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Forecasting
Anticipating service requirements over the short term
Operational purposesPlanning and scheduling resourcesExamples:
Manufacturing and distributing printers at HP Staffing levels (NS) etc.
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Objectives
What is forecastingWhat are the issuesWhat are the tools
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Forecasting
Developing predictions or estimates of future values Demand volume Price levels Lead times Resource availability ...
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Taco Bell
Labor is 30% of revenueMake to order environmentSignificant “seasonality”
52% of days sales during lunch 25% of days sales during busiest hour
Balance staff with demand
Feed the dog
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Value Meals
Drove demand Forecasting system in each store
forecasts arrivals within 15 minute intervals Simulation system
“predicts” congestion and lost salesOptimization system
Finds the minimum cost allocation of workers
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Forecasting System
Customer arrivals by 15-minute interval of day (e.g., 11:15-11:30 am Friday)
Fed by in-store computer system6-week moving averageEstimated savings: Over $40 Million
in 3 years.
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Independent vs Dependent
Independent Exogenously controlled Subject to random or unpredictable changes What we forecast
Dependent or Derived Calculated or derived from other sources Bill of Materials Related activity like packaging
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Phenomena To Capture
RandomnessTrend
Linear Exponential
Seasonality
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RandomnessMonthly Returns from The Dow
-15%
-10%
-5%
0%
5%
10%
15%
Feb
-47
Feb
-49
Feb
-51
Feb
-53
Feb
-55
Feb
-57
Feb
-59
Feb
-61
Feb
-63
Feb
-65
Feb
-67
Feb
-69
Feb
-71
Feb
-73
Feb
-75
Feb
-77
Feb
-79
Feb
-81
Feb
-83
Feb
-85
Feb
-87
Feb
-89
Feb
-91
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Linear TrendDow Jones Monthly Average
1500
1700
1900
2100
2300
2500
2700
2900
3100
3300
3500
Jan-88 Jul-88 Feb-89 Aug-89 Mar-90 Oct-90 Apr-91 Nov-91
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Exponential TrendIntel Quarterly Sales in Millions of Dollars
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
12/19/85 5/3/87 9/14/88 1/27/90 6/11/91 10/23/92 3/7/94 7/20/95
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SeasonalityCoca Cola Quarterly Sales in Millions of Dollars
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
$5,500
Q1-
86
Q3-
86
Q1-
87
Q3-
87
Q1-
88
Q3-
88
Q1-
89
Q3-
89
Q1-
90
Q3-
90
Q1-
91
Q3-
91
Q1-
92
Q3-
92
Q1-
93
Q3-
93
Q1-
94
Q3-
94
Q1-
95
Q3-
95
Q1-
96
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SeasonalityToys "R" Us Quarterly Revenues in Millions of Dollars
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
Q1-92 Q2-92 Q3-92 Q4-92 Q1-93 Q2-93 Q3-93 Q4-93 Q1-94 Q2-94 Q3-94 Q4-94 Q1-95 Q2-95 Q3-95 Q4-95
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Forecasting MethodsQualitative or Judgemental
Ask people who ought to knowHistorical Projection or Extrapolation
Moving Averages Exponential Smoothing Regression based methods Neural Networks
Econometric or Causal Regression Simulation
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Moving Averages
Simple, ubiquitousReduce random noiseOne Extreme
Predict next period = This periodAnother Extreme
Predict next period = Long run averageIntermediate View: K period moving avg.
Predict next period = Average of last K periods
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The Dow
1500
1700
1900
2100
2300
2500
2700
2900
3100
3300
3500
Jan-
88
Mar
-88
May
-88
Jul-8
8
Sep-8
8
Nov-8
8
Jan-
89
Mar
-89
May
-89
Jul-8
9
Sep-8
9
Nov-8
9
Jan-
90
Mar
-90
May
-90
Jul-9
0
Sep-9
0
Nov-9
0
Jan-
91
Mar
-91
May
-91
Jul-9
1
Sep-9
1
Nov-9
1
Jan-
92
Mar
-92
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Questions
1500
1700
1900
2100
2300
2500
2700
2900
3100
3300
3500
Jan-
88
Mar
-88
May
-88
Jul-8
8
Sep-8
8
Nov-8
8
Jan-
89
Mar
-89
May
-89
Jul-8
9
Sep-8
9
Nov-8
9
Jan-
90
Mar
-90
May
-90
Jul-9
0
Sep-9
0
Nov-9
0
Jan-
91
Mar
-91
May
-91
Jul-9
1
Sep-9
1
Nov-9
1
Jan-
92
Mar
-92
What’s the forecast for 6 months out?
Will a shorter span always be better?
Is moving average a good method here? Which will handle this
better?
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Which is better?Monthly Dow Returns
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
May-50 Jun-50 Jul-50 Aug-50 Sep-50 Oct-50 Nov-50 Dec-50 Jan-51 Feb-51 Mar-51 Apr-51 May-51
Average Error 3-month 1490% 6-month 619%
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Exponential Smoothing
Moving Averages Equal weight to older observations
Exponential Smoothing More weight to more recent observations
Forecast for next period is a weighted average of Observation for this period Forecast for this period
Alpha*Observation + (1-Alpha)*Past Forecast
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Initial Values
First ObservationAverage of previous observationsetc.
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Which is which?Monthly Dow Returns
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
Sep-89 Oct-89 Nov-89 Dec-89 Jan-90 Feb-90 Mar-90 Apr-90 May-90 Jun-90 Jul-90 Aug-90 Sep-90
Alpha = .01 or Alpha = .2
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Modeling Trend
Holt’s Method Forecast is weighted combination of
Current ObservationCurrent Forecast for Next Period
Forecast Trend as weighted combination of Current Trend in Forecasts
• (our estimate of trend)
Current Forecast for Trend • (differences in successive forecasts)
Why this way?
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With and Without TrendDow Monthly Averages
1500
1700
1900
2100
2300
2500
2700
2900
3100
3300
3500
Jan-
88
Mar
-88
May
-88
Jul-8
8
Sep-8
8
Nov-8
8
Jan-
89
Mar
-89
May
-89
Jul-8
9
Sep-8
9
Nov-8
9
Jan-
90
Mar
-90
May
-90
Jul-9
0
Sep-9
0
Nov-9
0
Jan-
91
Mar
-91
May
-91
Jul-9
1
Sep-9
1
Nov-9
1
Jan-
92
Mar
-92
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Intel’s TrendIntel Quarterly Sales in Millions of Dollars
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
12/19/85 5/3/87 9/14/88 1/27/90 6/11/91 10/23/92 3/7/94 7/20/95
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Exponential Growth
Forecasted Sales = et
Natural Log of Forecasted Sales Ln + t That’s linear growth
Take Natural Log of observationsForecast Natural Log of Sales Convert back to Forecast of Sales
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Seasonality
Deseasonalize the dataForecastSeasonalize the forecastSeasonal Factors
Ratio of Actual to “Average” Updated with Exp. Smooth. Weighted combination of
Actual/Deseasonalized ForecastCurrent Forecast of seasonal factor
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Seasonality
Deseasonalized Forecast Alpha*(Actual/Seasonal Factor)+ (1-Alpha)*(Past Deseasonalized Forecast)
Seasonalized Forecast Deseasonalized Forecast * Seasonal Factor
Updating the seasonal factors Gamma * (Actual/Deseasonalized Forecast) + (1- Gamma) * Previous estimate of seasonal
factor
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Initialization and Factors
LevelTrendSeasonality
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Coca Cola Quarterly Sales in Millions of Dollars
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
Q3-87
Q4-87
Q1-88
Q2-88
Q3-88
Q4-88
Q1-89
Q2-89
Q3-89
Q4-89
Q1-90
Q2-90
Q3-90
Q4-90
Q1-91
Q2-91
Q3-91
Q4-91
Q1-92
Q2-92
Q3-92
Q4-92
Q1-93
Q2-93
Q3-93
Q4-93
Q1-94
Q2-94
Q3-94
Q4-94
Q1-95
Q2-95
Q3-95
Q4-95
Q1-96
Q2-96
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Trend in Model of Coca Cola Quarterly Sales
-$600
-$500
-$400
-$300
-$200
-$100
$0
$100
$200
$300
$400
Q3-877
Q1-889
Q3-8811
Q1-8913
Q3-8915
Q1-9017
Q3-9019
Q1-9121
Q3-9123
Q1-9225
Q3-9227
Q1-9329
Q3-9331
Q1-9433
Q3-9435
Q1-9537
Q3-9539
Q1-9641
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Seasonal Factors in Model of Coca Cola Quarterly Sales
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Q3-877
Q1-889
Q3-8811
Q1-8913
Q3-8915
Q1-9017
Q3-9019
Q1-9121
Q3-9123
Q1-9225
Q3-9227
Q1-9329
Q3-9331
Q1-9433
Q3-9435
Q1-9537
Q3-9539
Q1-9641
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Seasonalized and Deseasonalized Forecasts of Coca Cola Quarterly Sales in Millions of Dollars
0.00
1,000.00
2,000.00
3,000.00
4,000.00
5,000.00
6,000.00
Q3-877
Q1-889
Q3-8811
Q1-8913
Q3-8915
Q1-9017
Q3-9019
Q1-9121
Q3-9123
Q1-9225
Q3-9227
Q1-9329
Q3-9331
Q1-9433
Q3-9435
Q1-9537
Q3-9539
Q1-9641
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Regression-Based Models
Time Series Find best fit of proposed model to past data Project that fit forward
Econometric Find exogenous factors driving value
WeatherEconomic factorsRainfall
Develop formula for (future) values based on these factors
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Example
Locating a new retail storeBuild a model of sales volume (profitability)
based on existing stores Population Wealth Competitors Access …
Predict sales for new store with this model
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Forecast Error
Building a Forecast Fit to historical data Project future data
Forecast Error How well does model fit historical data Do we need to tune or refine the model Can we offer confidence intervals about
our predictions
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Measuring Forecast Error
MAD or MAE average of the absolute errors
RMSE (root mean square error) Square root of average squared error
Sample std deviation Differs by 1 degree of freedom (N-1)
MAPE (mean absolute percentage error) Average absolute ratio of error to actual
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Forecasting is a necessary evil, try to reduce the need for it.
Complexity costs money, does it provide better forecasts?
Aggregation provides accuracy, but precludes local information
Forecast the right thing
Issues
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What about HP?
Why are forecasts bad in Europe?