Nội dung

Logistics Management LSM 730 Lecture 22 Dr. Khurrum S. Mughal 1-1 Qualitative Methods • Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts • Delphi method – involves soliciting forecasts about technological advances from experts 12-2 Is Time Series Pattern Forecastable? Whether a time series can be reasonably forecasted often depends on the time series’ degree of variability. Forecast a regular time series, but use other techniques for lumpy ones. How to tell the difference: Rule A time series is lumpy if X 3 where X mean of the series  standard deviation of series, regular, otherwise. CR (2004) Prentice Hall, Inc. 8-3 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 12-4 Moving Average • Naive forecast – demand in current period is used as next period’s forecast • Simple moving average – uses average demand for a fixed sequence of periods – stable demand with no pronounced behavioral patterns • Weighted moving average – weights are assigned to most recent data 12-5 Moving Average: Naïve Approach MONTH ORDERS PER MONTH Jan 120 Feb 90 Mar 100 Apr 75 May 110 Nov June 50 July 75 Aug 130 FORECAST 120 90 100 75 110 50 75 130 110 90 12-6 Simple Moving Average n D i MAn = i=1 n where n Di = number of periods in the moving average = demand in period i 12-7 3-month Simple Moving Average ORDERS MONTH Jan MONTH PER 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 MOVING AVERAGE – – – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 110.0 3  MA3 = = Di i=1 3 90 + 110 + 130 3 = 110 orders for Nov 12-8 5-month Simple Moving Average ORDERS MONTH Jan MONTH PER 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 MOVING AVERAGE – – – – – 99.0 85.0 82.0 88.0 95.0 91.0 5  MA5 = = Di i=1 5 90 + 110 + 130+75+50 5 = 91 orders for Nov 12-9 where a = smoothing constant usually 0.01 to 0.30 Ft +1 = forecast for next period At = actual demand in current period Ft = forecast in current period Weighted Moving Average which reduces to the basic, level only, exponential smoothing formula MA = Ft +1 = aAt + (1 - a )Ft 8-10 Exponential Smoothing Ft +1 = Dt + (1 - )Ft where: Ft +1 = forecast for next period Dt = actual demand for present period Ft = previously determined forecast for present period = weighting factor, smoothing constant 12-11 Effect of Smoothing Constant 0.0  1.0 If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft If = 0, then Ft +1 = 0Dt + 1 Ft = Ft Forecast does not reflect recent data If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data 12-12 Exponential Smoothing Formulas I. Level only Ft+1 IV. Forecast error =  At + (1-)Ft MAD = N å |A t t =1 N II. Level and trend or St = aAt + (1-a)(St-1 + Tt-1) Tt = ß(St - St-1) + (1-ß)Tt-1 Ft+1 = St + T t SF = - Ft | N å (A t t=1 - Ft ) 2 N and SF @ 1.25MAD. III. Level, trend, and seasonality St = a(At/It-L) + (1-a)(St-1 + Tt-1) It = g(At/St) + (1-g)It-L Tt = ß(St - St-1) + (1-ß)Tt-1 Ft+1 = (St + Tt)It-L+1 where L is the time period of one full seasonal cycle. CR (2004) Prentice Hall, Inc. 8-13 Example Exponential Smoothing Forecasting Time series data 1 Last year This year Quarter 2 3 4 1100 1200 700 900 1400 1000 ? Getting started Assume  = 0.2. Average first 4 quarters of data and use for previous forecast, say Fo CR (2004) Prentice Hall, Inc. 8-14 Example (Cont’d) Begin forecasting F0 (1200  700  900 1100) / 4 975 First quarter of 2nd year F1 0.2A0 (1 0.2)F0 0.2(1100)  0.8(975) 1000 Second quarter of 2nd year F2 0.2A1 (1 0.2)F1 0.2(1400)  0.8(1000) 1080 CR (2004) Prentice Hall, Inc. 8-15 Example (Cont’d) Third quarter of 2nd year F3 0.2A2 (1 0.2)F0 0.2(1000)  0.8(1080) 1064 Summarizing 1 Last year This year Forecast Quarter 2 3 4 1100 1200 700 900 1400 1000 ? 1000 1080 1064 CR (2004) Prentice Hall, Inc. 8-16 Classic Time Series Decomposition Model Basic formulation F=TSCR where F = forecast T = trend S = seasonal index C = cyclical index (usually 1) R = residual index (usually 1) Some time series data Last year This year CR (2004) Prentice Hall, Inc. 1 1200 1400 Quarter 2 3 700 900 1000 ? 4 1100 8-17 Classic Time Series Decomposition Model (Cont’d) Trend estimation Use simple regression analysis to find the trend equation of the form T = a  bt. Recall the basic formulas:  Yt  nY t b 2 2  t  nt and a Y  bt CR (2004) Prentice Hall, Inc. 8-18 Classic Time Series Decomposition Model (Cont’d) Redisplaying the data for ease of computation. 2 t Y Yt t 1 1200 1200 1 2 700 1400 4 3 900 2700 9 4 1100 4400 16 5 1400 7000 25 6 1000 6000 36 2 åt=21 åY=6300 åYt=22700 åt =91 CR (2004) Prentice Hall, Inc. 8-19 Classic Time Series Decomposition Model (Cont’d) Hence, 00/6) b 22700 6(21/6)(63 91 6(21/6)2 and a 6300  37.14(21/6) 920.01 6 then T = 920.01  27.14t Forecast for 3rd quarter of this year is: T = 920.01  37.14(7) = 1179.99 CR (2004) Prentice Hall, Inc. 8-20 Classic Time Series Decomposition Model (Cont’d) Compute seasonal indices The procedure is to form a ratio of actual demand to the estimated demand for a full seasonal cycle (4 quarters). One way is as follows. Seasonal t Y T Index, St 1 1200 957.15* 1.25** 2 700 994.29 0.70 3 900 1031.43 0.87 4 1100 1068.57 1.03 *T=920.01  37.14(1)=957.15 **St=1200/957.15=1.25 CR (2004) Prentice Hall, Inc. 8-21 Classic Time Series Decomposition Model (Cont’d) Compute seasonal indices Since C and R index values are usually 1, the adjusted seasonal forecast for the 3rd quarter of this year would be: F7 = 1179.99 x 0.87 = 1026.59 Forecast range The standard error of the forecast is: n SF  2  (Yt  Ft ) t 1 n 2 CR (2004) Prentice Hall, Inc. A degree of freedom is lost for the a and b values in forecast equation 8-22 Classic Time Series Decomposition Model (Cont’d) Tabled computations Qtr 1 2 3 4 1 2 3 t Yt 1 1200 2 700 3 900 4 1100 5 1400 6 1000 7 Tt 957.15 994.29 1031.43 1068.57 1105.71 1142.85 1179.99 St Ft 1.25 0.70 0.87 1.03 1.27 1404.25* 0.88 1005.71** 1026.59 *1105.71x1.27=1404.25 **1142.85x0.88=1005.71 CR (2004) Prentice Hall, Inc. 8-23