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Demand Forecasting : Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419. Forecasting Horizons. Long Term 5+ years into the future R&D, plant location, product planning Principally judgement-based Medium Term

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Demand Forecasting:Time Series ModelsProfessor Stephen R. LawrenceCollege of Business and AdministrationUniversity of ColoradoBoulder, CO 80309-0419

forecasting horizons
Forecasting Horizons
  • Long Term
    • 5+ years into the future
    • R&D, plant location, product planning
    • Principally judgement-based
  • Medium Term
    • 1 season to 2 years
    • Aggregate planning, capacity planning, sales forecasts
    • Mixture of quantitative methods and judgement
  • Short Term
    • 1 day to 1 year, less than 1 season
    • Demand forecasting, staffing levels, purchasing, inventory levels
    • Quantitative methods
short term forecasting needs and uses
Short Term Forecasting:Needs and Uses
  • Scheduling existing resources
    • How many employees do we need and when?
    • How much product should we make in anticipation of demand?
  • Acquiring additional resources
    • When are we going to run out of capacity?
    • How many more people will we need?
    • How large will our back-orders be?
  • Determining what resources are needed
    • What kind of machines will we require?
    • Which services are growing in demand? declining?
    • What kind of people should we be hiring?
types of forecasting models
Types of Forecasting Models
  • Types of Forecasts
    • Qualitative --- based on experience, judgement, knowledge;
    • Quantitative --- based on data, statistics;
  • Methods of Forecasting
    • Naive Methods --- eye-balling the numbers;
    • Formal Methods --- systematically reduce forecasting errors;
      • time series models (e.g. exponential smoothing);
      • causal models (e.g. regression).
    • Focus here on Time Series Models
  • Assumptions of Time Series Models
    • There is information about the past;
    • This information can be quantified in the form of data;
    • The pattern of the past will continue into the future.
forecasting examples
Forecasting Examples
  • Examples from student projects:
    • Demand for tellers in a bank;
    • Traffic on major communication switch;
    • Demand for liquor in bar;
    • Demand for frozen foods in local grocery warehouse.
  • Example from Industry: American Hospital Supply Corp.
    • 70,000 items;
    • 25 stocking locations;
    • Store 3 years of data (63 million data points);
    • Update forecasts monthly;
    • 21 million forecast updates per year.
simple moving average
Simple Moving Average
  • Forecast Ft is average of n previous observations or actuals Dt:
  • Note that the n past observations are equally weighted.
  • Issues with moving average forecasts:
    • All n past observations treated equally;
    • Observations older than n are not included at all;
    • Requires that n past observations be retained;
    • Problem when 1000's of items are being forecast.
simple moving average7
Simple Moving Average
  • Include n most recent observations
  • Weight equally
  • Ignore older observations

weight

1/n

...

n

2

1

3

today

exponential smoothing i
Exponential Smoothing I
  • Include all past observations
  • Weight recent observations much more heavily than very old observations:

weight

Decreasing weight given

to older observations

today

exponential smoothing i11
Exponential Smoothing I
  • Include all past observations
  • Weight recent observations much more heavily than very old observations:

weight

Decreasing weight given

to older observations

today

exponential smoothing i12
Exponential Smoothing I
  • Include all past observations
  • Weight recent observations much more heavily than very old observations:

weight

Decreasing weight given

to older observations

today

exponential smoothing i13
Exponential Smoothing I
  • Include all past observations
  • Weight recent observations much more heavily than very old observations:

weight

Decreasing weight given

to older observations

today

exponential smoothing concept
Exponential Smoothing: Concept
  • Include all past observations
  • Weight recent observations much more heavily than very old observations:

weight

Decreasing weight given

to older observations

today

exponential smoothing math17
Exponential Smoothing: Math
  • Thus, new forecast is weighted sum of old forecast and actual demand
  • Notes:
    • Only 2 values (Dt and Ft-1 ) are required, compared with n for moving average
    • Parameter a determined empirically (whatever works best)
    • Rule of thumb:  < 0.5
    • Typically,  = 0.2 or  = 0.3 work well
  • Forecast for k periods into future is:
complicating factors
Complicating Factors
  • Simple Exponential Smoothing works well with data that is “moving sideways” (stationary)
  • Must be adapted for data series which exhibit a definite trend
  • Must be further adapted for data series which exhibit seasonal patterns
holt s method double exponential smoothing

A trendy clothing boutique has had the following sales

over the past 6 months:

1 2 3 4 5 6

510 512 528 530 542 552

Holt’s Method:Double Exponential Smoothing
  • What happens when there is a definite trend?

Actual

Demand

Forecast

Month

holt s method double exponential smoothing22
Holt’s Method:Double Exponential Smoothing
  • Ideas behind smoothing with trend:
    • ``De-trend'' time-series by separating base from trend effects
    • Smooth base in usual manner using 
    • Smooth trend forecasts in usual manner using 
  • Smooth the baseforecast Bt
  • Smooth the trendforecast Tt
  • Forecast kperiods into future Ft+kwith base and trend
es with trend
ES with Trend

a = 0.2, b = 0.4

winter s method exponential smoothing w trend and seasonality
Winter’s Method: Exponential Smoothing w/ Trend and Seasonality
  • Ideas behind smoothing with trend and seasonality:
    • “De-trend’: and “de-seasonalize”time-series by separating base from trendand seasonalityeffects
    • Smooth base in usual manner using 
    • Smooth trend forecasts in usual manner using 
    • Smooth seasonality forecasts using g
  • Assume mseasons in a cycle
    • 12 months in a year
    • 4 quarters in a month
    • 3 months in a quarter
    • et cetera
winter s method exponential smoothing w trend and seasonality26
Winter’s Method: Exponential Smoothing w/ Trend and Seasonality
  • Smooth the base forecast Bt
  • Smooth the trend forecast Tt
  • Smooth the seasonality forecast St
winter s method exponential smoothing w trend and seasonality27
Winter’s Method: Exponential Smoothing w/ Trend and Seasonality
  • Forecast Ft with trend and seasonality
  • Smooth the trend forecast Tt
  • Smooth the seasonality forecast St
es with trend and seasonality
ES with Trend and Seasonality

a = 0.2, b = 0.4, g = 0.6

forecasting performance
Forecasting Performance

How good is the forecast?

  • Mean Forecast Error(MFE or Bias): Measures average deviation of forecast from actuals.
  • Mean Absolute Deviation(MAD): Measures average absolute deviation of forecast from actuals.
  • Mean Absolute Percentage Error(MAPE): Measures absolute error as a percentage of the forecast.
  • Standard Squared Error(MSE): Measures variance of forecast error
mean forecast error mfe or bias
Mean Forecast Error (MFE or Bias)
  • Want MFE to be as close to zero as possible -- minimum bias
  • A large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observations
  • Note that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is “on target”
  • Also called forecast BIAS
mean absolute deviation mad
Mean Absolute Deviation (MAD)
  • Measures absolute error
  • Positive and negative errors thus do not cancel out (as with MFE)
  • Want MAD to be as small as possible
  • No way to know if MAD error is large or small in relation to the actual data
mean absolute percentage error mape
Mean Absolute Percentage Error (MAPE)
  • Same as MAD, except ...
  • Measures deviation as a percentage of actual data
mean squared error mse
Mean Squared Error (MSE)
  • Measures squared forecast error -- error variance
  • Recognizes that large errors are disproportionately more “expensive” than small errors
  • But is not as easily interpreted as MAD, MAPE -- not as intuitive