Forecasting

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Forecasting

  1. 1. ForecastingDISC 333: SUPPLY CHAIN MANAGEMENT
  2. 2. Forecasting in Operations FunctionForecasting allows predicting future values of aseries based on past observations;In supply chain the primarily interest is inforecasting product demand;Trends, cycles and seasonal variation may be presentin past observations that help us to predict futuredemand more closely.
  3. 3. Forecasting Horizon in Supply Chain Planning Long (Months / Years) Capacity needs, Long-term sales patterns, Growth trends Intermediate (Weeks / Months) Product family sales, Labor needs, Resource requirements Short (Days / Weeks) Short-term sales, Shift schedule, Resource requirements
  4. 4. Characteristics of ForecastsThey are usually wrong.A good forecast is more than a single number.Aggregate forecasts are more accurate.The longer the forecast horizon, the less accurate theforecast will be.Forecasts should not be used to the exclusion ofknown information.
  5. 5. Benefits of ForecastingLower inventoriesReduced Stock-outsSmoother production and supply-chain plansReduced production costsImproved customer serviceEtc.
  6. 6. Forecasting MethodsQualitative (or Subjective) Methods: Forecasts based on subjective judgment or opinion Sales Force Composites Customer Surveys Jury of Executive Opinion Delphi MethodQuantitative (or Objective) Methods: Forecasts are derived based on an analysis of data. Time Series Forecasting Models Causal or Associative Models
  7. 7. Time Series Forecasting ModelsInformation can be inferred from the pattern of pastobservations and can be used to forecast future values ofthe series.Observations about past values are drawn at discrete pointsin time, usually equally spaced.Time series include various patterns of data: Trend Seasonality Cycles Randomness
  8. 8. Simple Moving Average Forecasting ModelA moving average of order N is simply the arithmeticaverage of the most recent N observations.For one step ahead forecasts for most recent Nobservations: t −1 Ft = (1 / N ) ∑ Ai = (1 / N )( At −1 + At − 2 + ... + At − N ) i =t − N or t  t −1  Ft +1 = (1 / N ) ∑ Ai = (1 / N )  At + ∑ Ai − At − N  i = t − N +1  i =t − N  Ft +1 = Ft + (1 / N )[ At − At − N ]
  9. 9. Example: Simple Moving AverageConsider a demand Period Demand MA(3) MA(6)process 2, 4, 6, 8,10, 12, 14, 16, 18, 20, 1 222, 24 in which 2 4there is a definite 3 6 4 8 4trend. 5 10 6 6 12 8Consider the MA(3) 7 14 10 7 8 16 12 9and MA(6) 9 18 14 11 10 20 16 13 11 22 18 15 12 24 20 17
  10. 10. Simple Moving Average Forecasting Model (Excel)Period Demand Forecast MA(3) Forecast MA(6) Moving Average MA(3) 1 2 #N/A #N/A 30 25 2 3 #N/A #N/A 20 Value 15 3 10 5 #N/A 10 Actual 5 Forecast 4 8 7 #N/A 0 1 2 3 4 5 6 7 8 9 10 11 12 5 12 10 #N/A Data Point 6 18 12.66666667 8.833333333 7 24 18 12.5 Moving Average MA(6) 8 26 22.66666667 16.33333333 30 9 20 23.33333333 18 Value 20 10 16 20.66666667 19.33333333 10 Actual 0 Forecast 11 22 19.33333333 21 1 2 3 4 5 6 7 8 9 10 11 12 12 24 20.66666667 22 Data Point Con: Less responsive to changes in demand.
  11. 11. Weighted Moving Average Forecasting Model t Ft +1 = ∑w A i =t − N +1 i iAllows more emphasis to be placed on recent or pastdata.Weights can be determined by experience of theforecaster.Still not responsive enough to track changes indemand.
  12. 12. Weighted Moving Average (Example)Perio d Demand Weights Forecast MA(3) 30 1 2 0.2 25 2 3 0.2 20 3 10 0.6 15 Actual 4 8 7 Forecast 10 5 12 7.4 6 18 10.8 5 7 24 14.8 0 1 2 3 4 5 6 7 8 9 10 11 12 8 26 20.4 9 20 2410 16 2211 22 18.812 24 20.4
  13. 13. Exponential Smoothing Forecasting ModelIs a sophisticated weighted moving average technique.Forecast for next period’s demand is the current period’s forecastadjusted by a fraction of the difference between the currentperiod’s actual demand and its forecast.Requires less data to be implemented, thus is more widelypracticed technique.Suitable for data that show little trend or seasonal patterns.Ft = α At −1 + (1 − α ) Ft −1where 0 < α ≤ 1 is the smoothing constant, determines relative weight placed on demandFt = Ft −1 − α ( Ft −1 − At −1 )Ft = Ft −1 − α et −1
  14. 14. Exponential Smoothing Forecasting ModelIf we forecast high in period t-1, et-1 is positive and theadjustment is to decrease the forecast. And vice versa.If α is large, more weight is given to the currentobservation and less weight on past observations,which results into a forecast that will react quickly tochanges in the demand pattern but may have muchgreater variation from period to period.
  15. 15. Exponential Smoothing (Example)Period Demand Forecast 1 2 #N/A Exponential Smoothing 2 3 2 30 3 10 2.7 25 4 8 7.81 20 5 12 7.943 Value 15 6 18 10.7829 Actual 10 7 24 15.83487 Forecast 5 8 26 21.550461 0 1 2 3 4 5 6 7 8 9 10 11 12 9 20 24.6651383 Data Point 10 16 21.3995415 11 22 17.6198624 α = 0.3 (assumed) 12 24 20.6859587
  16. 16. Trend Based Exponential Smoothing Forecasting Model Ft = α At −1 + (1 − α )( Ft −1 + Tt −1 ) Tt = β ( Ft − Ft −1 ) + (1 − β )Tt −1 and the trend - adjusted forecast is TAFt + m = Ft + mTtHigher the β higher the emphasis on recent trendchanges.α & β are determined by trial and error approach.
  17. 17. Linear Trend Forecasting ModelSimple linear regression can be used to fit a line to the timeseries historical data.Linear trend method minimizes the sum of squared deviationsto determine the characteristics of the linear equation: ( x1 , y1 ), ( x2 , y2 ),..., ( xn , yn ) be n paired data points for X & Y X = Independent Variable Y = Dependent Variable Suppose a linear relationship exists between X and Y, then ∧ Y = b +b X 0 1
  18. 18. Linear Trend Forecasting Model ∧where, Y = predicted value of Yx = time variableb 0 = intercept of the line, andb1 = slope of the line n∑ ( xy ) − ∑ x ∑ yb1 = n∑ x 2 − (∑ x ) 2b0 = ∑ y −b ∑ x1 n
  19. 19. Linear Trend Forecasting Model (Example)What is the trend line and forecast for Period-13 forthe following data? Period Demand Period Demand Period Demand 1 1600 5 2500 9 3900 2 2200 6 3500 10 4700 3 2000 7 3300 11 4300 4 1600 8 3200 12 4400
  20. 20. Linear Trend Forecasting Model (Example)Period Demand b1 = [12(282,800) – 78(37,200)] / (x) (y) x2 xy [12(650) -78*78] 1 1600 1 1600 = 286.71 2 2200 4 4400 3 2000 9 6000 4 1600 16 6400 • b0 = [37,000 – 286.71(78)]/12 5 2500 25 12500 = 1,236.4 6 3500 36 21000 7 3300 49 23100 8 3200 64 25600 Y = 1,236.4 + 286.71 x 9 3900 81 35100 10 4700 100 47000 11 4300 121 47300 F13 = 1236.4 + 286.71 (13) = 4963.5 12 4400 144 52800 ∑y = ∑x2 = ∑xy = 37200 650 282,800
  21. 21. Linear Trend Forecasting Model (Example)Period (x) Demand (y) Forecast 1 1600 1523.0769 5000 2 2200 1809.7902 4500 3 2000 2096.5035 4000 4 1600 2383.2168 3500 5 2500 2669.9301 3000 6 3500 2956.6434 2500 Actual 7 3300 3243.3566 2000 Forecast 8 3200 3530.0699 1500 9 3900 3816.7832 1000 10 4700 4103.4965 500 0 11 4300 4390.2098 1 2 3 4 5 6 7 8 9 10 11 12 12 4400 4676.9231Slope 286.7132867Intercept 1236.363636
  22. 22. Associative ModelsOne or several external variables are identified that arerelated to demand, which are easier to determine thandemand.Once the relationship between the external variable anddemand is determined, it can be used as a forecasting tool.Y = Phenomenon to be forecastedX1 , X2 ,…, Xn = Variables affecting the phenomenon, then Y = f(X1 , X2 ,…, X n)
  23. 23. Forecast AccuracyAt = observed demand during periods t, assume {At , t ≥ 1}Ft = forecast made for period t during period t-1, one step ahead forecastet = forecast error, thenet = Ft − AtIf e1 , e2 ,..., en = forecast errors observed over n periods nMAD = mean absolute deviation = (1 / n)∑ ei i =1 nMSE = mean squared error = (1 / n)∑ ei2 i =1 nMAPE = mean absolute percentage error = (1 / n)∑ ei / Di i =1
  24. 24. Forecast Accuracy n Running sum of forecast errors (RSFE) = ∑e t =1 t RSFE TrackingSignal = MADA number of parameters have been defined. Eachone of which provide some sort of advantage over theother.Many organizations set targets for Tracking Signal asa means to improve their forecasts.
  25. 25. Collaborative Planning, Forecasting, and Replenishment (CPFR)The objective of CPFR is to optimize the supply chainby improving demand forecasting, delivering theright product at the right time to the right location,reducing inventories across the supply chains,avoiding stock-outs, and improving customerservice.The real value of CPFR comes from an exchange offorecasting information rather than from moresophisticated forecasting algorithms to improveforecasting accuracy.
  26. 26. CPFR Process

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