1. Forecasting

2. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 2 Why Forecast? Assess long-term capacity needs Develop budgets, hiring plans, etc. Plan production or order materials Get agreement within firm and across supply chain partners

3. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 3 Forecast Characteristics Almost always wrong by some amount More accurate for groups or families More accurate for shorter time periods No substitute for calculated demand.

4. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 4 Quantitative Methods Used when situation is ‘stable’ and historical data exists –Existing products –Current technology Heavy use of mathematical techniques ******************************* E.g., forecasting sales of a mature product Qualitative Methods Used when situation is vague and little data exists –New products –New technology Involves intuition, experience ***************************** E.g., forecasting sales to a new market Forecasting Approaches

5. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 10, Slide 5 “Q2” Forecasting Quantitative, then qualitative factors to “filter” the answer

6. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 6 Qualitative Forecasting Executive opinions Sales force composite Consumer surveys Outside opinions Delphi method

7. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 7 Demand Forecasting Basic time series models Linear regression –For time series or causal modeling Measuring forecast accuracy Mini-case: Northcutt Bikes (A)

8. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 8 Time Series Models PeriodDemand 112 215 311 4 9 510 6 8 714 812 What assumptions must we make to use this data to forecast?

9. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 9 Time Series Components of Demand... Time Demand... randomness

10. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 10 Time Series with... Time Demand... randomness and trend

11. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 11 Time series with... Demand... randomness, trend and seasonality May

12. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 10, Slide 12 Idea Behind Time Series Models Distinguish between random fluctuations and true changes in underlying demand patterns.

13. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 13 Moving Average Models PeriodDemand 112 215 311 4 9 510 6 8 714 812 3-period moving average forecast for Period 8: =(14 + 8 + 10) / 3 =10.67 

14. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 14 Weighted Moving Averages Forecast for Period 8 =[(0.5  14) + (0.3  8) + (0.2  10)] / (0.5 + 0.3 + 0.1) =11.4 What are the advantages? What do the weights add up to? Could we use different weights? Compare with a simple 3-period moving average.

15. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 15 Table of Forecasts and Demand Values... Period Actual Demand Two-Period Moving Average Forecast Three-Period Weighted Moving Average Forecast Weights = 0.5, 0.3, 0.2 112 215 31113.5 491312.4 510 10.8 689.59.9 71498.8 8121111.4 9 1311.8

16. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 16... and Resulting Graph Note how the forecasts smooth out variations

17. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 17 Exponential Smoothing I Sophisticated weight averaging model Needs only three numbers: F t = Forecast for the current period t D t = Actual demand for the current period t  = Weight between 0 and 1

18. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 18 Exponential Smoothing II Formula F t+1 = F t +  (D t – F t ) =  ×  D t + (1 –  × F t Where did the current forecast come from? What happens as  gets closer to 0 or 1? Where does the very first forecast come from?

19. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 19 Exponential Smoothing Forecast with  = 0.3 F 2 = 0.3×12 + 0.7×11 = 3.6 + 7.7 = 11.3 F 3 = 0.3×15 + 0.7×11.3 = 12.41 Period Actual Demand Exponential Smoothing Forecast 11211.00 21511.30 31112.41 4911.99 51011.09 6810.76 7149.93 81211.15 9 11.41

20. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 20 Resulting Graph

21. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 10, Slide 21 Trends What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?

22. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 22 Same Exponential Smoothing Model as Before: Since the model is based on historical demand, it always lags the obvious upward trend Period Actual Demand Exponential Smoothing Forecast 11111.00 21211.00 31311.30 41411.81 51512.47 61613.23 71714.06 81814.94 9 15.86

23. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 23 Adjusting Exponential Smoothing for Trend Add trend factor and adjust using exponential smoothing Needs only two more numbers: T t = Trend factor for the current period t  = Weight between 0 and 1 Then: T t+1 =  × (F t+1 – F t ) + (1 –  ) × T t And the F t+1 adjusted for trend is = F t+1 + T t+1

24. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 24 Simple Linear Regression Time series OR causal model Assumes a linear relationship: y = a + b(x) y x

25. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 25 Definitions Y = a + b(X) Y = predicted variable (i.e., demand) X = predictor variable “X” can be the time period or some other type of variable (examples?)

26. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 26 The Trick is Determining a and b:

27. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 27 Example: Regression Used for Time Series Period (X)Demand (Y)X2X2 XY 11101 21904380 33209960 4410161640 5490252450 151520555540 Column Sums

28. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 28 Resulting Regression Model: Forecast = 10 + 98×Period

29. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 29 Example: Simplified Regression I If we redefine the X values so that their sum adds up to zero, regression becomes much simpler –a now equals the average of the y values –b simplifies to the sum of the xy products divided by the sum of the x 2 values

30. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 30 Example: Simplified Regression II Period (X) Period (X)' Demand (Y)X2XY 1-21104-220 21901-190 3032000 414101 524904980 0152010980

31. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 31 Dealing with Seasonality Quarter PeriodDemand Winter 021 80 Spring2 240 Summer3 300 Fall4 440 Winter 035 400 Spring6 720 Summer7 700 Fall8 880

32. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 32 What Do You Notice? Forecasted Demand = –18.57 + 108.57 x Period Period Actual Demand Regression Forecast Forecast Error Winter 0218090-10 Spring2240198.641.4 Summer3300307.1-7.1 Fall4440415.724.3 Winter 035400524.3-124.3 Spring6720632.987.2 Summer7700741.4-41.4 Fall888085030

33. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 33 Regression picks up trend, but not seasonality effect

34. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 34 Calculating Seasonal Index: Winter Quarter (Actual / Forecast) for Winter Quarters: Winter ‘02:(80 / 90) = 0.89 Winter ‘03:(400 / 524.3) = 0.76 Average of these two = 0.83 Interpret!

35. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 35 Seasonally adjusted forecast model For Winter Quarter [ –18.57 + 108.57×Period ] × 0.83 Or more generally: [ –18.57 + 108.57 × Period ] × Seasonal Index

36. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 36 Seasonally adjusted forecasts Forecasted Demand = –18.57 + 108.57 x Period Period Actual Demand Regression Forecast Demand/ Forecast Seasonal Index Seasonally Adjusted Forecast Forecast Error Winter 02180900.890.8374.335.67 Spring2240198.61.211.17232.977.03 Summer3300307.10.980.96294.985.02 Fall4440415.71.061.05435.194.81 Winter 035400524.30.760.83433.02-33.02 Spring6720632.91.141.17742.42-22.42 Summer7700741.40.940.96712.13-12.13 Fall88808501.041.05889.84-9.84

37. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 37 Would You Expect the Forecast Model to Perform This Well With Future Data?

38. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 38 More Regression Models I Non-linear models –Example:y = a + b × ln(x)

39. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 39 More Regression Models II Multiple regression –More than one independent variable y x z y = a + b1 × x + b2 × z

40. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 40 Causal Models Time series assume that demand is a function of time. This is not always true. 1. Pounds of BBQ eaten at party. 2. Dollars spent on drought relief. 3. Lumber sales. Linear regression can be used in these situations as well.

41. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 41 Measuring Forecast Accuracy How do we know:  If a forecast model is “best”?  If a forecast model is still working?  What types of errors a particular forecasting model is prone to make? Need measures of forecast accuracy

42. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 42 Measures of Forecast Accuracy Error = Actual demand – Forecast or E t = D t – F t

43. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 43 Mean Forecast Error (MFE) For n time periods where we have actual demand and forecast values:

44. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 44 Mean Absolute Deviation (MAD) For n time periods where we have actual demand and forecast values: What does this tell us that MFE doesn’t?

45. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 45 Example What is the MFE? The MAD? Interpret!

46. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 46 MFE and MAD: A Dartboard Analogy Low MFE and MAD: The forecast errors are small and unbiased

47. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 47 An Analogy (continued) Low MFE, but high MAD: On average, the arrows hit the bulls eye (so much for averages!)

48. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield Chapter 9, Slide 48 An Analogy (concluded) High MFE and MAD: The forecasts are inaccurate and biased