Date post: | 22-Nov-2014 |
Category: |
Documents |
Upload: | rozaimi-saad |
View: | 1,207 times |
Download: | 6 times |
10/16/2010
1
44 ForecastingForecasting
PowerPoint presentation to accompanyPowerPoint presentation to accompany
4 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall
PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e
PowerPoint slides by Jeff Heyl
OutlineOutline
Global Company Profile: Disney WorldWhat Is Forecasting?
F ti Ti H i
4 - 2© 2011 Pearson Education, Inc. publishing as Prentice Hall
Forecasting Time HorizonsThe Influence of Product Life CycleTypes Of Forecasts
Outline Outline –– ContinuedContinuedThe Strategic Importance of Forecasting
Human ResourcesCapacity
4 - 3© 2011 Pearson Education, Inc. publishing as Prentice Hall
CapacitySupply Chain Management
Seven Steps in the Forecasting System
Outline Outline –– ContinuedContinuedForecasting Approaches
Overview of Qualitative MethodsOverview of Quantitative Methods
4 - 4© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time-Series ForecastingDecomposition of a Time SeriesNaive Approach
Outline Outline –– ContinuedContinuedTime-Series Forecasting (cont.)
Moving AveragesExponential Smoothing
4 - 5© 2011 Pearson Education, Inc. publishing as Prentice Hall
Exponential Smoothing with Trend AdjustmentTrend ProjectionsSeasonal Variations in DataCyclical Variations in Data
Outline Outline –– ContinuedContinuedAssociative Forecasting Methods: Regression and Correlation Analysis
Using Regression Analysis for
4 - 6© 2011 Pearson Education, Inc. publishing as Prentice Hall
g g yForecastingStandard Error of the EstimateCorrelation Coefficients for Regression LinesMultiple-Regression Analysis
10/16/2010
2
Outline Outline –– ContinuedContinuedMonitoring and Controlling Forecasts
Adaptive SmoothingF F ti
4 - 7© 2011 Pearson Education, Inc. publishing as Prentice Hall
Focus ForecastingForecasting in the Service Sector
Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :
1. Understand the three time horizons and which models apply for each use
4 - 8© 2011 Pearson Education, Inc. publishing as Prentice Hall
and which models apply for each use2. Explain when to use each of the four
qualitative models3. Apply the naive, moving average,
exponential smoothing, and trend methods
Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :
4. Compute three measures of forecast accuracy
4 - 9© 2011 Pearson Education, Inc. publishing as Prentice Hall
accuracy5. Develop seasonal indexes6. Conduct a regression and correlation
analysis7. Use a tracking signal
Forecasting at Disney WorldForecasting at Disney World
Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and AnaheimRevenues are derived from people – how
4 - 10© 2011 Pearson Education, Inc. publishing as Prentice Hall
Revenues are derived from people how many visitors and how they spend their moneyDaily management report contains only the forecast and actual attendance at each park
Forecasting at Disney WorldForecasting at Disney World
Disney generates daily, weekly, monthly, annual, and 5-year forecastsForecast used by labor management, maintenance operations finance and
4 - 11© 2011 Pearson Education, Inc. publishing as Prentice Hall
maintenance, operations, finance, and park schedulingForecast used to adjust opening times, rides, shows, staffing levels, and guests admitted
Forecasting at Disney WorldForecasting at Disney World
20% of customers come from outside the USAEconomic model includes gross domestic product cross-exchange rates
4 - 12© 2011 Pearson Education, Inc. publishing as Prentice Hall
domestic product, cross-exchange rates, arrivals into the USAA staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year
10/16/2010
3
Forecasting at Disney WorldForecasting at Disney World
Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000
4 - 13© 2011 Pearson Education, Inc. publishing as Prentice Hall
school districts around the worldAverage forecast error for the 5-year forecast is 5%Average forecast error for annual forecasts is between 0% and 3%
What is Forecasting?What is Forecasting?Process of predicting a future eventUnderlying basis of all business
??
4 - 14© 2011 Pearson Education, Inc. publishing as Prentice Hall
decisionsProductionInventoryPersonnelFacilities
Short-range forecastUp to 1 year, generally less than 3 monthsPurchasing, job scheduling, workforce levels, job assignments, production levels
Medium-range forecast
Forecasting Time HorizonsForecasting Time Horizons
4 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall
g3 months to 3 yearsSales and production planning, budgeting
Long-range forecast3+ yearsNew product planning, facility location, research and development
Distinguishing DifferencesDistinguishing Differences
Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes
4 - 16© 2011 Pearson Education, Inc. publishing as Prentice Hall
processesShortShort--termterm forecasting usually employs different methodologies than longer-term forecastingShortShort--termterm forecasts tend to be more accurate than longer-term forecasts
Influence of Product Life Influence of Product Life CycleCycle
Introduction and growth require longer forecasts than maturity and decline
Introduction Introduction –– Growth Growth –– Maturity Maturity –– DeclineDecline
4 - 17© 2011 Pearson Education, Inc. publishing as Prentice Hall
forecasts than maturity and declineAs product passes through life cycle, forecasts are useful in projecting
Staffing levelsInventory levelsFactory capacity
Product Life CycleProduct Life CycleBest period to increase market share
R&D engineering is critical
Practical to change price or quality image
Strengthen niche
Poor time to change image, price, or quality
Competitive costs become criticalDefend market
Cost control critical
Introduction Growth Maturity Decline
egy/
Issu
es
4 - 18© 2011 Pearson Education, Inc. publishing as Prentice Hall
position
Com
pany
Str
ate
Figure 2.5
Internet search engines
Sales
Drive-through restaurants
CD-ROMs
Analog TVs
iPods
Boeing 787
LCD & plasma TVs
Avatars
Xbox 360
10/16/2010
4
Product Life CycleProduct Life CycleProduct design and development criticalFrequent product and process design
Introduction Growth Maturity Decline
y/Is
sues
Forecasting criticalProduct and process reliabilityCompetitive
d t
StandardizationFewer product changes, more minor changesOptimum capacity
Little product differentiationCost minimizationOvercapacity in the i d t
4 - 19© 2011 Pearson Education, Inc. publishing as Prentice Hall
process design changesShort production runsHigh production costsLimited modelsAttention to quality
OM
Str
ateg
y product improvements and optionsIncrease capacityShift toward product focusEnhance distribution
Increasing stability of processLong production runsProduct improvement and cost cutting
industryPrune line to eliminate items not returning good marginReduce capacity
Figure 2.5
Types of ForecastsTypes of Forecasts
Economic forecastsAddress business cycle – inflation rate, money supply, housing starts, etc.
Technological forecasts
4 - 20© 2011 Pearson Education, Inc. publishing as Prentice Hall
Technological forecastsPredict rate of technological progressImpacts development of new products
Demand forecastsPredict sales of existing products and services
Strategic Importance of Strategic Importance of ForecastingForecasting
Human Resources – Hiring, training, laying off workersC it C it h t
4 - 21© 2011 Pearson Education, Inc. publishing as Prentice Hall
Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market shareSupply Chain Management – Good supplier relations and price advantages
Seven Steps in ForecastingSeven Steps in Forecasting1. Determine the use of the forecast2. Select the items to be forecasted3. Determine the time horizon of the
forecast
4 - 22© 2011 Pearson Education, Inc. publishing as Prentice Hall
o ecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast7. Validate and implement results
The Realities!The Realities!
Forecasts are seldom perfectMost techniques assume an underlying stability in the system
4 - 23© 2011 Pearson Education, Inc. publishing as Prentice Hall
underlying stability in the systemProduct family and aggregated forecasts are more accurate than individual product forecasts
Forecasting ApproachesForecasting Approaches
Used when situation is vague and little data exist
Qualitative MethodsQualitative Methods
4 - 24© 2011 Pearson Education, Inc. publishing as Prentice Hall
New productsNew technology
Involves intuition, experiencee.g., forecasting sales on Internet
10/16/2010
5
Forecasting ApproachesForecasting Approaches
Used when situation is ‘stable’ and historical data exist
Quantitative MethodsQuantitative Methods
4 - 25© 2011 Pearson Education, Inc. publishing as Prentice Hall
Existing productsCurrent technology
Involves mathematical techniquese.g., forecasting sales of color televisions
Overview of Qualitative Overview of Qualitative MethodsMethods
1. Jury of executive opinionPool opinions of high-level experts, sometimes augment by statistical
4 - 26© 2011 Pearson Education, Inc. publishing as Prentice Hall
sometimes augment by statistical models
2. Delphi methodPanel of experts, queried iteratively
Overview of Qualitative Overview of Qualitative MethodsMethods
3. Sales force compositeEstimates from individual
l i d f
4 - 27© 2011 Pearson Education, Inc. publishing as Prentice Hall
salespersons are reviewed for reasonableness, then aggregated
4. Consumer Market SurveyAsk the customer
Involves small group of high-level experts and managersGroup estimates demand by working together
Jury of Executive OpinionJury of Executive Opinion
4 - 28© 2011 Pearson Education, Inc. publishing as Prentice Hall
Combines managerial experience with statistical modelsRelatively quick‘Group-think’disadvantage
Sales Force CompositeSales Force Composite
Each salesperson projects his or her salesCombined at district and national
4 - 29© 2011 Pearson Education, Inc. publishing as Prentice Hall
levelsSales reps know customers’ wantsTends to be overly optimistic
Delphi MethodDelphi MethodIterative group process, continues until consensus is reached
Decision Makers(Evaluate
responses and make decisions)
4 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall
reached3 types of participants
Decision makersStaffRespondents
Staff(Administering
survey)
Respondents(People who can make valuable
judgments)
10/16/2010
6
Consumer Market SurveyConsumer Market Survey
Ask customers about purchasing plansWhat consumers say, and what
4 - 31© 2011 Pearson Education, Inc. publishing as Prentice Hall
they actually do are often differentSometimes difficult to answer
Overview of Quantitative Overview of Quantitative ApproachesApproaches
1. Naive approach2. Moving averages
time series
4 - 32© 2011 Pearson Education, Inc. publishing as Prentice Hall
3. Exponential smoothing
4. Trend projection5. Linear regression
time-series models
associative model
Set of evenly spaced numerical dataObtained by observing response variable at regular time periods
Time Series ForecastingTime Series Forecasting
4 - 33© 2011 Pearson Education, Inc. publishing as Prentice Hall
Forecast based only on past values, no other variables important
Assumes that factors influencing past and present will continue influence in future
Trend Cyclical
Time Series ComponentsTime Series Components
4 - 34© 2011 Pearson Education, Inc. publishing as Prentice Hall
Seasonal Random
Components of DemandComponents of Demand
or s
ervi
ce
Trend component
Seasonal peaks
4 - 35© 2011 Pearson Education, Inc. publishing as Prentice Hall
Dem
and
for p
rodu
ct o
| | | |1 2 3 4
Time (years)
Average demand over 4 years
Actual demand line
Random variation
Figure 4.1
Persistent, overall upward or downward patternChanges due to population, t h l lt t
Trend ComponentTrend Component
4 - 36© 2011 Pearson Education, Inc. publishing as Prentice Hall
technology, age, culture, etc.Typically several years duration
10/16/2010
7
Regular pattern of up and down fluctuationsDue to weather, customs, etc.Occurs within a single year
Seasonal ComponentSeasonal Component
4 - 37© 2011 Pearson Education, Inc. publishing as Prentice Hall
Occurs within a single year Number of
Period Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52
Repeating up and down movementsAffected by business cycle, political, and economic factors
Cyclical ComponentCyclical Component
4 - 38© 2011 Pearson Education, Inc. publishing as Prentice Hall
Multiple years durationOften causal or associative relationships
0 5 10 15 20
Erratic, unsystematic, ‘residual’ fluctuationsDue to random variation or unforeseen events
Random ComponentRandom Component
4 - 39© 2011 Pearson Education, Inc. publishing as Prentice Hall
eventsShort duration and nonrepeating
M T W T F
Naive ApproachNaive ApproachAssumes demand in next period is the same as demand in most recent period
e.g., If January sales were 68, then
4 - 40© 2011 Pearson Education, Inc. publishing as Prentice Hall
e g , Ja ua y sa es e e 68, t eFebruary sales will be 68
Sometimes cost effective and efficientCan be good starting point
MA is a series of arithmetic means Used if little or no trendUsed often for smoothing
Moving Average MethodMoving Average Method
4 - 41© 2011 Pearson Education, Inc. publishing as Prentice Hall
Used often for smoothingProvides overall impression of data over time
Moving average =∑ demand in previous n periods
n
January 10February 12
Actual 3-MonthMonth Shed Sales Moving Average
Moving Average ExampleMoving Average Example
10101212
4 - 42© 2011 Pearson Education, Inc. publishing as Prentice Hall
yMarch 13April 16May 19June 23July 26
(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3
1313(1010 + 1212 + 1313)/3 = 11 2/3
10/16/2010
8
Graph of Moving AverageGraph of Moving Average
es
30 –28 –26 –24 –22
Actual Sales
Moving Average Forecast
4 - 43© 2011 Pearson Education, Inc. publishing as Prentice Hall
| | | | | | | | | | | |J F M A M J J A S O N D
Shed
Sal 22 –
20 –18 –16 –14 –12 –10 –
Used when some trend might be present
Older data usually less importantW i ht b d i d
Weighted Moving AverageWeighted Moving Average
4 - 44© 2011 Pearson Education, Inc. publishing as Prentice Hall
Weights based on experience and intuition
Weightedmoving average =
∑ (weight for period n)x (demand in period n)
∑ weights
Actual 3-Month WeightedMonth Shed Sales Moving Average
Weighted Moving AverageWeighted Moving AverageWeights Applied Period
33 Last month22 Two months ago11 Three months ago6 Sum of weights
4 - 45© 2011 Pearson Education, Inc. publishing as Prentice Hall
January 10February 12March 13April 16May 19June 23July 26
[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2
101012121313
[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6
Increasing n smooths the forecast but makes it less sensitive to changes
Potential Problems WithPotential Problems WithMoving AverageMoving Average
4 - 46© 2011 Pearson Education, Inc. publishing as Prentice Hall
changesDo not forecast trends wellRequire extensive historical data
Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average
30 –
25 –
and
Weighted moving average
4 - 47© 2011 Pearson Education, Inc. publishing as Prentice Hall
20 –
15 –
10 –
5 –
Sale
s de
ma
| | | | | | | | | | | |J F M A M J J A S O N D
Actual sales
Moving average
Figure 4.2
Form of weighted moving averageWeights decline exponentiallyMost recent data weighted most
Exponential SmoothingExponential Smoothing
4 - 48© 2011 Pearson Education, Inc. publishing as Prentice Hall
Requires smoothing constant (α)Ranges from 0 to 1Subjectively chosen
Involves little record keeping of past data
10/16/2010
9
Exponential SmoothingExponential Smoothing
New forecast = Last period’s forecast+ α (Last period’s actual demand
– Last period’s forecast)
4 - 49© 2011 Pearson Education, Inc. publishing as Prentice Hall
Ft = Ft – 1 + α(At – 1 - Ft – 1)
where Ft = new forecastFt – 1 = previous forecast
α = smoothing (or weighting) constant (0 ≤ α ≤ 1)
Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20
4 - 50© 2011 Pearson Education, Inc. publishing as Prentice Hall
Smoothing constant α .20
Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20
4 - 51© 2011 Pearson Education, Inc. publishing as Prentice Hall
Smoothing constant α .20
New forecast = 142 + .2(153 – 142)
Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20
4 - 52© 2011 Pearson Education, Inc. publishing as Prentice Hall
Smoothing constant α .20
New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars
Effect ofEffect ofSmoothing ConstantsSmoothing Constants
Weight Assigned toMost 2nd Most 3rd Most 4th Most 5th Most
R t R t R t R t R t
4 - 53© 2011 Pearson Education, Inc. publishing as Prentice Hall
Recent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant (α) α(1 - α) α(1 - α)2 α(1 - α)3 α(1 - α)4
α = .1 .1 .09 .081 .073 .066
α = .5 .5 .25 .125 .063 .031
Impact of Different Impact of Different αα
225 –
200 –
nd
Actual demand
α = .5
4 - 54© 2011 Pearson Education, Inc. publishing as Prentice Hall
175 –
150 – | | | | | | | | |1 2 3 4 5 6 7 8 9
Quarter
Dem
an
α = .1
10/16/2010
10
Impact of Different Impact of Different αα
225 –
200 –
nd
Actual demand
α = .5Chose high values of αwhen underlying average
4 - 55© 2011 Pearson Education, Inc. publishing as Prentice Hall
175 –
150 – | | | | | | | | |1 2 3 4 5 6 7 8 9
Quarter
Dem
an
α = .1
when underlying average is likely to changeChoose low values of αwhen underlying average is stable
Choosing Choosing αα
The objective is to obtain the most accurate forecast no matter the technique
4 - 56© 2011 Pearson Education, Inc. publishing as Prentice Hall
We generally do this by selecting the We generally do this by selecting the model that gives us the lowest forecast model that gives us the lowest forecast errorerror
Forecast error = Actual demand - Forecast value
= At - Ft
Common Measures of ErrorCommon Measures of Error
Mean Absolute Deviation (MAD)
MAD =∑ |Actual - Forecast|
4 - 57© 2011 Pearson Education, Inc. publishing as Prentice Hall
MAD n
Mean Squared Error (MSE)
MSE =∑ (Forecast Errors)2
n
Common Measures of ErrorCommon Measures of Error
Mean Absolute Percent Error (MAPE)
4 - 58© 2011 Pearson Education, Inc. publishing as Prentice Hall
MAPE =∑100|Actuali - Forecasti|/Actuali
n
n
i = 1
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50
4 - 59© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50
MAD =∑ |deviations|
n
= 82.45/8 = 10.31For α = .10
4 - 60© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62
= 98.62/8 = 12.33For α = .50
10/16/2010
11
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 1,526.54/8 = 190.82
For α = .10
MSE =∑ (forecast errors)2
n
4 - 61© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33
,
= 1,561.91/8 = 195.24For α = .50
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 44.75/8 = 5.59%
For α = .10
MAPE =∑100|deviationi|/actuali
n
n
i = 1
4 - 62© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33MSE 190.82 195.24
%
= 54.05/8 = 6.76%For α = .50
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50
4 - 63© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%
Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
When a trend is present, exponential smoothing must be modified
4 - 64© 2011 Pearson Education, Inc. publishing as Prentice Hall
Forecast including (FITt) = trend
Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend
Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
Ft = α(At - 1) + (1 - α)(Ft - 1 + Tt - 1)
4 - 65© 2011 Pearson Education, Inc. publishing as Prentice Hall
Tt = β(Ft - Ft - 1) + (1 - β)Tt - 1
Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17
4 - 66© 2011 Pearson Education, Inc. publishing as Prentice Hall
2 173 204 195 246 217 318 289 3610
Table 4.1
10/16/2010
12
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17
4 - 67© 2011 Pearson Education, Inc. publishing as Prentice Hall
2 173 204 195 246 217 318 289 3610
Table 4.1
F2 = αA1 + (1 - α)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)
= 2.4 + 10.4 = 12.8 units
Step 1: Forecast for Month 2
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.80
4 - 68© 2011 Pearson Education, Inc. publishing as Prentice Hall
2 17 12.803 204 195 246 217 318 289 3610
Table 4.1
T2 = β(F2 - F1) + (1 - β)T1
T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 units
Step 2: Trend for Month 2
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.80 1.92
4 - 69© 2011 Pearson Education, Inc. publishing as Prentice Hall
2 17 12.80 1.923 204 195 246 217 318 289 3610
Table 4.1
FIT2 = F2 + T2
FIT2 = 12.8 + 1.92= 14.72 units
Step 3: Calculate FIT for Month 2
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.80 1.92 14.72
4 - 70© 2011 Pearson Education, Inc. publishing as Prentice Hall
2 17 12.80 1.92 14.723 204 195 246 217 318 289 3610
Table 4.1
15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
man
d
35 –
30 –
25 –
Actual demand (At)
4 - 71© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 4.3
| | | | | | | | |1 2 3 4 5 6 7 8 9
Time (month)
Prod
uct d
em 20 –
15 –
10 –
5 –
0 –
Forecast including trend (FITt)with α = .2 and β = .4
Trend ProjectionsTrend ProjectionsFitting a trend line to historical data points to project into the medium to long-range
Linear trends can be found using the least squares technique
4 - 72© 2011 Pearson Education, Inc. publishing as Prentice Hall
y = a + bx^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis interceptb = slope of the regression linex = the independent variable
^
10/16/2010
13
Least Squares MethodLeast Squares Methoden
t Var
iabl
e
Deviation5
Deviation7
Deviation6
Actual observation (y-value)
4 - 73© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time period
Valu
es o
f Dep
end
Figure 4.4
Deviation1(error) Deviation2
Deviation4
Deviation3
Trend line, y = a + bx^
Least Squares MethodLeast Squares Method
ent V
aria
ble
Deviation5
Deviation7
Deviation6
Actual observation (y-value)
4 - 74© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time period
Valu
es o
f Dep
end
Figure 4.4
Deviation1(error) Deviation2
Deviation4
Deviation3
Trend line, y = a + bx^
Least squares method minimizes the sum of the
squared errors (deviations)
Least Squares MethodLeast Squares MethodEquations to calculate the regression variables
y = a + bx^
4 - 75© 2011 Pearson Education, Inc. publishing as Prentice Hall
b =Σxy - nxyΣx2 - nx2
a = y - bx
Least Squares ExampleLeast Squares ExampleTime Electrical Power
Year Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 525
4 - 76© 2011 Pearson Education, Inc. publishing as Prentice Hall
b = = = 10.54∑xy - nxy∑x2 - nx2
3,063 - (7)(4)(98.86)140 - (7)(42)
a = y - bx = 98.86 - 10.54(4) = 56.70
2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86
Time Electrical Power Year Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 525
Least Squares ExampleLeast Squares Example
The trend line is
y = 56 70 + 10 54x^
4 - 77© 2011 Pearson Education, Inc. publishing as Prentice Hall
b = = = 10.54∑xy - nxy∑x2 - nx2
3,063 - (7)(4)(98.86)140 - (7)(42)
a = y - bx = 98.86 - 10.54(4) = 56.70
2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86
y = 56.70 + 10.54x
Least Squares ExampleLeast Squares Example
160 –150 –140 –130 –120 –em
and
Trend line,y = 56.70 + 10.54x^
4 - 78© 2011 Pearson Education, Inc. publishing as Prentice Hall
| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011
110 –100 –
90 –80 –70 –60 –50 –
Year
Pow
er d
e
10/16/2010
14
Least Squares RequirementsLeast Squares Requirements
1. We always plot the data to insure a linear relationship
2 We do not predict time periods far
4 - 79© 2011 Pearson Education, Inc. publishing as Prentice Hall
2. We do not predict time periods far beyond the database
3. Deviations around the least squares line are assumed to be random
Seasonal Variations In DataSeasonal Variations In Data
The multiplicative seasonal model
4 - 80© 2011 Pearson Education, Inc. publishing as Prentice Hall
seasonal model can adjust trend data for seasonal variations in demand
Seasonal Variations In DataSeasonal Variations In Data
1. Find average historical demand for each season 2. Compute the average demand over all seasons 3 C l i d f h
Steps in the process:Steps in the process:
4 - 81© 2011 Pearson Education, Inc. publishing as Prentice Hall
3. Compute a seasonal index for each season 4. Estimate next year’s total demand5. Divide this estimate of total demand by the
number of seasons, then multiply it by the seasonal index for that season
Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
4 - 82© 2011 Pearson Education, Inc. publishing as Prentice Hall
pMay 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94
Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
0.957
Seasonal index = Average 2007-2009 monthly demand
Average monthly demand
4 - 83© 2011 Pearson Education, Inc. publishing as Prentice Hall
pMay 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94
Average monthly demand
= 90/94 = .957
Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
4 - 84© 2011 Pearson Education, Inc. publishing as Prentice Hall
pMay 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851
10/16/2010
15
Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
Expected annual demand = 1,200
Forecast for 2010
4 - 85© 2011 Pearson Education, Inc. publishing as Prentice Hall
pMay 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851
p
Jan x .957 = 961,200
12
Feb x .851 = 851,200
12
Seasonal Index ExampleSeasonal Index Example
140 –
130 –
120 –
110nd
2010 Forecast2009 Demand 2008 Demand2007 Demand
4 - 86© 2011 Pearson Education, Inc. publishing as Prentice Hall
110 –
100 –
90 –
80 –
70 –| | | | | | | | | | | |J F M A M J J A S O N D
Time
Dem
an
San Diego HospitalSan Diego Hospital
10,200 –
10,000 –
9,800 –Day
s
9659 9702 9745
Trend Data
4 - 87© 2011 Pearson Education, Inc. publishing as Prentice Hall
,
9,600 –
9,400 –
9,200 –
9,000 – | | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Inpa
tient
D
9530
9551
9573
9594
9616
9637
96599680
9702
9724 9766
Figure 4.6
San Diego HospitalSan Diego Hospital
1.06 –
1.04 –
1.02 –
ent D
ays 1.04
1.021.01
1.031.04
1 00
Seasonal Indices
4 - 88© 2011 Pearson Education, Inc. publishing as Prentice Hall
1.00 –
0.98 –
0.96 –
0.94 –
0.92 – | | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Inde
x fo
r Inp
ati 0.99 1.00
0.98
0.97
0.990.97
0.96
Figure 4.7
San Diego HospitalSan Diego Hospital
10,200 –
10,000 –
9,800 –Day
s
99119764
9691
9949
9724
10068
Combined Trend and Seasonal Forecast
4 - 89© 2011 Pearson Education, Inc. publishing as Prentice Hall
,
9,600 –
9,400 –
9,200 –
9,000 – | | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Inpa
tient
D
Figure 4.8
9265
9520
9691
94119542
9355
9572
Associative ForecastingAssociative Forecasting
Used when changes in one or more independent variables can be used to predict
the changes in the dependent variable
4 - 90© 2011 Pearson Education, Inc. publishing as Prentice Hall
Most common technique is linear regression analysis
We apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example
10/16/2010
16
Associative ForecastingAssociative ForecastingForecasting an outcome based on predictor variables using the least squares technique
y = a + bx^
4 - 91© 2011 Pearson Education, Inc. publishing as Prentice Hall
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis interceptb = slope of the regression linex = the independent variable though to
predict the value of the dependent variable
^
Associative Forecasting Associative Forecasting ExampleExample
Sales Area Payroll($ millions), y ($ billions), x
2.0 13.0 32.5 4 4 0
4 - 92© 2011 Pearson Education, Inc. publishing as Prentice Hall
2.0 22.0 13.5 7
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sale
s
Area payroll
Associative Forecasting Associative Forecasting ExampleExample
Sales, y Payroll, x x2 xy2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02 0 2 4 4 0
4 - 93© 2011 Pearson Education, Inc. publishing as Prentice Hall
2.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2.5
b = = = .25∑xy - nxy∑x2 - nx2
51.5 - (6)(3)(2.5)80 - (6)(32)
a = y - bx = 2.5 - (.25)(3) = 1.75
Associative Forecasting Associative Forecasting ExampleExample
y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)
If payroll next year is estimated to be 4.0 –
4 - 94© 2011 Pearson Education, Inc. publishing as Prentice Hall
$6 billion, then:
Sales = 1.75 + .25(6)Sales = $3,250,000
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Nod
el’s
sal
es
Area payroll
3.25
Standard Error of the Standard Error of the EstimateEstimate
A forecast is just a point estimate of a future valueThis point is actually the
4.0 –
4 - 95© 2011 Pearson Education, Inc. publishing as Prentice Hall
actually the mean of a probability distribution
Figure 4.9
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Nod
el’s
sal
es
Area payroll
3.25
Standard Error of the Standard Error of the EstimateEstimate
Sy,x =∑(y - yc)2
n - 2
4 - 96© 2011 Pearson Education, Inc. publishing as Prentice Hall
where y = y-value of each data pointyc = computed value of the dependent
variable, from the regression equation
n = number of data points
10/16/2010
17
Standard Error of the Standard Error of the EstimateEstimate
Computationally, this equation is considerably easier to use
∑y2 a∑y b∑xy
4 - 97© 2011 Pearson Education, Inc. publishing as Prentice Hall
We use the standard error to set up prediction intervals around the
point estimate
Sy,x =∑y2 - a∑y - b∑xy
n - 2
Standard Error of the Standard Error of the EstimateEstimate
4.0 –
Sy,x = =∑y2 - a∑y - b∑xyn - 2
39.5 - 1.75(15) - .25(51.5)6 - 2
Sy x = .306
4 - 98© 2011 Pearson Education, Inc. publishing as Prentice Hall
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Nod
el’s
sal
es
Area payroll
3.25y,x
The standard error of the estimate is $306,000 in sales
How strong is the linear relationship between the variables?Correlation does not necessarily imply causality!
CorrelationCorrelation
4 - 99© 2011 Pearson Education, Inc. publishing as Prentice Hall
imply causality!Coefficient of correlation, r, measures degree of association
Values range from -1 to +1
Correlation CoefficientCorrelation Coefficient
r = nΣxy - ΣxΣy
[nΣx2 - (Σx)2][nΣy2 - (Σy)2]
4 - 100© 2011 Pearson Education, Inc. publishing as Prentice Hall
Correlation CoefficientCorrelation Coefficient
r = nΣxy - ΣxΣy
[nΣx2 - (Σx)2][nΣy2 - (Σy)2]
y
x(a) Perfect positive correlation: r = +1
y
x(b) Positive correlation: 0 < r < 1
4 - 101© 2011 Pearson Education, Inc. publishing as Prentice Hall
0 r 1
y
x(c) No correlation: r = 0
y
x(d) Perfect negative correlation: r = -1
Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x
Values range from 0 to 1
CorrelationCorrelation
4 - 102© 2011 Pearson Education, Inc. publishing as Prentice Hall
Values range from 0 to 1Easy to interpret
For the Nodel Construction example:r = .901r2 = .81
10/16/2010
18
Multiple Regression Multiple Regression AnalysisAnalysis
If more than one independent variable is to be used in the model, linear regression can be
extended to multiple regression to d t l i d d t i bl
4 - 103© 2011 Pearson Education, Inc. publishing as Prentice Hall
accommodate several independent variables
y = a + b1x1 + b2x2 …^
Computationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the
computercomputer
Multiple Regression Multiple Regression AnalysisAnalysis
y = 1 80 + 30x 5 0x^
In the Nodel example, including interest rates in the model gives the new equation:
4 - 104© 2011 Pearson Education, Inc. publishing as Prentice Hall
y = 1.80 + .30x1 - 5.0x2
An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales
Sales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000
Measures how well the forecast is di ti t l l
Monitoring and Controlling Monitoring and Controlling ForecastsForecasts
Tracking SignalTracking Signal
4 - 105© 2011 Pearson Education, Inc. publishing as Prentice Hall
predicting actual valuesRatio of cumulative forecast errors to mean absolute deviation (MAD)
Good tracking signal has low valuesIf forecasts are continually high or low, the forecast has a bias error
Monitoring and Controlling Monitoring and Controlling ForecastsForecasts
Tracking signal
Cumulative errorMAD=
4 - 106© 2011 Pearson Education, Inc. publishing as Prentice Hall
Tracking signal =
∑(Actual demand in period i -
Forecast demand in period i)
(∑|Actual - Forecast|/n)
Tracking SignalTracking Signal
Tracking signal
+Upper control limit
Signal exceeding limit
4 - 107© 2011 Pearson Education, Inc. publishing as Prentice Hall
0 MADs
–Lower control limit
Time
Acceptable range
Tracking Signal ExampleTracking Signal ExampleCumulative
Absolute AbsoluteActual Forecast Cumm Forecast Forecast
Qtr Demand Demand Error Error Error Error MAD
1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.5
4 - 108© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
10/16/2010
19
CumulativeAbsolute Absolute
Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD
1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.5
Tracking Signal ExampleTracking Signal ExampleTrackingSignal
(Cumm Error/MAD)
-10/10 = -1-15/7.5 = -2
4 - 109© 2011 Pearson Education, Inc. publishing as Prentice Hall
3 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
0/10 = 0-10/10 = -1
+5/11 = +0.5+35/14.2 = +2.5
The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits
Adaptive ForecastingAdaptive Forecasting
It’s possible to use the computer to continually monitor forecast error and adjust the values of the α and βcoefficients used in exponential
4 - 110© 2011 Pearson Education, Inc. publishing as Prentice Hall
coefficients used in exponential smoothing to continually minimize forecast errorThis technique is called adaptive smoothing
Focus ForecastingFocus ForecastingDeveloped at American Hardware Supply, based on two principles:1. Sophisticated forecasting models are not
always better than simple ones2. There is no single technique that should
4 - 111© 2011 Pearson Education, Inc. publishing as Prentice Hall
g qbe used for all products or services
This approach uses historical data to test multiple forecasting models for individual itemsThe forecasting model with the lowest error is then used to forecast the next demand
Forecasting in the Service Forecasting in the Service SectorSector
Presents unusual challengesSpecial need for short term recordsN d diff tl f ti f
4 - 112© 2011 Pearson Education, Inc. publishing as Prentice Hall
Needs differ greatly as function of industry and productHolidays and other calendar eventsUnusual events
Fast Food Restaurant Fast Food Restaurant ForecastForecast
20% –
15% –
10%ntag
e of
sal
es
4 - 113© 2011 Pearson Education, Inc. publishing as Prentice Hall
10% –
5% –
11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11
(Lunchtime) (Dinnertime)Hour of day
Perc
en
Figure 4.12
FedEx Call Center ForecastFedEx Call Center Forecast
12% –
10% –
8% –
4 - 114© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 4.12
6% –
4% –
2% –
0% –
Hour of dayA.M. P.M.
2 4 6 8 10 12 2 4 6 8 10 12
10/16/2010
20
4 - 115© 2011 Pearson Education, Inc. publishing as Prentice Hall
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.