1. 1-1 Logistics Management LSM 730 Dr. Khurrum S. Mughal Lecture 22

2. 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

3. 8-3 CR (2004) Prentice Hall, Inc. 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 where regular, otherwise.

4. 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

5. 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

6. Moving Average: Naïve Approach 12-6 Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH - 120 90 100 75 110 50 75 130 110 90 Nov - FORECAST

7. Simple Moving Average 12-7 MA n = n i = 1  DiDi n where n =number of periods in the moving average D i =demand in period i

8. 3-month Simple Moving Average 12-8 Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1  DiDi 3 = 90 + 110 + 130 3 = 110 orders for Nov – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MOVING AVERAGE

9. 5-month Simple Moving Average 12-9 MA 5 = 5 i = 1  DiDi 5 = 90 + 110 + 130+75+50 5 = 91 orders for Nov Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE

10. 8-10 Weighted Moving Average period current in forecast period current in demand actual period next for forecast 0.30 to 0.01 usually constant smoothing where )1( formula smoothing exponential only, level basic, the to reduces which 1 1        t t t ttt F A F FAFMA  

11. Exponential Smoothing 12-11 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

12. 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t + 0.80 F t If  = 0, then F t +1 = 0  D t + 1 F t = 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 Effect of Smoothing Constant 12-12

13. 8-13 I.Level only F t+1 =  A t + (1-  )F t II.Level and trend S t =  A t + (1-  )(S t-1 + T t-1 ) T t = ß(S t - S t-1 ) + (1-ß)T t-1 F t+1 = S t + T t III.Level, trend, and seasonality S t =  (A t /I t-L ) + (1-  )(S t-1 + T t-1 ) I t =  (A t /S t ) + (1-  )I t-L T t = ß(S t - S t-1 ) + (1-ß)T t-1 F t+1 = (S t + T t )I t-L+1 whereL is the time period of one full seasonal cycle. IV.Forecast error MAD= |A t    F N t t N | 1 or S (AF) N F tt 2 t1 N     and S F  1.25MAD. Exponential Smoothing Formulas CR (2004) Prentice Hall, Inc.

14. 8-14 CR (2004) Prentice Hall, Inc. Example Exponential Smoothing Forecasting Time series data 1234 Last year12007009001100 This year14001000? Quarter Getting started Assume  = 0.2. Average first 4 quarters of data and use for previous forecast, say F o

15. 8-15 CR (2004) Prentice Hall, Inc. Example (Cont’d) Begin forecasting First quarter of 2nd year Second quarter of 2nd year

16. 8-16 CR (2004) Prentice Hall, Inc. Example (Cont’d) Third quarter of 2nd year Summarizing 1234 Last year12007009001100 This year14001000? Fore- cast100010801064 Quarter

17. 8-17 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 1234 Last year12007009001100 This year14001000? Quarter CR (2004) Prentice Hall, Inc.

18. 8-18 CR (2004) Prentice Hall, Inc. 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: and

19. 8-19 CR (2004) Prentice Hall, Inc. Classic Time Series Decomposition Model (Cont’d) Redisplaying the data for ease of computation. tYYtt 2 11200 1 270014004 390027009 41100440016 51400700025 6 1000600036  t=21  Y = 6300  Yt = 22700  t 2 = 91

20. 8-20 Classic Time Series Decomposition Model (Cont’d) Hence, and 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.

21. 8-21 CR (2004) Prentice Hall, Inc. 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. tYT Seasonal Index, S t 11200957.15*1.25** 2700994.290.70 39001031.430.87 411001068.571.03 * T =920.01  37.14(1)=957.15 ** S t =1200/957.15=1.25

22. 8-22 CR (2004) Prentice Hall, Inc. 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: F 7 = 1179.99 x 0.87 = 1026.59 Forecast range The standard error of the forecast is: A degree of freedom is lost for the a and b values in forecast equation

23. 8-23 CR (2004) Prentice Hall, Inc. Classic Time Series Decomposition Model (Cont’d) QtrtY t T t S t F t 111200957.151.25 22700994.290.70 339001031.430.87 4411001068.571.03 1514001105.711.271404.25* 2610001142.850.881005.71** 371179.991026.59 *1105.71x1.27=1404.25 **1142.85x0.88=1005.71 Tabled computations