Forecasting February 26, 2007

Laws of Forecasting Three Laws of Forecasting –Forecasts are always wrong! –Detailed forecasts are worse than aggregate forecasts! –The further into the future, the less reliable the forecast will be!

Forecasting Starting point of all Production Planning systems Qualitative Forecasting techniques Quantitative Forecasting techniques Choice of technique varies with the Product Life Cycle

Product Development Stage Should we enter into this business? What segments? What are the alternative growth opportunities for product X? How have established products similar to X fared? How should we allocate R&D efforts and funds? Where will be the market 5 years, 10 years from now?

Preliminaries What is the purpose of forecast? How is it to be used? –Accuracy and power required by the techniques Requirements for entering a business vs. next year’s budget –Impact of promotions and other marketing devices –Techniques vary with cost, scope and accuracy –Forecaster should fix the level of tolerance of accuracy Helps in managing the trade-offs Accurate forecast reduces inventory (cost of inventory vs. cost of forecasting)

Qualitative Forecasting Relies on expertise of people Data is scarce Usually used for technological forecasts (long term forecasts) Delphi Method, Market Research, Panel Consensus

Quantitative Forecasting Time Series models –Predict a future parameter as a function of past values of that parameter (e.g., historical demand) –Systematic variation is captured (seasonality, trend) –Cyclic patterns –Growth (decline) rates of the trends –Assume future is like past (hence useful for short term forecasts) –Managers need to look at the turning points in future that change the past trends

Time Series Forecasting Time period i = 1,2,…..t (most recent data) A(i): Actual observations f(t+λ):Forecasts for t + λ, λ = 1,2,……, F(t):smoothed estimate (current position of the process under consideration) T(t):smoothed trend Time Series Modelf(t+λ), λ =1,2,3,…,A(i), i =1,2,…t

Time Series Forecasting Moving-Average Model Exponential Smoothing Model Exponential Smoothing with a Linear Trend Model Winter’s Method (adds seasonal multipliers to the exponential smoothing with linear trend model)

Quantitative Forecasting Causal models –Most sophisticated –Predict a future parameter (e.g., demand for a product) as a function of other parameters (e.g., interest rates, marketing strategy).

Causal Forecasting Opening a fast food restaurant –Demand forecast? –Predictable parameters Population in the vicinity Competition –Use statistics (e.g., regression) to estimate the parameters Y = b 0 + b 1 x 1 + b 2 X 2

Components of an Observation Observed demand (O) = Systematic component (S) + Random component (R) Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) Systematic component: Expected value of demand Random component: The part of the forecast that deviates from the systematic component Forecast error: difference between forecast and actual demand

Time Series Forecasting Forecast demand for the next four quarters.

Time Series Forecasting

Basic Approach to Demand Forecasting Understand the objectives of forecasting Integrate demand planning and forecasting Identify major factors that influence the demand forecast Understand and identify customer segments Determine the appropriate forecasting technique Establish performance and error measures for the forecast

Patterns of Demand Quantity Time (a) Horizontal: Data cluster about a horizontal line.

Patterns of Demand Quantity Time (b) Trend: Data consistently increase or decrease.

Patterns of Demand Quantity |||||||||||| JFMAMJJASOND Months (c) Seasonal: Data consistently show peaks and valleys. Year 1 Year 2

Patterns of Demand Quantity |||||| Years (c) Cyclical: Data reveal gradual increases and decreases over extended periods.

Demand Forecast Applications DEMAND FORECAST APPLICATIONS Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Total sales Groups or families of products or services Staff planning Production planning Master production scheduling Purchasing Distribution Causal Judgment Forecast quantityIndividual products or services Decision areaInventory management Final assembly scheduling Workforce scheduling Master production scheduling ForecastingTime series techniqueCausal Judgment Total sales Facility location Capacity planning Process management Causal Judgment

Causal Methods Linear Regression Dependent variable Independent variable XY Estimate of Y from regressionequation Regressionequation: Y = a + bX Actualvalue of Y Value of X used to estimate Y Deviation, or error {

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = – (1.75)

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = , or 183,015 units

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) If current stock = 62,500 units, Production = 183,015 – 62,500 = 120,015 units

Time-Series Methods Simple Moving Averages Week — — — — — |||||| Patient arrivals Actual patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals — — — — — Week |||||| Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals arrivals — — — — — Week |||||| Patient WeekArrivals Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals arrivals — — — — — Week |||||| Patient WeekArrivals Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals Week — — — — — |||||| Patient WeekArrivals F4 =F4 =F4 =F4 = Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals — — — — — Week |||||| Patient WeekArrivals F 4 = Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals — — — — — Week |||||| Patient WeekArrivals F 4 = Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals Week — — — — — |||||| Patient WeekArrivals F5 =F5 =F5 =F5 = Patient arrivals

Time-Series Methods Simple Moving Averages Actual patient arrivals — — — — — Week |||||| Patient WeekArrivals F 5 = Patient arrivals

Time-Series Methods Simple Moving Averages Week — — — — — |||||| Patient arrivals Actual patient arrivals 3-week MA forecast 6-week MA forecast

Time-Series Methods Exponential Smoothing — — — — —Week |||||| Exponential Smoothing  = 0.10 F t +1 = F t +  (D t – F t ) Patient arrivals

Time-Series Methods Exponential Smoothing — — — — —Week |||||| Exponential Smoothing  = 0.10 F 4 = 0.10(411) (390) F 3 = ( )/2 F 3 = ( )/2 D 3 = 411 F t +1 = F t +  (D t – F t ) Patient arrivals

Time-Series Methods Exponential Smoothing — — — — —Week |||||| F 4 = Exponential Smoothing  = 0.10 F 3 = ( )/2 F 3 = ( )/2 D 3 = 411 F t +1 = F t +  (D t – F t ) Patient arrivals

Time-Series Methods Exponential Smoothing Week — — — — — |||||| F 4 = F 4 = D 4 = 415 Exponential Smoothing  = 0.10 F 4 = F 5 = F t +1 = F t +  (D t – F t ) Patient arrivals

Time-Series Methods Exponential Smoothing Week — — — — — |||||| Patient arrivals

Time-Series Methods Exponential Smoothing — — — — — Patient arrivals Week |||||| Exponential smoothing  = 0.10

Time-Series Methods Exponential Smoothing — — — — — Patient arrivals Week |||||| week MA forecast 6-week MA forecast Exponential smoothing  = 0.10

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Actual blood test requests

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week A 1 = 0.2(27) (28 + 3) T 1 = 0.2( ) (3) Medanalysis, Inc. Demand for blood analysis A 0 = 28 patients T 0 = 3 patients  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week A 1 = 30.2 T 1 = 2.8 Medanalysis, Inc. Demand for blood analysis A 0 = 28 patients T 0 = 3 patients  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 Forecast 2 = = 33

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A 2 = 30.2 D 2 = 44 T 1 = 2.8  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 A 2 = 0.2(44) ( ) T 2 = 0.2( ) (2.8)

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A 2 = 30.2 D 2 = 44 T 1 = 2.8  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 A 2 = 35.2 T 2 = 3.2 Forecast = = 38.4

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Actual blood test requests Trend-adjusted forecast

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Trend-adjusted forecast Actual blood test requests Number of time periods15.00 Demand smoothing coefficient (  )0.20 Initial demand value28.00 Trend-smoothing coefficient (  )0.20 Estimate of trend3.00

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — — — — — — Patient arrivals Week Trend-adjusted forecast Actual blood test requests – – – – – – – – – – TABLE 13.2FORECASTS FOR MEDANALYSIS SmoothedTrendForecast WeekArrivalsAverageAverageForecastError

Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests SmoothedTrendForecast WeekArrivalsAverageAverageForecastError – – – – – – – – – – SUMMARY Average demand49.80 Mean square error76.13 Mean absolute deviation7.35 Forecast for week Forecast for week Forecast for week

QuarterYear 1Year 2Year 3Year Total Total Time-Series Methods Seasonal Influences

Seasonal Patterns Period Demand |||||||||||||||| (a) Multiplicative pattern

Seasonal Patterns Period |||||||||||||||| Demand (b) Additive pattern

Choosing a Method Forecast Error Measures of Forecast Error E t = D t – F t  |E t | n Et2Et2nnEt2Et2nnn CFE =  E t  = MSE = MAD = MAPE =  [ |E t | (100) ] / D t n  (E t – E ) 2 n – 1

Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) % – – – Total– % Choosing a Method Forecast Error

Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % Measures of Error

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % CFE = – 15 Measures of Error

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % CFE = – 15 Measures of Error E = = – – 15 8

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % MSE = = CFE = – 15 Measures of Error E = = – – 15 8

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % MSE = = CFE = – 15 Measures of Error E = = – – 15 8  = 27.4

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = E = = – – 15 8  = 27.4

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = MAPE = = 10.2% 81.3% 8 E = = – – 15 8  = 27.4

Choosing a Method Forecast Error Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = MAPE = = 10.2% 81.3% 8 E = = – – 15 8  = 27.4

Summary of Learning Objectives What are the roles of forecasting for an enterprise and a supply chain? What are the components of a demand forecast? How is demand forecast given historical data using time series methodologies? How is a demand forecast analyzed to estimate forecast error?