Forecasting - Introduction to Operations Management - Lecture Slides, Slides of Production and Operations Management

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Forecasting

Forecasting – Quantitative

• Time series analysis : uses only past records of demand to forecast future demand - moving averages - exponential smoothing - ARIMA
• Causal methods : uses explanatory variables (timing of advertising campaigns, price changes) - multiple regression - econometric models

Simple models

• Notation
  • Dt = Actual demand in time period t
  • Ft = Forecast for period t
  • Et = Dt - Ft = Forecast error for period t

Simple models

• Last Point model
  • Yesterday’s demand will be today’s forecast
    • Ft+1 = Dt
  • Not a good model cause it does no learning, it is just a follower
• Average Model
  • Take the average of all known data to make prediction
  • F (^) t+1 = average(D 1 ,D 2 ,... , D (^) t)
  • Very old data is probably useless to us, so why include in the model?

Simple Exponential Smoothing (SES)

• Initialization: F 2 = D (^1)
• Learning: F (^) t+1 = LSD (^) t + (1-LS)Ft
• Predicting: F (^) t+k = Ft+
  • Future forecasts are equal to the last forecast
• LS = level smoother
  • Lower LS, higher the volatility
  • Higher LS, lower the volatility, however we will be doing less prediction and more following - Must have some sort of compromise - At LS=0, all values will be same as the initialized forecast, - At LS=1, the graph will follow the demand perfectly one day late » Really worthless

Performance Measures

• Remember that for performance measures, you must have a demand and a corresponding forecast.
• What is error if there is nothing to compare to?

Mean Absolute Deviation (MAD)

• (1/n) Σ |E (^) t |
• Similar to bias, but no negative values
• No way of telling which direction the error

is occurring, just that there is error

Mean Square Error (MSE) and Standard Error (SE)

• (1/(n-1)) Σ Et^2
• Places more emphasis on large error terms
• Heavily influenced by outlier terms and also not in units of the error

• SE = (MSE) 1/

• Same units as error
• Dampens the effect of the error terms

More Complex Forecasting

Models

Double Exponential Smoothing (DES)

• Takes level and trend into account
• Trend = change in the level
• Initialization:
  • L 2 = (D 1 +D 2 )/
  • T 2 = D 2 -D 1
• Learning:
  • L (^) t = LS*Dt+(1-LS)(L (^) t-1 +Tt-1 )
  • Tt = TS(L (^) t-L (^) t-1 )+(1-TS)T (^) t-

Triple Exponential Smoothing (TES)

• Takes level, trend and seasonality into

account

• Use if you see seasonal trends in the data

and if the data appears to be non-linear

TES - Initialization

• P is the number of seasons in a dataset
  • Ex) weeky = 7, monthly = 12, hourly = 24, quarterly = 4
• The initialization window is equal to P, we

allow P terms to pass before we begin to

forecast

TES - Learning

• The one-time forecast is

F t+1 = (L t +T t )/S t+1-P

• If Ft+1 is a Tuesday, S (^) t+1-P is the previous

Tuesday’s seasonality

TES - Learning

• Lt = LS(D (^) t /S (^) t-p )+(1-LS)(Lt-1 +T (^) t-1 )
• We want to remove the effect of

seasonality from level

• We want to know what December sales

would be like if it weren’t Christmas, we

want the deseasonalized level

• The old data is already deseasonalized

(L (^) t-1 +Tt-1 )(St+1-p /St+1-p )