2. 3-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Chapter 3 Forecasting

3. 3-2 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting FORECAST: A statement about the future Used to help managers –Plan the system –Plan the use of the system

4. 3-3 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecast Uses Plan the system –Generally involves long-range plans related to: Types of products and services to offer Facility and equipment levels Facility location Plan the use of the system –Generally involves short- and medium-range plans related to: Inventory management Workforce levels Purchasing Budgeting

5. 3-4 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases I see that you will get an A this quarter. Common Features

6. 3-5 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use Cost effective

7. 3-6 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast”

8. 3-7 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Types of Forecasts Judgmental - uses subjective inputs (qualitative) Time series - uses historical data assuming the future will be like the past (quantitative) Associative models - uses explanatory variables to predict the future

9. 3-8 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Judgmental Forecasts (Qualitative) C onsumer surveys D elphi method E xecutive opinions –Opinions of managers and staff S ales force.

10. 3-9 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Time Series Forecasts (Quantitative) Trend - long-term movement in data Seasonality - short-term regular variations in data Irregular variations - caused by unusual circumstances Random variations - caused by chance CYCLE- wave like variations lasting more than one year

11. 3-10 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecast Variations Trend Irregular variation Cycles Seasonal variations 90 89 88 Figure 3-1 cycle

12. 3-11 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting The Forecast of Forecasts Naïve Simple Moving Average Weighted Moving Average Exponential Smoothing ES with Trend and Seasonality

13. 3-12 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Simple to use Virtually no cost Data analysis is nonexistent Easily understandable Cannot provide high accuracy Naïve Forecast

14. 3-13 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting NAÏVE METHOD No smoothing of data

15. 3-14 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Techniques for Averaging Moving average Weighted moving average Exponential smoothing

16. 3-15 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Simple Moving Average Smoothes out randomness by averaging positive and negative random elements over several periods n - number of periods (this example uses 4)

17. 3-16 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Points to Know on Moving Averages Pro: Easy to compute and understand Con: All data points were created equal…. …. Weighted Moving Average

18. 3-17 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Weighted Moving Average Similar to a moving average methods except that it assigns more weight to the most recent values in a time series. n -- number of periods  i – weight applied to period t-i+1 0.60.30.1

19. 3-18 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Exponential Smoothing Simpler equation, equivalent to WMA  – exponential smoothing parameter (0< 

20. 3-19 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting F 2= 37 + (0.30)(37-37) = 37 F 3 =37+ (0.30)(40-37) = 37.9 Exponential Smoothing (α=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

21. 3-20 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb4037.0037.00 3Mar4137.9038.50 4Apr3738.8339.75 5May 4538.2838.37 6Jun5040.2941.68 7Jul 4343.2045.84 8Aug 4743.1444.42 9Sep 5644.3045.71 10Oct5247.8150.85 11Nov5549.0651.42 12Dec 5450.8453.21 13Jan–51.7953.61 Exponential Smoothing (cont.)

22. 3-21 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting 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

23. 3-22 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting 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 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = 38.5 + 0.45 = 38.95 T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = 53.61 + 1.36 = 54.96

24. 3-23 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Adjusted Exponential Smoothing: Example FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan3737.00–– 2Feb4037.000.0037.00 3Mar4138.500.4538.95 4Apr3739.750.6940.44 5May 4538.370.0738.44 6Jun5038.370.0738.44 7Jul 4345.841.9747.82 8Aug 4744.420.9545.37 9Sep 5645.711.0546.76 10Oct5250.852.2858.13 11Nov5551.421.7653.19 12Dec 5453.211.7754.98 13Jan–53.611.3654.96

25. 3-24 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Equation b is the line slope. Y t = a + bt 0 1 2 3 4 5 t Y a

26. 3-25 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n    Yes… Linear Regression!!

27. 3-26 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Equation Example

28. 3-27 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Calculation y = 143.5 + 6.3t a= 812- 6.3(15) 5 = b= 5 (2499)- 15(812) 5(55)- 225 = 12495-12180 275-225 = 6.3 143.5 Look on page 85

29. 3-28 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Disadvantage of simple linear regression 1-apply only to linear relationship with an independent variable. 2-one needs a considerable amount of data to establish the relationship ( at least 20). 3-all observations are weighted equally

30. 3-29 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting 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

31. 3-30 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Mean Absolute Deviation (MAD) where t= period number t= period number A t = demand in period t A 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  A t - F t  n MAD =

32. 3-31 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting MAD Example 13737.00–– 24037.003.003.00 34137.903.103.10 43738.83-1.831.83 54538.286.726.72 65040.299.699.69 74343.20-0.200.20 84743.143.863.86 95644.3011.7011.70 105247.814.194.19 115549.065.945.94 125450.843.153.15 55749.3153.39 PERIODDEMAND, A t F t (  =0.3)(A t - F t ) |A t - F t |  A t - F t  n MAD= = = 4.85 53.39 11

33. 3-32 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD =  |A t - F t |  A t Cumulative error E =  e t Average error (E )= etetnnetetnnn

34. 3-33 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Comparison of Forecasts FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30)4.859.6%49.314.48 Exponential smoothing (  = 0.50)4.048.5%33.213.02 Adjusted exponential smoothing3.817.5%21.141.92 (  = 0.50,  = 0.30)

35. 3-34 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecast Control Tracking signal –monitors the forecast to see if it is biased high or low Tracking signal = =  (A t - F t ) MADEMAD

36. 3-35 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Tracking Signal Values 13737.00––– 24037.003.003.003.00 34137.903.106.103.05 43738.83-1.834.272.64 54538.286.7210.993.66 65040.299.6920.684.87 74343.20-0.2020.484.09 84743.143.8624.344.06 95644.3011.7036.045.01 105247.814.1940.234.92 115549.065.9446.175.02 125450.843.1549.324.85 DEMANDFORECAST,ERROR  E = PERIODA t F t A t - F t  (A t - F t )MAD TS 3 = = 2.00 6.10 3.05 Tracking signal for period 3 –1.002.001.623.004.255.016.007.198.189.2010.17TRACKINGSIGNAL

37. 3-36 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Sources of forecast errors The model may be inadequate. Irregular variation may be occur. The forecasting technique may be used incorrectly or the results misinterpreted. There are always random variation in the data.

38. 3-37 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting End Notes The two most important factors in choosing a forecasting technique: –Cost –Accuracy Keep it SIMPLE! =FORECAST(70,{23,34,12},{67,76,56}) (if you can…let the computer do it)