + (1 - ) + (1 - ))TTtt - 1 - 1

Exponential Smoothing with Trend Adjustment Example

ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding

MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt

11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010




11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010

F2 = A1 + (1 - )(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2




11 1212 1111 22 13.0013.0022 1717 12.8012.8033 202044 191955 242466 212177 313188 282899 3636

1010

T2 = (F2 - F1) + (1 - )T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2




11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.9233 202044 191955 242466 212177 313188 282899 3636

1010

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2




11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.92 14.7214.7233 202044 191955 242466 212177 313188 282899 3636

1010

15.1815.18 2.102.10 17.2817.2817.8217.82 2.322.32 20.1420.1419.9119.91 2.232.23 22.1422.1422.5122.51 2.382.38 24.8924.8924.1124.11 2.072.07 26.1826.1827.1427.14 2.452.45 29.5929.5929.2829.28 2.322.32 31.6031.6032.4832.48 2.682.68 35.1635.16


| | | | | | | | |

11 22 33 44 55 66 77 88 99

Time (month)Time (month)

Pro

du

ct d

eman

dP

rod

uct

dem

and

35 35 –

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

0 0 –

Actual demand Actual demand ((AAtt))

Forecast including trend Forecast including trend ((FITFITtt))

withwith = .2 = .2 andand = .4 = .4

Seasonal Variations In DataRegularly repeating movements (upward or

downward) in a time series that can be tie to recurring events. Multiplicative seasonal method a method whereby

seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.

Seasonal Variations In Data

1.1. Find average historical demand for each Find average historical demand for each season season

2.2. Compute the average demand over all Compute the average demand over all seasons seasons

3.3. Compute a seasonal index for each season Compute a seasonal index for each season

4.4. Estimate next year’s total demandEstimate next year’s total demand

5.5. Divide this estimate of total demand by the Divide this estimate of total demand by the number of seasons, then multiply it by the number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season

Steps in the process:Steps in the process:

Seasonal Index Example

JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494

DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 2005-20072005-2007 MonthlyMonthly IndexIndex


JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494


0.9570.957

Seasonal index = average 2005-2007 monthly demand

average monthly demand

= 90/94 = .957

JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 8282 7878 8080 8080 9494 0.8510.851



JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 8282 7878 8080 8080 9494 0.8510.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2008


140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –| | | | | | | | | | | |


TimeTime

Dem

and

Dem

and

2008 Forecast2008 Forecast

2007 Demand 2007 Demand

2006 Demand2006 Demand

2005 Demand2005 Demand


Associative Forecasting

Used when changes in one or more Used when changes in one or more independent variables can be used to independent variables can be used to predict the changes in the dependent predict the changes in the dependent variablevariable

Most common technique is linear Most common technique is linear regression analysisregression analysis

Regression Analysis

Forecasting an outcome based on Forecasting an outcome based on predictor variables using the least predictor variables using the least squares techniquesquares technique

y y = = a a + + bxbx^̂

where ywhere y= computed value of the = computed value of the variable to be predicted (dependent variable to be predicted (dependent variable)variable)aa= y-axis intercept= y-axis interceptbb= slope of the regression line= slope of the regression linexx= the independent variable though = the independent variable though to predict the value of the to predict the value of the dependent variabledependent variable

^̂

Least Squares Method

Time periodTime period

Va

lue

s o

f D

ep

end

en

t V

ari

able

Figure 4.4Figure 4.4

DeviationDeviation11

(error)(error)







Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂

Time periodTime period

Va

lue

s o

f D

ep

end

en

t V

ari

able









Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂

Least squares method minimizes the sum of the

squared errors (deviations)


Equations to calculate the regression variablesEquations to calculate the regression variables

b =b =xy - nxyxy - nxy

xx22 - nx - nx22

y y = = a a + + bxbx^̂

a = y - bxa = y - bx


Associative Forecasting Example

SalesSales Local PayrollLocal Payroll($ millions), y($ millions), y ($ billions), x($ billions), x

2.02.0 113.03.0 332.52.5 442.02.0 222.02.0 113.53.5 77

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

Sales, y Payroll, x x2 xy

2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5

xx = ∑ = ∑xx/6 = 18/6 = 3/6 = 18/6 = 3

yy = ∑ = ∑yy/6 = 15/6 = 2.5/6 = 15/6 = 2.5

bb = = = .25 = = = .25∑∑xy - nxyxy - nxy

∑∑xx22 - nx - nx22

51.5 - (6)(3)(2.5)51.5 - (6)(3)(2.5)

80 - (6)(380 - (6)(322))

aa = = yy - - bbx = 2.5 - (.25)(3) = 1.75x = 2.5 - (.25)(3) = 1.75


4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

y y = 1.75 + .25= 1.75 + .25xx^̂ Sales Sales = 1.75 + .25(= 1.75 + .25(payrollpayroll))

If payroll next year If payroll next year is estimated to be is estimated to be $6$6 billion, then: billion, then:

Sales Sales = 1.75 + .25(6)= 1.75 + .25(6)SalesSales = $3,250,000 = $3,250,000

3.25


Standard Error of the Estimate

A forecast is just a point estimate of a A forecast is just a point estimate of a future valuefuture value

This point is This point is actually the actually the mean of a mean of a probability probability distributiondistribution

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

3.25

wherewhere yy == y-value of each data y-value of each data pointpoint

yycc == computed value of the computed value of the dependent variable, from the dependent variable, from the regression equationregression equation

nn == number of data pointsnumber of data points

SSy,xy,x = =∑∑((y - yy - ycc))22

n n - 2- 2


Computationally, this equation is Computationally, this equation is considerably easier to useconsiderably easier to use

We use the standard error to set up We use the standard error to set up prediction intervals around the prediction intervals around the

point estimatepoint estimate

SSy,xy,x = =∑∑yy22 - a - a∑∑y - by - b∑∑xyxy

n n - 2- 2


4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

3.25

SSy,xy,x = = = =∑∑yy22 - a - a∑∑y - by - b∑∑xyxyn n - 2- 2

39.5 - 1.75(15) - .25(51.5)39.5 - 1.75(15) - .25(51.5)6 - 26 - 2

SSy,xy,x = = .306.306

The standard error The standard error of the estimate is of the estimate is $306,000$306,000 in sales in sales


How strong is the linear relationship between the variables?

Coefficient of correlation, r, measures degree of association

Values range from -1 to +1

Correlation

r = r = nnxyxy - - xxy y

[[nnxx22 - ( - (xx))22][][nnyy22 - ( - (yy))22]]

y

x(a) Perfect positive correlation: r = +1

y

x(b) Positive correlation: 0 < r < 1

y

x(c) No correlation: r = 0

y

x(d) Perfect negative correlation: r = -1

Measuring Forecast Error

Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))

MAD =MAD =∑∑ |Actual - Forecast||Actual - Forecast|

nn

Mean Squared Error Mean Squared Error ((MSEMSE))

MSE =MSE =∑∑ ((Forecast ErrorsForecast Errors))22

nn

Mean Absolute Percent Error Mean Absolute Percent Error ((MAPEMAPE))

MAPE =MAPE =∑∑100100|Actual|Actualii - Forecast - Forecastii|/Actual|/Actualii

nn

nn

i i = 1= 1

Measuring Forecast Error

Comparison of Forecast Error

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62



11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62

MAD =∑ |deviations|

n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33

For = .50




11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE =∑ (forecast errors)2

n




11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%

For = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1




11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24MAPEMAPE 5.59%5.59% 6.76%6.76%


Measures how well the forecast is predicting actual values

Good tracking signal has low values If forecasts are continually high or low, the

forecast has a bias error +ve signal : demand greater then forecast

Monitoring and Controlling Forecasts

Tracking SignalTracking Signal

Tracking Tracking signalsignal

RSFERSFEMADMAD==

Tracking Tracking signalsignal ==

∑∑(Actual demand in (Actual demand in period i - period i -

Forecast demand Forecast demand in period i)in period i)

∑∑|Actual - Forecast|/n|Actual - Forecast|/n))

Monitoring and Controlling Forecasts

Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)

Tracking Signal

Tracking signalTracking signal

++

00 MADs MADs

––

Upper control limitUpper control limit

Lower control limitLower control limit

TimeTime

Signal exceeding limitSignal exceeding limit

Acceptable Acceptable rangerange

Tracking Signal Example

CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2

CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2

TrackingSignal

(RSFE/MAD)

-10/10 = -1-15/7.5 = -2

0/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variation of the tracking signal The variation of the tracking signal between between -2.0-2.0 and and +2.5+2.5 is within acceptable is within acceptable limitslimits

Tracking Signal Example

Forecasting in the Service Sector

Presents unusual challenges Special need for short term records Holidays and other calendar events Unusual events

Fast Food Restaurant Forecast

20% 20% –

15% 15% –

10% 10% –

5% 5% –

11-1211-12 1-21-2 3-43-4 5-65-6 7-87-8 9-109-1012-112-1 2-32-3 4-54-5 6-76-7 8-98-9 10-1110-11

(Lunchtime)(Lunchtime) (Dinnertime)(Dinnertime)

Hour of dayHour of day

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CHAPTER 2 FORECASTING. LEARNING OBJECTIVES Define forecasting, forecasts approaches Understand the...

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