1. 8-1 Forecasting Supply Chain Requirements CR (2004) Prentice Hall, Inc. Chapter 8 I hope you'll keep in mind that economic forecasting is far from a perfect science. If recent history's any guide, the experts have some explaining to do about what they told us had to happen but never did. Ronald Reagan, 1984

2. 8-2 Forecasting in Inventory Strategy CR (2004) Prentice Hall, Inc. PLANNING ORGANIZING CONTROLLING Transport Strategy Transport fundamentals Transport decisions Customer service goals The product Logistics service Ord. proc. & info. sys. Inventory Strategy Forecasting Inventory decisions Purchasing and supply scheduling decisions Storage fundamentals Storage decisions Location Strategy Location decisions The network planning process PLANNING ORGANIZING CONTROLLING Transport Strategy Transport fundamentals Transport decisions Customer service goals The product Logistics service Ord. proc. & info. sys. Inventory Strategy Forecasting Inventory decisions Purchasing and supply scheduling decisions Storage fundamentals Storage decisions Location Strategy Location decisions The network planning process

3. 8-3 What’s Forecasted in the Supply Chain? Demand, sales or requirements Purchase prices Replenishment and delivery times CR (2004) Prentice Hall, Inc.

4. 8-4 CR (2004) Prentice Hall, Inc. Some Forecasting Method Choices Historical projection Moving average Exponential smoothing Causal or associative Regression analysis Qualitative Surveys Expert systems or rule-based Collaborative

5. 8-5 CR (2004) Prentice Hall, Inc. Typical Time Series Patterns: Random

6. 8-6 CR (2004) Prentice Hall, Inc. Typical Time Series Patterns: Random with Trend

7. 8-7 CR (2004) Prentice Hall, Inc. Typical Time Series Patterns: Random with Trend & Seasonal

8. 8-8 CR (2004) Prentice Hall, Inc. Typical Time Series Patterns: Lumpy Time Sales

9. 8-9 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.

10. 8-10 Moving Average Basic formula where i = time period t = current time period n = length of moving average in periods A i = demand in period i CR (2004) Prentice Hall, Inc.

11. 8-11 Example 3-Month Moving Average Forecasting Month, i Demand for month, i Total demand during past 3 months 3-month moving average............ 20120.. 21130360/3120 22110380/3126.67 23140 360/3120 24110380/3126.67 25130 26 ? CR (2004) Prentice Hall, Inc.

12. 8-12 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()1( )1( then form, in exponential are )( weightsIf 1... 1 1 3 3 2 2 1 1 1 2211                  t t t ttt nt n tt tt n i i nn F A F FAFMA A AA AA w wwhere AwAwAwMA     

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 CR (2004) Prentice Hall, Inc. Example (Cont’d) Measuring forecast error as MAD or RMSE (std. error of forecast) 1 degree of freedom lost in level-only model, but 2 in level-trend and 3 in level-trend-seasonal models

18. 8-18 CR (2004) Prentice Hall, Inc. Example (Cont’d) Using S F and assuming n =2 Note To compute a reasonable average for S F, n should range over at least one seasonal cycle in most cases.

19. S F = 408 Example (Cont’d) Range of the forecast F 3 =1064 Range If forecast errors are normally distributed and the forecast is at the mean of the distribution, i.e.,, a forecast confidence band can be computed. The error distribution for the level-only model results is: Bias should be 0 or close to it in a model of good fit CR (2004) Prentice Hall, Inc. 8-19

20. 8-20 CR (2004) Prentice Hall, Inc. Example (Cont’d) From a normal distribution table, z @95% =1.96. The actual time series value Y for quarter 3 is expected to range between: or 264  Y  1864 8001064 )408(96.11064 )( 3    F S z FY

21. 8-21 CR (2004) Prentice Hall, Inc. Correcting for Trend in ES The trend-corrected model is S t =  A t  (1 –  )(S t-1  T t-1 ) T t =  (S t – S t-1 )  (1 –  )T t-1 F t+1 = S t  T t where S is the forecast without trend correction. Assuming  = 0.2,  = 0.3, S -1 = 975, and T -1 = 0 Forecast for quarter 1 of this year S 0 = 0.2(1100)  0.8(975 + 0) = 1000 T 0 = 0.3(1000 – 975)  0.7(0) = 8 F 1 = 1000  8 = 1008

22. 8-22 Forecast for quarter 2 of this year S 0 T 0 S 1 = 0.2(1400)  0.8(1000  8) = 1086.4 T 1 = 0.3(1086.4 – 1000)  0.7(8) = 31.5 F 2 = 1086.4  31.5 = 1117.9 Forecast for quarter 3 of this year S 2 = 0.2(1000)  0.8(1086.4  31.5) = 1094.3 T 2 = 0.3(1094.3 – 1086.4)  0.7(31.5) = 24.4 F 3 = 1094.3  24.4 = 1118.7, or 1119 CR (2004) Prentice Hall, Inc. Correcting for Trend in ES (Cont’d)

23. 8-23 CR (2004) Prentice Hall, Inc. Correcting for Trend in ES (Cont’d) Summarizing with trend correction 1234 Last year12007009001100 This year14001000? Fore- cast100811181119 Quarter

24.  01 Fore- cast error CR (2004) Prentice Hall, Inc. Optimizing  for ES Minimize average forecast error 8-24

25. CR (2004) Prentice Hall, Inc. Controlling Model Fit in ES Tracking signal monitors the fit of the model to detect when the model no longer accurately represents the data where the Mean Squared Error (MSE) is If tracking signal exceeds a specified value (control limit), revise smoothing constant(s). n is a reasonable number of past periods depending on the application 8-25

26. 8-26 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.

27. 8-27 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

28. 8-28 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

29. 8-29 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.

30. 8-30 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

31. 8-31 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

32. 8-32 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

33. 8-33 CR (2004) Prentice Hall, Inc. Classic Time Series Decomposition Model (Cont’d) There is inadequate data to make a meaningful estimate of S F. However, we would proceed as follows: Then, F t  z(S F )  Y  F t  z(S F ) Normally, a larger sample size would be used giving a positive value for S F

34. 8-34 CR (2004) Prentice Hall, Inc. Regression Analysis Basic formulation F =  o   1 X 1   2 X 2  …   n X n Example Bobbie Brooks, a manufacturer of teenage women’s clothes, was able to forecast seasonal sales from the following relationship F = constant   1 (no. nonvendor accounts)   2 (consumer debt ratio)

35. CR (2004) Prentice Hall, Inc. Sales period (1) Time period, t (2) Sales ( D t ) ($000s) (3) DtDt  t (4) t2t2 (5) Trend value (Tt(Tt ) (6)= (2)/(5) Seasonal index Forecast ($000s) Summer1$9,458 9,458 1$12,0530.78 Trans-season211,54223,084412,5390.92 Fall314,48943,467913,0251.11 Holiday415,75463,0161613,5121.17 Spring517,26986,3452513,9981.23 Summer611,51469,0843614,4840.79 Trans-season712,62388,3614914,9700.84 Fall816,086128,6886415,4561.04 Holiday918,098162,8828115,9421.14 Spring1021,030210,30010016,4281.28 Summer1112,788140,66812116,9150.76 Trans-season1216,072192,86414417,4010.92 Fall13?17,887 * $18,602 Holiday14 ? 18,373 * 20,945 Totals78176,7231,218,217650 Regression Forecasting Using Bobbie Brooks Sales Data N = 12  DtDt  t = 1,218,217  t2t2 = 650 == (,/),. 176723121472692 == 781265 /. Regression equation is: T t = 11,567.08 + 486.13 t *Forecasted values 8-35

36. 8-36 Combined Model Forecasting Combines the results of several models to improve overall accuracy. Consider the seasonal forecasting problem of Bobbie Brooks. Four models were used. Three of them were two forms of exponential smoothing and a regression model. The fourth was managerial judgement used by a vice president of marketing using experience. Each forecast is then weighted according to its respective error as shown below. Calculation of forecast weights Model type (1) Forecast error (2) Percent of total error (3)= 1.0/(2) Inverse of error proportion (4)= (3)/48.09 Model weights MJ9.00.4662.150.04 R0.70.03627.770.58 ES 1 1.20.06315.870.33 ES 2 8.40.4352.300.05 Total19.31.00048.091.00 CR (2004) Prentice Hall, Inc.

37. 8-37 Combined Model Forecasting (Cont’d) Weighted Average Fall Season Forecast Using Multiple Forecasting Techniques Forecast type (1) Model forecast (2) Weighting factor (3)= (1)  (2) Weighted proportion Regression model (R)$20,367,0000.58$11,813,000 Exponential Smoothing ES 1 20,400,0000.336,732,000 Combined exponential smoothing-- regression model (ES 2 ) 17,660,0000.05883,000 Managerial judgment (MJ)19,500,0000.04 780,000 Weighted average forecast $20,208,000 CR (2004) Prentice Hall, Inc.

38. Multiple Model Errors 8-38

39. 8-39 CR (2004) Prentice Hall, Inc. Actions When Forecasting is Not Appropriate  Seek information directly from customers  Collaborate with other channel members  Apply forecasting methods with caution (may work where forecast accuracy is not critical)  Delay supply response until demand becomes clear  Shift demand to other periods for better supply response  Develop quick response and flexible supply systems

40. 8-40 CR (2004) Prentice Hall, Inc. Collaborative Forecasting Demand is lumpy or highly uncertain Involves multiple participants each with a unique perspective—“two heads are better than one” Goal is to reduce forecast error The forecasting process is inherently unstable

41. 8-41 CR (2004) Prentice Hall, Inc. Collaborative Forecasting: Key Steps Establish a process champion Identify the needed Information and collection processes Establish methods for processing information from multiple sources and the weights assigned to multiple forecasts Create methods for translating forecast into form needed by each party Establish process for revising and updating forecast in real time Create methods for appraising the forecast Show that the benefits of collaborative forecasting are obvious and real

42. 8-42 CR (2004) Prentice Hall, Inc. Managing Highly Uncertain Demand  Delay forecasting as long as possible  Prioritize supply by product’s degree of uncertainty (supply to the more certain products first)  Apply the principle of postponement to the most uncertain products (delay committing to a final product form until an order is received)  Create flexible supply to changing demand (alter capacity and output rates through subcontracting, computer technology, multi-purpose processes, etc.)  Be able to respond quickly to uncertain demand levels