Modul ke: Fakultas Program Studi Teori Peramalan Forecasting Strategic Role of Forecasting in Supply Chain Management, Components of Forecasting Demand, Time Series Methods Regression Methods, Forecast Accuracy Zulfa Fitri Ikatrinasari, Dr. 03 Ekonomi dan Bisnis Manajemen

Predicting the future Predicting the future Qualitative forecast methods Qualitative forecast methods – subjective Quantitative forecast methods Quantitative forecast methods – based on mathematical formulas Copyright 2009 John Wiley & Sons, Inc. Forecasting

Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Continuous replenishment Continuous replenishment – supplier and customer share continuously updated data – typically managed by the supplier – reduces inventory for the company – speeds customer delivery Variations of continuous replenishment Variations of continuous replenishment – quick response – JIT (just-in-time) – VMI (vendor-managed inventory) – stockless inventory Copyright 2009 John Wiley & Sons, Inc. Forecasting and Supply Chain Management

The Effect of Inaccurate Forecasting on the Supply Chain

Quality Management Accurately forecasting customer demand is a key to providing good quality service Strategic Planning Successful strategic planning requires accurate forecasts of future products and markets Copyright 2009 John Wiley & Sons, Inc. Forecasting

Depend on Depend on – time frame – demand behavior – causes of behavior Copyright 2009 John Wiley & Sons, Inc. Types of Forecasting Methods

Indicates how far into the future is forecast Indicates how far into the future is forecast – Short- to mid-range forecast typically encompasses the immediate future daily up to two years – Long-range forecast usually encompasses a period of time longer than two years Copyright 2009 John Wiley & Sons, Inc. Time Frame

Constant Constant - fluctuated around an average stable Trend Trend – a gradual, long-term up or down movement of demand Random variations Random variations – movements in demand that do not follow a pattern Cycle Cycle – an up-and-down repetitive movement in demand Seasonal pattern Seasonal pattern – an up-and-down repetitive movement in demand occurring periodically Copyright 2009 John Wiley & Sons, Inc. Demand Behavior

Forms of Forecast Movement Copyright 2009 John Wiley & Sons, Inc.12-9 Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement

Time series Time series – statistical techniques that use historical demand data to predict future demand Regression methods Regression methods – attempt to develop a mathematical relationship between demand and factors that cause its behavior Qualitative Qualitative – use management judgment, expertise, and opinion to predict future demand Copyright 2009 John Wiley & Sons, Inc Forecasting Methods

Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts Delphi method – involves soliciting forecasts about technological advances from experts Copyright 2009 John Wiley & Sons, Inc. Qualitative Methods

Forecasting Process Copyright 2009 John Wiley & Sons, Inc. 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data No Yes

Assume that what has occurred in the past will continue to occur in the future Relate the forecast to only one factor - time Include – moving average – exponential smoothing – linear trend line Copyright 2009 John Wiley & Sons, Inc. Time Series

Naive forecast Naive forecast – demand in current period is used as next period’s forecast Simple moving average Simple moving average – uses average demand for a fixed sequence of periods – stable demand with no pronounced behavioral patterns Weighted moving average Weighted moving average – weights are assigned to most recent data Copyright 2009 John Wiley & Sons, Inc. Moving Average

Moving Average: Naïve Approach Copyright 2009 John Wiley & Sons, Inc.

Simple Moving Average Copyright 2009 John Wiley & Sons, Inc.

3-month Simple Moving Average Copyright 2009 John Wiley & Sons, Inc. Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH ––– MOVINGAVERAGE

5-month Simple Moving Average Copyright 2009 John Wiley & Sons, Inc. Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 5 = = 91 orders for Nov ––––– MOVINGAVERAGE

Smoothing Effects Copyright 2009 John Wiley & Sons, Inc – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

Weighted Moving Average Copyright 2009 John Wiley & Sons, Inc. Adjusts moving average method to more closely reflect data fluctuations Adjusts moving average method to more closely reflect data fluctuations F t+1 = W.X t + W t-1.X t W t-N+1.X t-N+1

Weighted Moving Average Example Copyright 2009 John Wiley & Sons, Inc. MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 = (0.50)(90) + (0.33)(110) + (0.17)(130) = orders November Forecast

Exponential Smoothing Copyright 2009 John Wiley & Sons, Inc. Averaging method Averaging method Weights most recent data more strongly Weights most recent data more strongly Reacts more to recent changes Reacts more to recent changes Widely used, accurate method Widely used, accurate method

Exponential Smoothing (cont.) Copyright 2009 John Wiley & Sons, Inc. F t +1 =  X t + (1 -  )F t where: F t +1 =forecast for next period X t =actual demand for present period F t =previously determined forecast for present period  =weighting factor, smoothing constant

Effect of Smoothing Constant Copyright 2009 John Wiley & Sons, Inc. 0.0  1.0 If  = 0.20, then F t +1 = 0.20  X t F t If  = 0, then F t +1 = 0  X t + 1 F t = F t Forecast does not reflect recent data If  = 1, then F t +1 = 1  X t + 0 F t =  X t Forecast based only on most recent data

Exponential Smoothing ( α =0.30) Copyright 2009 John Wiley & Sons, Inc. F 2 =  X 1 + (1 -  )F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 =  X 2 + (1 -  )F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 =  X 12 + (1 -  )F 12 = (0.30)(54) + (0.70)(50.84) = PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

Copyright 2009 John Wiley & Sons, Inc. Exponential Smoothing (cont.) FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–

Exponential Smoothing (cont.) Copyright 2009 John Wiley & Sons, Inc – – – – – – – 0 0 – ||||||||||||| Actual Orders Month  = 0.50  = 0.30

Adjusted Exponential Smoothing Copyright 2009 John Wiley & Sons, Inc. AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor T t +1 =  (F t +1 - F t ) + (1 -  ) T t where T t = the last period trend factor  = a smoothing constant for trend

Adjusted Exponential Smoothing ( β =0.30) Copyright 2009 John Wiley & Sons, Inc. PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 T 3 =  (F 3 - F 2 ) + (1 -  ) T 2 = (0.30)( ) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = = T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 = (0.30)( ) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = = 54.97

Adjusted Exponential Smoothing: Example Copyright 2009 John Wiley & Sons, Inc. FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan37-–– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–

Adjusted Exponential Smoothing Forecasts Copyright 2009 John Wiley & Sons, Inc – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Forecast (  = 0.50) Adjusted forecast (  = 0.30)

Linear Trend Line Copyright 2009 John Wiley & Sons, Inc. y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x b = a = y - b x where n =number of periods x == mean of the x values y == mean of the y values  xy - nxy  x 2 - nx 2  x n  y n

Least Squares Example Copyright 2009 John Wiley & Sons, Inc. x (PERIOD) y (DEMAND) xyx

Least Squares Example (cont.) Copyright 2009 John Wiley & Sons, Inc. x = = 6.5 y = = b = = =1.72 a = y - bx = (1.72)(6.5) = (12)(6.5)(46.42) (6.5) 2  xy - nxy  x 2 - nx

Copyright 2009 John Wiley & Sons, Inc. Linear trend line y = x Forecast for period 13 y = (13)= units – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Linear trend line

Seasonal Adjustments Copyright 2009 John Wiley & Sons, Inc. Repetitive increase/ decrease in demand Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

Seasonal Adjustment (cont.) Copyright 2009 John Wiley & Sons, Inc Total DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD S 2 = = = 0.20 D2D2DDD2D2DD S 4 = = = 0.37 D4D4DDD4D4DD S 3 = = = 0.15 D3D3DDD3D3DD

Seasonal Adjustment (cont.) Copyright 2009 John Wiley & Sons, Inc. SF 1 = (S 1 ) (F 5 ) = (0.28)(58.17) = SF 2 = (S 2 ) (F 5 ) = (0.20)(58.17) = SF 3 = (S 3 ) (F 5 ) = (0.15)(58.17) = 8.73 SF 4 = (S 4 ) (F 5 ) = (0.37)(58.17) = y = x = (4) = For 2005

Forecast error – difference between forecast and actual demand – MAD mean absolute deviation – MAPD mean absolute percent deviation – Cumulative error – Average error or bias Copyright 2009 John Wiley & Sons, Inc. Forecast Accuracy

Mean Absolute Deviation (MAD) Copyright 2009 John Wiley & Sons, Inc. where t = period number t = period number D t = demand in period t D t = demand in period t F t = forecast for period t F t = forecast for period t n = total number of periods n = total number of periods  = absolute value  D t - F t  n MAD =

MAD Example Copyright 2009 John Wiley & Sons, Inc –– PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |  D t - F t  n MAD= = =

Other Accuracy Measures Copyright 2009 John Wiley & Sons, Inc. Mean absolute percent deviation (MAPD) MAPD =  |D t - F t |  D t Cumulative error E =  e t Average error E = etetnnetetnnn

Comparison of Forecasts Copyright 2009 John Wiley & Sons, Inc. FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30) % Exponential smoothing (  = 0.50) % Adjusted exponential smoothing % (  = 0.50,  = 0.30) Linear trend line %––

Tracking signal – monitors the forecast to see if it is biased high or low – 1 MAD ≈ 0.8 б – Control limits of 2 to 5 MADs are used most frequently Copyright 2009 John Wiley & Sons, Inc. Forecast Control Tracking signal = =  (D t - F t ) MADEMAD

Tracking Signal Values Copyright 2009 John Wiley & Sons, Inc ––– DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD TS 3 = = Tracking signal for period 3 – TRACKINGSIGNAL

Tracking Signal Plot Copyright 2009 John Wiley & Sons, Inc. 3  3  – 2  2  – 1  1  – 0  0  – -1  -1  – -2  -2  – -3  -3  – ||||||||||||| Tracking signal (MAD) Period Exponential smoothing (  = 0.30) Linear trend line

Statistical Control Charts Copyright 2009 John Wiley & Sons, Inc.  = = = =  (D t - F t ) 2 n - 1 Using  we can calculate statistical control limits for the forecast error Using  we can calculate statistical control limits for the forecast error Control limits are typically set at  3  Control limits are typically set at  3 

Statistical Control Charts Copyright 2009 John Wiley & Sons, Inc. Errors – – – 0 0 – – – – ||||||||||||| Period UCL = +3  LCL = -3 

Linear regression – a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation Correlation – a measure of the strength of the relationship between independent and dependent variables Copyright 2009 John Wiley & Sons, Inc. Regression Methods

Linear Regression Copyright 2009 John Wiley & Sons, Inc. y = a + bx a = y - b x b = where a =intercept b =slope of the line x == mean of the x data y == mean of the y data  xy - nxy  x 2 - nx 2  x n  y n

Linear Regression Example Copyright 2009 John Wiley & Sons, Inc. xy (WINS)(ATTENDANCE) xyx

Linear Regression Example (cont.) Copyright 2009 John Wiley & Sons, Inc. x = = y = = b = = = 4.06 a = y - bx = (4.06)(6.125) =  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

Linear Regression Example (cont.) Copyright 2009 John Wiley & Sons, Inc. ||||||||||| ,000 60,000 – 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – Linear regression line, y = x Wins, x Attendance, y y = x y = (7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

Correlation and Coefficient of Determination Copyright 2009 John Wiley & Sons, Inc. Correlation, r Correlation, r Measure of strength of relationship Measure of strength of relationship Varies between and Varies between and Coefficient of determination, r 2 Coefficient of determination, r 2 Percentage of variation in dependent variable resulting from changes in the independent variable Percentage of variation in dependent variable resulting from changes in the independent variable

Computing Correlation Copyright 2009 John Wiley & Sons, Inc. n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947

Multiple Regression Copyright 2009 John Wiley & Sons, Inc. Study the relationship of demand to two or more independent variables y =  0 +  1 x 1 +  2 x 2 … +  k x k where  0 =the intercept  1, …,  k =parameters for the independent variables x 1, …, x k =independent variables

Terima Kasih Zulfa Fitri Ikatrinasari, Dr.