Here are the steps to forecast attendance for 2000 using exponential smoothing with α = 0.3: 1) Set the initial forecast F0 = actual attendance for the first period, which is 50 2) Plug into the exponential smoothing equation: F1 = α*A1 + (1-α)*F0 = 0.3*60 + (1-0.3)*50 = 54 3) Continue using the exponential smoothing equation for subsequent periods: F2 = 0.3*70 + (1-0.3)*54 = 58.8 F3 = 0.3*80 + (1-0.3)*58.8 = 63.72 4) The forecast for

1. Demand Forecasting Methods
Professor & Lawyer.Professor & Lawyer.
Puttu Guru Prasad,Puttu Guru Prasad,
M.Com. M.B.A., L.L.B., M.Phil, PGDFTM, APSET.M.Com. M.B.A., L.L.B., M.Phil, PGDFTM, APSET.
ICFAI TMF, (PhD) at JNTUK,ICFAI TMF, (PhD) at JNTUK,
Expert Resource person at APHRDI, Bapatla,Expert Resource person at APHRDI, Bapatla,
Senior Faculty for Management Studies,Senior Faculty for Management Studies,
Certified NSS Program Officer,Certified NSS Program Officer,
Coordinator – College BeautificationCoordinator – College Beautification
S&HS&H Department,Department, VVIT,VVIT, Nambur,Nambur,
93 94 96 98 98, 807 444 95 39,93 94 96 98 98, 807 444 95 39,
My Blog: puttuguru.blogspot.inMy Blog: puttuguru.blogspot.in

2. MGMT6020Forecast
Learning Objectives
When you complete this chapter, you should be
able to :
Identify or DefineIdentify or Define::
ForecastingForecasting
Categories of forecastsCategories of forecasts
Time horizonsTime horizons
Approaches to measure forecastsApproaches to measure forecasts
Explain and Apply:Explain and Apply:
Moving averagesMoving averages
Exponential smoothingExponential smoothing
Trend and seasonal projectionsTrend and seasonal projections
Measures of forecast accuracyMeasures of forecast accuracy

3. MGMT6020Forecast
Why Forecasting?
 Forecasting lays a ground for reducing the risk inForecasting lays a ground for reducing the risk in
all decision making because many of the decisionsall decision making because many of the decisions
need to be made under uncertainty.need to be made under uncertainty.
 In business applications, forecasting serves as aIn business applications, forecasting serves as a
starting point of major decisions in finance,starting point of major decisions in finance,
marketing, productions, and purchasing.marketing, productions, and purchasing.
Under what condition there is no value forUnder what condition there is no value for
forecasting?forecasting?

4. MGMT6020Forecast
Decisions Relevant to Demand
Forecasts
 Select product portfolioSelect product portfolio
 Predicting new facility locationPredicting new facility location
 Anticipating capacity needsAnticipating capacity needs
 Identifying labor requirementsIdentifying labor requirements
 Projecting material requirementsProjecting material requirements
 Developing production schedulesDeveloping production schedules
 Creating maintenance schedulesCreating maintenance schedules

5. MGMT6020Forecast
Forecasting at Tupperware
 Via forecasting, managers make importantVia forecasting, managers make important
decisionsdecisions
 Each of 50 profit centers around the world isEach of 50 profit centers around the world is
responsible for computerized monthly,responsible for computerized monthly,
quarterly, and 12-month sales projectionsquarterly, and 12-month sales projections
 These projections are aggregated by productThese projections are aggregated by product
family and region, then globally, atfamily and region, then globally, at
Tupperware’s World HeadquartersTupperware’s World Headquarters
 Tupperware uses all techniques discussed in textTupperware uses all techniques discussed in text

6. MGMT6020Forecast
Successful Forecasting
= Science + Art
 "Science" implies that the body of the forecasting"Science" implies that the body of the forecasting
knowledge lies on the solid ground of quantitativeknowledge lies on the solid ground of quantitative
forecasting methods and their correct utilization forforecasting methods and their correct utilization for
various business situations.various business situations.
 "Art" represents a combination of a decision"Art" represents a combination of a decision
maker's experience, logic, and intuition tomaker's experience, logic, and intuition to
supplement the forecasting quantitative analysis.supplement the forecasting quantitative analysis.
 Both the science and art of forecasting are essentialBoth the science and art of forecasting are essential
in developing accurate forecasts.in developing accurate forecasts.
 All managers are forecasters!All managers are forecasters!

7. MGMT6020Forecast
Forecast Categories
TYPESTYPES
QualitativeQualitative Executive opinionsExecutive opinions
Sales force surveysSales force surveys
Delphi methodDelphi method
Consumer surveysConsumer surveys
QuantitativeQuantitative Times series methodsTimes series methods
Associative (causal)Associative (causal)
methodsmethods

8. MGMT6020Forecast
Forecast Categories
TIME HORIZONTIME HORIZON
Long-termLong-term For duration of 3-5For duration of 3-5
years or more (onyears or more (on
annual basis)annual basis)
Medium-termMedium-term For duration of up to threeFor duration of up to three
years (usually on quarterlyyears (usually on quarterly
or monthly basis)or monthly basis)
Short-termShort-term Up to one year, usually lessUp to one year, usually less
than three months (onthan three months (on
daily, weekly)daily, weekly)

9. MGMT6020Forecast
Facts in Forecasting
 Main assumption: Past pattern repeats itself into the
future.
 Forecasts are rarely perfect: Don't expect forecasts to
be exactly equal to the actual data.
 The science and art of forecasting try to minimize, but
not to eliminate, forecast errors. Forecast errors mean
the difference between actual and forecasted values.
 Forecasts for a group of products are usually more
accurate than these for individual products; a shorter
period tend to be more accurate.
 Computer and IT are critical parts of the modern
forecasting in large corporations.

10. MGMT6020Forecast
Seven Steps in Forecasting
(Demands)
 Determine the use of the forecastDetermine the use of the forecast
 Select the items to be forecastSelect the items to be forecast
 Determine the time horizon of the forecastDetermine the time horizon of the forecast
 Select the forecasting model(s)Select the forecasting model(s)
 Gather the dataGather the data
 Make the forecastMake the forecast
 Validate and implement resultsValidate and implement results

11. MGMT6020Forecast
Quantitative Methods
 A time series is an uninterrupted set of dataA time series is an uninterrupted set of data
observations that have been ordered inobservations that have been ordered in
equally spaced intervals (units of time).equally spaced intervals (units of time).
 Associative (causal) forecasting is based onAssociative (causal) forecasting is based on
identification of variables (factors) that canidentification of variables (factors) that can
predict values of the variable in question.predict values of the variable in question.

12. MGMT6020Forecast
Quantitative Forecasting Models
·· Time Series ModelsTime Series Models
Naive ForecastNaive Forecast
Simple Moving AveragesSimple Moving Averages
Weighted Moving AveragesWeighted Moving Averages
Simple Exponential SmoothingSimple Exponential Smoothing
Exponential Smoothing withExponential Smoothing with
TrendTrend
Linear Trend ProjectionLinear Trend Projection
Time Series DecompositionTime Series Decomposition
·· Associative (Causal)Associative (Causal)
ModelsModels
Simple Linear RegressionSimple Linear Regression
Multiple Linear RegressionMultiple Linear Regression
Nonlinear RegressionNonlinear Regression

13. MGMT6020Forecast
Time Series Pattern: Stationary
 The result of manyThe result of many
influences that actinfluences that act
independently so as toindependently so as to
yield nonsystematicyield nonsystematic
and non-repeatingand non-repeating
patterns about somepatterns about some
average value.average value.
 Forecasting methods:Forecasting methods:
naive, moving average,naive, moving average,
exponential smoothingexponential smoothing

14. MGMT6020Forecast
Time Series Pattern: Trend
 It represents a generalIt represents a general
increase or decrease inincrease or decrease in
a time series overa time series over
several consecutiveseveral consecutive
periods (some sourcesperiods (some sources
present six-seven orpresent six-seven or
more periods).more periods).
 Forecasting methods:Forecasting methods:
linear trend projection,linear trend projection,
exponential smoothingexponential smoothing
with trend, etc.with trend, etc.

15. MGMT6020Forecast
Time Series Pattern: Seasonal
 Seasonal PatternsSeasonal Patterns
represent patterns thatrepresent patterns that
are periodic andare periodic and
recurrent (usually on arecurrent (usually on a
quarterly, monthly, orquarterly, monthly, or
annual basis).annual basis).
 Forecasting methods:Forecasting methods:
exponential smoothingexponential smoothing
with trend andwith trend and
seasonality, time seriesseasonality, time series
decomposition, etc.decomposition, etc.

16. MGMT6020Forecast
Time Series Pattern: Cyclical
 The result of economic andThe result of economic and
business expansions (increasingbusiness expansions (increasing
demand) and contractionsdemand) and contractions
(recessions and depressions)(recessions and depressions)
and usually repeat every two-and usually repeat every two-
five years. Cyclical influencesfive years. Cyclical influences
are difficult to forecast becauseare difficult to forecast because
cyclical demands are recurrentcyclical demands are recurrent
but not periodic (they happen inbut not periodic (they happen in
different intervals of time withdifferent intervals of time with
great variability of demands).great variability of demands).
 Forecasting methods: timeForecasting methods: time
series decomposition, multipleseries decomposition, multiple
regressionregression

17. MGMT6020Forecast
Product Demand Charted over 4
Years with Trend and Seasonality
Year
1
Year
2
Year
3
Year
4
Seasonal peaks Trend component
Actual
demand line
Average demand
over four years
Demandforproductorservice
Random
variation

18. MGMT6020Forecast
 Set of evenly spaced numerical dataSet of evenly spaced numerical data
 Obtained by observing response variable atObtained by observing response variable at
regular time periodsregular time periods
 Forecast based only on past valuesForecast based only on past values
 Assumes that factors influencing past andAssumes that factors influencing past and
present will continue influence in futurepresent will continue influence in future
 ExampleExample
Year:Year: 19931993 19941994 19951995 19961996 19971997
Sales:Sales: 78.778.7 63.563.5 89.789.7 93.293.2 92.192.1
What is a Time Series?

19. MGMT6020Forecast
Naïve Approach
 Assumes demand in next period is the same asAssumes demand in next period is the same as
demand in most recent perioddemand in most recent period
e.g., If May sales were 48, then June sales will bee.g., If May sales were 48, then June sales will be
around 48around 48
 Sometimes it is effective & cost efficientSometimes it is effective & cost efficient
e.g. when the demand is steady or changes slowlye.g. when the demand is steady or changes slowly
when inventory cost is lowwhen inventory cost is low
when unmet demand will not losewhen unmet demand will not lose

20. MGMT6020Forecast
 MA is a series of arithmetic meansMA is a series of arithmetic means
 Used if little or no trend, seasonal, and cyclicalUsed if little or no trend, seasonal, and cyclical
patternspatterns
 Used oftenUsed often for smoothingfor smoothing
 Provides overall impression of data over timeProvides overall impression of data over time
 EquationEquation
MAMA
nn
nn
== ∑∑ Demand inDemand in PreviousPrevious PeriodsPeriods
Moving Average Method

21. MGMT6020Forecast
You’re manager of a museum store that sellsYou’re manager of a museum store that sells
historical replicas. You want to forecast saleshistorical replicas. You want to forecast sales
of item (123) forof item (123) for 20002000 using ausing a 33-period moving-period moving
average.average.
19951995 44
19961996 66
19971997 55
19981998 33
19991999 77
© 1995 Corel Corp.
Moving Average Example

22. MGMT6020Forecast
Moving Average Solution
Time Response
Yi
Moving
Total
(n=3)
Moving
Average
(n=3)
1995 4 NA NA
1996 6 NA NA
1997 5 NA NA
1998 3 4+6+5=15 15/3 = 5
1999 7
2000 NA

23. MGMT6020Forecast
Moving Average Solution
Time Response
Yi
Moving
Total
(n=3)
Moving
Average
(n=3)
1995 4 NA NA
1996 6 NA NA
1997 5 NA NA
1998 3 4+6+5=15 15/3 = 5
1999 7 6+5+3=14 14/3=4 2/3
2000 NA

24. MGMT6020Forecast
Moving Average Solution
Time Response
Yi
Moving
Total
(n=3)
Moving
Average
(n=3)
1995 4 NA NA
1996 6 NA NA
1997 5 NA NA
1998 3 4+6+5=15 15/3=5.0
1999 7 6+5+3=14 14/3=4.7
2000 NA 5+3+7=15 15/3=5.0

25. MGMT6020Forecast
95 96 97 98 99 00
Year
Sales
2
4
6
8 Actual
Forecast
Moving Average Graph

26. MGMT6020Forecast
 Used when trend is presentUsed when trend is present
Older data usually less importantOlder data usually less important
 Weights based on intuitionWeights based on intuition
Often lay between 0 & 1, & sum to 1.0Often lay between 0 & 1, & sum to 1.0
 EquationEquation
WMA =WMA =
ΣΣ(Weight for period(Weight for period nn) (Demand in period) (Demand in period nn))
ΣΣWeightsWeights
Weighted Moving Average
Method

27. MGMT6020Forecast
Actual Demand, Moving Average,
Weighted Moving Average
0
5
10
15
20
25
30
35
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
SalesDemand
Actual sales
Moving average
Weighted moving average

28. MGMT6020Forecast
 IncreasingIncreasing nn makes forecast less sensitivemakes forecast less sensitive
to changesto changes
 Do not forecast trend well due to the delayDo not forecast trend well due to the delay
between actual outcome and forecastbetween actual outcome and forecast
 Difficult to trace seasonal and cyclicalDifficult to trace seasonal and cyclical
patternspatterns
 Require much historical dataRequire much historical data
 Weighted MA may perform betterWeighted MA may perform better
Disadvantages of Moving
Average Methods

29. MGMT6020Forecast
 Form of weighted moving averageForm of weighted moving average
 Weights decline exponentiallyWeights decline exponentially
 Most recent data weighted mostMost recent data weighted most
 Requires smoothing constant (Requires smoothing constant (αα))
 Ranges from 0 to 1Ranges from 0 to 1
 Subjectively chosenSubjectively chosen
 Involves little record keeping of past dataInvolves little record keeping of past data
Exponential Smoothing Method

30. MGMT6020Forecast
 FFtt == FFtt-1-1 ++ αα((AAtt-1-1 -- FFtt-1-1))
== ααAAtt-1-1 + (1 -+ (1 - αα)) FFtt-1-1
 FFtt = Forecast value= Forecast value
 AAtt = Actual value= Actual value
 αα = Smoothing constant= Smoothing constant
 FFtt == ααAAtt - 1- 1 ++ αα(1-(1-αα))AAtt - 2- 2 ++ αα(1-(1- αα))22
·A·Att - 3- 3
++ αα(1-(1- αα))33
AAtt - 4- 4 + ... ++ ... + αα(1-(1- αα))t-t-11
·A·A00
 Use for computing forecastUse for computing forecast
Exponential Smoothing
Equations

31. MGMT6020Forecast
You’re organizing a Kwanza meeting. YouYou’re organizing a Kwanza meeting. You
want to forecast attendance forwant to forecast attendance for 20002000 usingusing
exponential smoothing (exponential smoothing (αα = .10= .10). The). The
1995 (made in 1994) forecast was1995 (made in 1994) forecast was 175175..
Actual data:Actual data:
19951995 180180
19961996 168168
19971997 159159
19981998 175175
19991999 190190
© 1995 Corel Corp.
Exponential Smoothing
Example

32. MGMT6020Forecast
Ft = Ft-1 + α ·(At-1 - Ft-1)
TimeTime Actual
Forecast, Ft
(αα == .10.10))
19951995 180 175.00 (Given)
19961996 168168
19971997 159159
19981998 175175
19991999 190190
20002000 NANA
175.00 +175.00 +
Exponential Smoothing Solution

33. MGMT6020Forecast
Exponential Smoothing Solution
TimeTime Actual
Forecast, Ft
(αα == .10.10))
19951995 180180 175.00 (Given)175.00 (Given)
19961996 168168 175.00 +175.00 + .10.10((
19971997 159159
19981998 175175
19991999 190190
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

34. MGMT6020Forecast
Exponential Smoothing Solution
TimeTime ActualActual
Forecast,Forecast, FFtt
((αα == .10.10))
19951995 180180 175.00 (Given)175.00 (Given)
19961996 168168 175.00 +175.00 + .10.10(180(180 --
19971997 159159
19981998 175175
19991999 190190
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

35. MGMT6020Forecast
Exponential Smoothing Solution
Time Actual
Forecast, Ft
(αα == .10.10))
19951995 180180 175.00 (Given)175.00 (Given)
19961996 168168 175.00 +175.00 + .10.10(180(180 - 175.00- 175.00))
19971997 159159
19981998 175175
19991999 190190
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

36. MGMT6020Forecast
Exponential Smoothing Solution
TimeTime ActualActual
Forecast,Forecast, FFtt
((αα == .10.10))
19951995 180180 175.00 (Given)175.00 (Given)
19961996 168168 175.00 +175.00 + .10.10(180(180 - 175.00- 175.00)) = 175.50= 175.50
19971997 159159
19981998 175175
19991999 190190
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

37. MGMT6020Forecast
Exponential Smoothing Solution
Time Actual
Forecast, Ft
(αα == .10.10))
1995 180 175.00 (Given)
19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50
19971997 159159 175.50175.50 ++ .10.10(168 -(168 - 175.50175.50)) = 174.75= 174.75
19981998 175175
19991999 190190
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

38. MGMT6020Forecast
Exponential Smoothing Solution
Time Actual
Forecast, Ft
(α = .10)
19951995 180180 175.00 (Given)175.00 (Given)
1996 168 175.00 + .10(180 - 175.00) = 175.50
19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75
19981998 175175
19991999 190190
20002000 NANA
174.75174.75 ++ .10.10(159(159 -- 174.75174.75))= 173.18= 173.18
Ft = Ft-1 + α ·(At-1 - Ft-1)

39. MGMT6020Forecast
Exponential Smoothing Solution
Time Actual
Forecast, Ft
(α = .10)
1995 180 175.00 (Given)
19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50
19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75
19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18
19991999 190190 173.18 +173.18 + .10.10(175(175 - 173.18- 173.18)) = 173.36= 173.36
20002000 NANA
Ft = Ft-1 + α ·(At-1 - Ft-1)

40. MGMT6020Forecast
Exponential Smoothing Solution
Time Actual
Forecast, Ft
(α = .10)
19951995 180180 175.00 (Given)175.00 (Given)
19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50
19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75
19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18
19991999 190190 173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36
20002000 NANA 173.36173.36 ++ .10.10(190(190 - 173.36- 173.36) = 175.02) = 175.02
Ft = Ft-1 + α ·(At-1 - Ft-1)

41. MGMT6020Forecast
Year
Sales
140
150
160
170
180
190
93 94 95 96 97 98
Actual
Forecast
Exponential Smoothing Graph

42. MGMT6020Forecast
Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10%

43. MGMT6020Forecast
Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10% 9%

44. MGMT6020Forecast
Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10% 9% 8.1%

45. MGMT6020Forecast
Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10% 9% 8.1%
90%

46. MGMT6020Forecast
Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10% 9% 8.1%
90% 9%

47. MGMT6020Forecast
Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2
At - 3 + ...
Forecast Effects of
Smoothing Constant α
Weights
Prior Period
α
2 periods ago
α(1 - α)
3 periods ago
α(1 - α)2
α=
α= 0.10
α= 0.90
10% 9% 8.1%
90% 9% 0.9%

48. MGMT6020Forecast
 You want to achieve:You want to achieve:
 Smallest forecast errorSmallest forecast error
Mean square error (MSE)Mean square error (MSE)
Mean absolute deviation (MAD)Mean absolute deviation (MAD)
 No pattern or direction in forecastNo pattern or direction in forecast
errorerror
Error = (Error = (YYii -- YYii) = (Actual - Forecast)) = (Actual - Forecast)
Seen in plots of errors over timeSeen in plots of errors over time
Guidelines for Selecting
Forecasting Model
^

49. MGMT6020Forecast
How to Choose α
Seek to minimize the Mean Absolute Deviation (MAD)
If: Forecast error = demand - forecast
Then:
n
errorsforecast∑
=MAD
Note that the sum of all weights in exponential
smoothing equals to 1. It is popular because of the
simplicity of data keeping.

50. MGMT6020Forecast
Measuring Forecast Accuracy
 Mean Squared Error (MSE)Mean Squared Error (MSE)
represents the variance of errors in a forecast. This criterionrepresents the variance of errors in a forecast. This criterion
is most useful if you want to minimize the occurrence of ais most useful if you want to minimize the occurrence of a
major error(s).major error(s).
n
e
=
n
)2
Ft-At(
n
1=t=MSE
2
t
n
1=t
∑∑

51. MGMT6020Forecast
Exponential Smoothing with
Trend Adjustment
Forecast including trend (FITt)
= exponentially smoothed forecast (Ft)
+ exponentially smoothed trend (Tt)

52. MGMT6020Forecast
Ft = α(Actual demand this period)
+ (1- α)(Forecast last period+Trend estimate last period)
Ft = α(At-1) + (1- α)Ft-1 + Tt-1
or
Tt = β(Forecast this period - Forecast last period)
+ (1- β)(Trend estimate last period
Tt = β(Ft - Ft-1) + (1- β)Tt-1
or
Exponential Smoothing with
Trend Adjustment - continued

53. MGMT6020Forecast
 FFtt = exponentially smoothed forecast of the= exponentially smoothed forecast of the
data series in perioddata series in period tt
 TTtt = exponentially smoothed trend in period= exponentially smoothed trend in period tt
 AAtt = actual demand in period= actual demand in period tt
 αα = smoothing constant for the average= smoothing constant for the average
 ββ = smoothing constant for the trend= smoothing constant for the trend
Exponential Smoothing with
Trend Adjustment - continued

54. MGMT6020Forecast
Comparison of Forecasts
0
5
10
15
20
25
30
35
40
Jan Feb Mar Apr May Jun Jul Aug Sep
Month
ProductDemand
Actual Demand
Exponential smoothing
Exponential smoothing +
Trend

55. MGMT6020Forecast
 Used for forecasting linear trend lineUsed for forecasting linear trend line
 Assumes relationship between responseAssumes relationship between response
variable,variable, Y,Y, and time,and time, X,X, is a linearis a linear
functionfunction
 Estimated by least squares methodEstimated by least squares method
 Minimizes sum of squared errorsMinimizes sum of squared errors
iY a bXi= +
Linear Trend Projection

56. MGMT6020Forecast
Y a bXi i= +
b > 0
b < 0
a
a
Y
Time, X
Linear Trend Projection Model

57. MGMT6020Forecast
 Slope (Slope (bb))
 EstimatedEstimated YY changes bychanges by bb for each 1 unitfor each 1 unit
increase inincrease in XX
IfIf bb = 2, then sales (= 2, then sales (YY) is expected to increase) is expected to increase
by 2 for each 1 unit increase in advertisingby 2 for each 1 unit increase in advertising
((XX))
 Y-intercept (Y-intercept (aa))
 Average value ofAverage value of YY whenwhen XX = 0= 0
IfIf aa = 4, then average sales (= 4, then average sales (YY) is expected to) is expected to
be 4 when advertising (be 4 when advertising (XX) is 0) is 0
Interpretation of Coefficients

58. MGMT6020Forecast
How to Find a and b: Least
Squares Equations
Equation: ii bxaYˆ +=
Slope:
22
1=
1=
−∑
−∑
=
xnx
yxnyx
b
i
n
i
ii
n
i
Y-Intercept: xbya −=
Criteria of finding a and b:

59. MGMT6020Forecast
Measuring Forecast Accuracy
 Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)
measures the average absolute error of a forecast. A sign ofmeasures the average absolute error of a forecast. A sign of
an error, which represents over- or underestimation, isan error, which represents over- or underestimation, is
really not important in most cases; we are rather concernedreally not important in most cases; we are rather concerned
with the value of deviation.with the value of deviation.
where:where:
AAtt = actual value in period t,= actual value in period t,
FFtt = forecasted value in period t,= forecasted value in period t,
eett = forecast error in period t,= forecast error in period t,
n = number of periods.n = number of periods.
n
|e|
=
n
|F-A|
=MAD
t
n
1=t
tt
n
1=t
∑∑

60. MGMT6020Forecast
Measuring Forecast Accuracy
 Mean Squared Error (MSE)Mean Squared Error (MSE)
represents the variance of errors in a forecast. This criterionrepresents the variance of errors in a forecast. This criterion
is most useful if you want to minimize the occurrence of ais most useful if you want to minimize the occurrence of a
major error(s).major error(s).
n
e
=
n
)2
Ft-At(
n
1=t=MSE
2
t
n
1=t
∑∑

61. MGMT6020Forecast
 Include seasonal and cyclical patternsInclude seasonal and cyclical patterns
 In decomposition, a time series is described as a function ofIn decomposition, a time series is described as a function of
four components:four components:
Y = T*C*S*IY = T*C*S*I multiplicative model (commonly used)multiplicative model (commonly used)
Y = T+C+S+IY = T+C+S+I additive modeladditive model
where:where:
Y =Y = actual value of time seriesactual value of time series
T =T = trend componenttrend component
C =C = cyclical componentcyclical component
S =S = seasonal componentseasonal component
I =I = irregular (random) componentirregular (random) component
General Description of TS Models:
Time Series Decomposition

62. MGMT6020Forecast
Multiplicative Seasonal Model
 FindFind average historical demandaverage historical demand for eachfor each
“season”“season” by summing the demand forby summing the demand for
that season in each year, and dividing bythat season in each year, and dividing by
the number of years for which you havethe number of years for which you have
data.data.
 Compute theCompute the average demand over allaverage demand over all
seasonsseasons by dividing the total averageby dividing the total average
annual demand by the number of seasons.annual demand by the number of seasons.

63. MGMT6020Forecast
Multiplicative Seasonal Model
 Compute aCompute a seasonal indexseasonal index by dividingby dividing
that season’s historical demand (fromthat season’s historical demand (from
step 1) by the average demand over allstep 1) by the average demand over all
seasons.seasons.
 Estimate next year’s total demand byEstimate next year’s total demand by
using smoothed linear trend projectionusing smoothed linear trend projection
modelmodel
 Divide this estimate of total demand byDivide this estimate of total demand by
the number of seasons, then multiply itthe number of seasons, then multiply it
by the seasonal index for that season.by the seasonal index for that season.
This provides theThis provides the seasonal forecastseasonal forecast..

64. MGMT6020Forecast
Example of Multiplicative
Seasonal Model
The following trend projection is used to predict quarterly
demand: Y = 350 - 2.5t, where t = 1 in the first quarter of
1998. Seasonal (quarterly) relatives are Quarter 1 = 1.5;
Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is
the seasonally adjusted forecast for the four quarters of 2000?
(10%)
Period Projection Adjusted
9 327.5 491.25
10 325 260
11 322.5 354.75
12 320 192

65. MGMT6020Forecast
Seven Steps in Forecasting
(Demands)
 Determine the use of the forecastDetermine the use of the forecast
 Select the items to be forecastSelect the items to be forecast
 Determine the time horizon of the forecastDetermine the time horizon of the forecast
 Select the forecasting model(s)Select the forecasting model(s)
 Gather the dataGather the data
 Make the forecastMake the forecast
 Validate and implement resultsValidate and implement results

66. MGMT6020Forecast
Past Data of Nurse Demand: What
patterns can be observed?
0
5
10
15
20
1
3
5
7
9
11
Time Period
NumberofNurses
Number of
Nurses

67. MGMT6020Forecast
Forecasting Issues During a
Product’s Life
Introduction Growth Maturity Decline
Standardization
Less rapid product
changes - more minor
changes
Optimum capacity
Increasing stability of
process
Long production runs
Product improvement
and cost cutting
Little product
differentiation
Cost minimization
Over capacity in the
industry
Prune line to eliminate
items not returning
good margin
Reduce capacity
Forecasting critical
Product and process
reliability
Competitive product
improvements and
options
Increase capacity
Shift toward product
focused
Enhance distribution
Product design and
development critical
Frequent product and
process design changes
Short production runs
High production costs
Limited models
Attention to quality
Best period to
increase market
share
R&D product
engineering
critical
Practical to change
price or quality image
Strengthen niche
Cost control
critical
Poor time to change
image, price, or quality
Competitive costs
become critical
Defend market position
OMStrategy/IssuesCompanyStrategy/Issues
HDTV
CD-ROM
Color copiers
Drive-thru restaurants Fax machines
Station
wagons
Sales
3 1/2”
Floppy
disks
Internet

68. MGMT6020Forecast
 Measures how well the forecast is predictingMeasures how well the forecast is predicting
actual valuesactual values
 Ratio of running sum of forecast errorsRatio of running sum of forecast errors
(RSFE) to mean absolute deviation (MAD)(RSFE) to mean absolute deviation (MAD)
 Good tracking signal has low valuesGood tracking signal has low values
 Should be within upper and lower controlShould be within upper and lower control
limitslimits
Tracking Signal
( )
MAD
errorforecast
ˆ
1 ∑∑
=
−
== =
MAD
yy
MAD
RSFE
TS
n
i
ii

69. MGMT6020Forecast
Plot of a Tracking Signal
Time
Lower control limit
Upper control limit
Signal exceeded limit
Tracking signal
Acceptable range
MAD
+
0
-

70. MGMT6020Forecast
Time (Years)
Error
0
Desired Pattern
Time (Years)
Error
0
Trend Not Fully
Accounted for
Pattern of Forecast Error:
Identified Only by Observation

71. MGMT6020Forecast
Predicting Cyclical Factors
Leading indicatorsLeading indicators
 Investment (public/private)Investment (public/private)
 ExportExport
 Business purchasingBusiness purchasing
 Consumer confidenceConsumer confidence
 Government expendingGovernment expending

72. Advanced Forecasting Methods
 To improve the accuracy, more complicatedTo improve the accuracy, more complicated
models might be required. For example,models might be required. For example,
 Adaptive smoothingAdaptive smoothing
 Focus forecastingFocus forecasting