Forecasting

Lecture Outline   Strategic Role of Forecasting in Supply Chain Management and TQM   Components of Forecasting Demand   Time Series Methods   Forecast Accuracy   Regression Methods

Forecasting  Predicting the Future  Qualitative forecast methods subjective subjective  Quantitative forecast methods based on mathematical formulas based on mathematical formulas

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

Forecasting and TQM   Accurate forecasting customer demand is a key to providing good quality service   Continuous replenishment and JIT complement TQM eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM smoothes process flow with no defective items meets expectations about on-time delivery, which is perceived as good-quality service

Types of Forecasting Methods  Depend on time frame time frame demand behavior demand behavior causes of behavior causes of behavior

Time Frame  Indicates how far into the future is forecast Short- to mid-range forecast Short- to mid-range forecast typically encompasses the immediate future typically encompasses the immediate future daily up to two years daily up to two years Long-range forecast Long-range forecast usually encompasses a period of time longer than two years usually encompasses a period of time longer than two years

Demand Behavior  Trend a gradual, long-term up or down movement of demand a gradual, long-term up or down movement of demand  Random variations movements in demand that do not follow a pattern movements in demand that do not follow a pattern  Cycle an up-and-down repetitive movement in demand an up-and-down repetitive movement in demand  Seasonal pattern an up-and-down repetitive movement in demand occurring periodically an up-and-down repetitive movement in demand occurring periodically

Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement Forms of Forecast Movement

Forecasting Methods  Qualitative use management judgment, expertise, and opinion to predict future demand use management judgment, expertise, and opinion to predict future demand  Time series statistical techniques that use historical demand data to predict future demand statistical techniques that use historical demand data to predict future demand  Regression methods attempt to develop a mathematical relationship between demand and factors that cause its behavior attempt to develop a mathematical relationship between demand and factors that cause its behavior

Qualitative Methods   Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts   Delphi method involves soliciting forecasts about technological advances from experts

Forecasting Process 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

Time Series   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

Moving Average  Naive forecast demand the current period is used as next period’s forecast demand the current period is used as next period’s forecast  Simple moving average stable demand with no pronounced behavioral patterns stable demand with no pronounced behavioral patterns  Weighted moving average weights are assigned to most recent data

Moving Average: Naïve Approach Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Nov - FORECAST

Simple Moving Average MA n = n i = 1  DiDiDiDi n where n =number of periods in the moving average D i =demand in period i

3-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDiDiDi 3 = = orders for Nov ––– MOVINGAVERAGE

5-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 5 = 5 i = 1  DiDiDiDi 5 = = orders for Nov ––––– MOVINGAVERAGE

Smoothing Effects – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

Weighted Moving Average WMA n = i = 1  Wi DiWi DiWi DiWi Di where W i = the weight for period i, between 0 and 100 percent  W i =  Adjusts moving average method to more closely reflect data fluctuations

Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 WMA 3 = 3 i = 1  Wi DiWi DiWi DiWi Di = = orders November Forecast

 Averaging method  Weights most recent data more strongly  Reacts more to recent changes  Widely used, accurate method Exponential Smoothing

F t +1 =  D t + (1 -  )F t where: F t +1 =forecast for next period D t =actual demand for present period F t =previously determined forecast for present period  =weighting factor, smoothing constant Exponential Smoothing (cont.)

Effect of Smoothing Constant 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t F t If  = 0, then F t +1 = 0  D t + 1 F t 0 = F t Forecast does not reflect recent data If  = 1, then F t +1 = 1  D t + 0 F t =  D t Forecast based only on most recent data

F 2 =  D 1 + (1 -  )F 1 == F 3 =  D 2 + (1 -  )F 2 == F 13 =  D 12 + (1 -  )F 12 == Exponential Smoothing (α=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

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.)

70 70 – – – – – – – 0 0 – ||||||||||||| Actual Orders Month Exponential Smoothing (cont.)  = 0.50  = 0.30

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

Adjusted Exponential Smoothing (β=0.30) 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 == AF 3 = F 3 + T 3 = = T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 == AF 13 = F 13 + T 13 = =

Adjusted Exponential Smoothing: Example FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan –– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–

Adjusted Exponential Smoothing Forecasts – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Forecast (  = 0.50) Adjusted forecast (  = 0.30)

y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x Linear Trend Line 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 x (PERIOD) y (DEMAND) xyx

x = = y = = b = = = a = y - bx =  xy - nxy  x 2 - nx 2 Least Squares Example (cont.)

Linear trend line y = x Forecast for period 13 y = (13)= units – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Linear trend line

Seasonal Adjustments  Repetitive increase/ decrease in demand  Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

Seasonal Adjustment (cont.) Total DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = D1D1DDD1D1DD S 2 = = = D2D2DDD2D2DD S 4 = = = D4D4DDD4D4DD S 3 = = = D3D3DDD3D3DD

Seasonal Adjustment (cont.) SF 1 = (S 1 ) (F 5 ) = = SF 2 = (S 2 ) (F 5 ) = = SF 3 = (S 3 ) (F 5 ) = = SF 4 = (S 4 ) (F 5 ) = = y = = = For 2006

Forecast Accuracy   Forecast error difference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias

Mean Absolute Deviation (MAD) 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 –– PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |

Other Accuracy Measures 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 FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30) % Exponential smoothing (  = 0.50) % Adjusted exponential smoothing % (  = 0.50,  = 0.30) Linear trend line %––

Forecast Control   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 Tracking signal = =  (D t - F t ) MADEMAD

Tracking Signal Values ––– DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD – TRACKINGSIGNAL

Tracking Signal Plot 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  = = = =  (D t - F t ) 2 n - 1  Using  we can calculate statistical control limits for the forecast error  Control limits are typically set at  3 

Statistical Control Charts Errors – – – 0 0 – – – – ||||||||||||| Period UCL = +3  LCL = -3 

Regression Methods   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

Linear Regression 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 xy (WINS)(ATTENDANCE) xyx

Linear Regression Example (cont.) 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

||||||||||| ,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 Linear Regression Example (cont.) y = x y = (7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

Correlation and Coefficient of Determination  Correlation, r  Measure of strength of relationship  Varies between and  Coefficient of determination, r 2  Percentage of variation in dependent variable resulting from changes in the independent variable

Computing Correlation 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