Topic 5 Forecasting Models

1. Topic �5Forecasting Models

2. FORECASTING Forecasting vs. Prediction: Forecasting: Estimating future by casting forward from past data. Prediction: Estimating future based on any subjective consideration other than just past data. Three Time Ranges of Forecasting: Long Range Forecasting (over 1 years) Intermediate Range Forecasting (6 - 12 months) Short Range Forecasting (less than 6 months)

3. Some Examples of Things That Must Be Forecasted in POM

4. FORECASTING What to Forecast: Demand/Price/Wage/Supply/Labor/Sales/... Economic Growth/Technology Development/.... Impact of Inaccurate Forecasting: (If Plans are based on your Forecasting) If Forecasting is Consistently Higher than Actual: If Forecasting is Consistently Lower than Actual:

7. Forecasting Techniques Qualitative Approach: Delphi Methods (Expert's Subjective Rating) Marketing Research and Analysis (Customer Survey) Historical Analogy (Knowledge of similar products) .................. Quantitative Approach: (Two General Techniques) Time Series Models: Simple Moving Average Weighted Moving Average Exponential Smoothing (Simple/Adaptive/....) Causal Relationship Models: Regression Analysis Linear vs. Non-Linear Single vs. Multi-variable Econometric Models

8. Selection of Forecasting Techniques Principle of Forecasting: When past data (independent variables) are good indicators of the future of dependent variables. Factors in Selecting Forecasting Methods: Data Availability Cost & Accuracy Tradeoff Time Horizon

9. Selection of Forecasting Techniques Qualitative Techniques: (Subjective) Used when: Data Unavailable Unknown Pattern Change (Examples: Sales of New Product/Technological Changing/..) Quantitative Techniques: (Objective) Time Series Models: Used when the most recent past data are good indicators (e.g., short range forecasting for scheduling). Causal Relationship Models: Used when dependent variables are close related to some underlying factors. (e.g., intermediate range forecasting of sales)

12. Qualitative Approach: Subjective and Judgmental Used when data are unavailable Used when future events are known Used for long range forecasts of new products sales, Technological change, and long-range predictions

13. Time-Series Analysis Objective and Quantitative Uses past data to project the future Used for short range forecast for operations, production and inventory planning and control

14. Casual Relationships Objective and Quantitative Assumes that demand is related to some underlying factor(s) in the environment Requires knowledge of relationships among variables Substantial data needed Used for short and medium range forecasts of existing products, sales, margins, other financial data

16. Eight Steps to Forecasting Determine the use of the forecast- what objective are we trying to obtain? Select the item or quantities that are to be forecasted. Determine the time horizon of the forecast- is it 1-10 days (short term), one moth to one year (medium term), or more than one year (long term)? Select the forecasting model or models. Gather the data needed to make the forecast. Validate the forecasting model. Make the forecast. Implement the results.

17. Basic Time-Series Forecasting Models 1. Simple Moving Average: Given Number of Periods (n) to be averaged. Ft = (?i Ai)/n = (At-1 + At-2 + �.. At-n)/n 2. Weighted Moving Average: Given (n) and Weights (wi) Ft = (?i wi ?Ai) = (wt-1?At-1 + wt-2?At-2 + �.. wt-n?At-n)

18. Basic Time-Series Forecasting Models 3. Simple Exponential Smoothing: Given a (smooth Constant). Ft = Ft-1 + a?(At-1 � Ft-1) = a?At-1 + (1 � a)Ft-1 The determination of (n), (wi), and (a) must be based on the analysis of the patterns to be forecasted (e.g., smooth vs. sharp, or stable vs. variation).

19. Exercise-1Supplement p.5-21

20. Exercise #1 Assume that your stock of merchandise is maintained based on the forecast demand. If the distributor�s sales personnel call on the first day of each month, compute your forecast sales by each of the three methods requested here.

21. b) Using a weighted moving average, what is the forecast for September with weights of 0.20, 0.30, and 0.50 for June, July and August, respectively? W1= 0.5; W2= 0.3; W3= 0.2 F9= 170(0.5) + 180(0.3) + 140(0.2) = 167

22. c) Using simple exponential smoothing and assuming that the forecast for June had been 130, calculate the forecast for September with a smoothing constant alpha of 0.30. F6= 130, 2= 0.3 F7= F6+ 2(At �F6)= 130+0.3(140-130) =133 F8 =133+0.3(180-133)=147.10 F9 =149.1+0.3(170-147.10)=154

23. Note : the determination of (n), (wi), and a must be based on the analysis of the pattern to be forecasted (e.g., smooth vs. sharp, or stable vs. variation) How to determine n? (small vs. large) How to select wi? (even vs. uneven) (subjective) How to select a? (small vs. large) Relationship the three above are basically the same � just an extension of one to another. Basic time-series forecasting

24. Weighting of Past Data in Exponential Smoothing

28. Exponential Smoothing Weights

29. Time-Series MethodsSimple Moving Averages And this adds the 6-week moving average which would be derived in the same fashion. And this adds the 6-week moving average which would be derived in the same fashion.

30. Time-Series MethodsExponential Smoothing Just for discussion, we have added in the 3 and 6-week moving average forecasts developed earlier in the Chapter.Just for discussion, we have added in the 3 and 6-week moving average forecasts developed earlier in the Chapter.

32. Forecasting Error Measurement Forecasting Error in (t): Et = (At - Ft) 2. Bias (Mean Error): Bias = ? (Et)/n = ? (At � Ft)/n (Bias is a measure of the direction of forecasting error) 3. MAD (Mean Absolute Deviation): MAD = ? | (At � Ft)| /n (MAD is a measure of the size of forecasting error regardless of the direction) 4. Track Signal (TS): TS = Bias/MAD (-1 < TS < 1) (TS is a measure of forecasting error including both Direction and Size.) 5. Other Measures

33. Choosing a MethodTracking Signals This slide completes Figure 13.9 and shows the use of a tracking signal.This slide completes Figure 13.9 and shows the use of a tracking signal.

34. Exercise #2

35. b) If the forecasts for period 1 to period 9 were 30, 35, 42, 42, 40, 50, 53, 61, 59, respectively, determine the bias, MAD and tracking signal. How would you improve the forecasting accuracy in this situation?

36. Elements of Time Series Analysis

39. Elements of Time Series Analysis Base Level: (B) Demand at Time = 0 Trend (Linear): (T) General Direction of Demand Growth Seasonal Effects: (S) Pattern that repeat every year (quarter/..) Cyclical Effects: (C) Pattern that Repeat other than a Year. Random Errors: (R) Errors resulting from unpredictable events.

40. Historical Product Demand Consisting of a Growth Trend, Cyclical Factor, and Seasonal Demand

41. Trend Patterns in Time Series Data

42. Advanced Time Series Models(Base, Trend, Seasonal, and Cyclical Effects) 1) Base Level Model: (no Trend/Seasonal/Cyclical) Ft,k = Bt (forecast for the Kth period made at period t) Updating after At known. Bt = Bt-1 + a (At - Bt-1) 2) Base and Linear-Trend Model: (no Seasonal/Cyclical) Ft,k = Bt + K?Tt Updating after At known. Bt = (Bt-1 + Tt-1) + a?[At - (Bt-1 + Tt-1)] Tt = Tt-1 + �?[(Bt - Bt-1) - Tt-1)] � is the Trend Smooth Constant (0 < � < 1).

43. ExerciseSupplement p.5-22 to 5-25

44. Example: Base level Forecasting (p.5-22) At the end of February, Base value computed in January=95 units Forecast made in January for February and all other succeeding months=95 units The actual demand in February was 105 units Base smoothing constant=0.20

46. Advanced Time Series Models(Base, Trend, Seasonal, and Cyclical Effects) 3) Base and Seasonal Model: (no Trend/Cyclical) Ft,k = Bt?SIt+k Updating after At known. Bt = Bt-1 + a?(At/SIt+k - Bt-1) SIt+k = SIt+k + ??(At/Bt - SIt+k) ? is the Seasonal Smooth Constant (0 < ? < 1). 4) Base, Trend, and Seasonal Model: (no Cyclical) Ft,k = (Bt + k?Tt)?SIt+k Updating after At known. Bt = (Bt-1 + Tt-1) + a?[(At/SIt+k � (Bt-1 + Tt-1)) Tt = Tt-1 + �?[(Bt - Bt-1) - Tt-1)] SIt+k = SIt+k + ??(At/Bt - SIt+k) (a, �, and ? , three Smooth Constants in this model.)

47. Example: Trend Forecasting (p.5-23) At the and of June (Month 6) The base value computed in June was 100 units. The trend value computed in June was 2 units. The smoothing constants for Base level and trend are 0.20 and 0.10, respectively

49. Decomposition of Various Effects from a given Data Set: F = (B + T)*S*C + R Measuring Trend Separate Cyclical Effect Separate Seasonal Effect Calculate Random Errors

50. The Decomposition Process

51. Example: Trend and Seasonal Forecasting Current Month is June(Month 6) The base level computed in June was 300 units per month The trend value computed in June was 4 units per month Parameters: a=0.10 �=0.20 ?=0.30 Given: Listed below are the monthly current values of the seasonal index:

52. Compute the forecast for July (Month 7), August (Month 8) and September (Month 9). Update the Base value. Update the trend value.

53. d) Update the July seasonal factor. e) Compute the new forecasts made in July for August (Month 8) and September (month 9).

55. Regression Forecasting Models In many cases, the Demand (to be forecasted) is dependent more upon some leading factors (independent variables) other than the time and past data. Regression Forecasting Models are developed for those situations based on Least-Square method. 1. Linear Regression Models: (Simple vs Multiple) Y = a + b1?X1 + b2?X2 + ...... + bn?Xn When n=1, it becomes the Simple Regression Model, Y = a + b?X (a: Intercept, b: Slope)

56. Examples of Various Values of the Correlation Coefficient

57. Regression Forecasting Models 2. Non-Linear Regression Models: (no general model) Y = a + b1?X1 + b2?X21, or Y = �(X1, X2, X3, .....) Other Applications of Regression Analysis: Social Science Study (Literature/Art/Physiology/....) All statistical studies concerning the relationships between two or more factors and How the relationships can be explained.

59. Formulation of Regression Models 1. Determine Dependent Variable (Y) (what to be forecasted) and Independent Variables (X's) (what believed be major indicators). 2. Collect sample data of all related variables. 3. Plot the data (scatter diagram) to show possible patterns of relationship. 4. Select an appropriate regression model that best fits the pattern. 5. Compute the coefficients of the model (various methods) and construct forecasting equations of the model. 6. Evaluate the model (fitness) by measuring the correlation (R) between Y and X's and standard deviations (SD). 7. Validate the model by testing the assumptions underlying the model through Residual Error (ei) Analysis.

60. Formulation of Regression Models Assumptions underlying Simple Regression Model: Linearity of ei ( ei = Yi - Yi) Homogeneity of ei Independence of ei. Normality of ei.

61. Practical Forecasting Problems Practical Forecasting Issues: Inaccuracy Inconsistency Cost and Accuracy Tradeoff (Simple model may perform better than complicated ones.) Data Unavailability Fitness and Predictability (A model best "fit" the past data may not be best "predictive" for the future, due to a pattern change.)

62. Practical Forecasting Problems New Direction in Forecasting: Integrated (pyramid) Forecasting Systems (reduce inconsistency) Combinational Forecasting Models: (reduce inaccuracy) Model Combination Forecasting Result Combination

63. Using QM-Windows Software to do Forecasting Problems.Supplement p.5-27Problem #2, #3

64. Written Assignment-3 is due..