Forecasting

1. Forecasting Y.-H. Chen, Ph.D. Production / Operations Management International College Ming-Chuan University

2. Forecasting Outline • Introduction • Forecasting Process • Forecasting Methods • Forecast Accuracy and Control • Forecast Method Selection and Usage

3. I see that you willget an A this semester. Introduction A forecast • is a statement of future, • is a basis for planning, • is not for forecasting demand only, • requires a skillful blending of art and science, • assumes that the underlying system will continue to exist in the future, and • is rarely perfect.

4. “The forecast” Step 6 Monitor the forecast Step 5 Prepare the forecast Step 4 Gather and analyze data Step 3 Select a forecasting technique Step 2 Establish a time horizon Step 1 Determine purpose of forecast Forecasting Process

5. Elements of A Good Forecast • The forecast horizon must cover the time necessary to implement possible changes. • The degree of accuracy should be stated. • The forecast should be reliable; it should work consistently. • The forecast should be expressed in meaningful units. • The forecast should be in writing. • The forecast should be simply to understand and use, or consistent with historical data intuitively.

6. Timely Accurate Reliable Easy to use Written Meaningful Additional Properties • Forecasts for groups of items tend to be more accurate than forecasts for individual items, because forecasting errors among items in a group usually have a canceling effect. • Forecast accuracy decreases as the time period covered by the forecast increases.

7. Forecasting Methods • Basic Methods • Judgmental Forecast • Statistical (Time Series) Forecast • Trend • Seasonality • Cycle • Association

8. Basic Forecasting Methods • Judgmental Forecast • Statistical (Time Series) Forecast • Averaging • Weighted Moving Average • Exponential Smoothing

9. Judgmental Forecast Executive opinions. Mostly for long-range planning and introduction of new products. The view of one person may prevail. Direct customer contact composites. • Unable to distinguish between what customers would like to do and what they will actually do. • Could overly influenced by recent sales experiences. Low sales could lead to low estimates. • Conflict of interest. Low sales estimates lead to better sales performance. Consumer survey or point-of-sales (POS) data. • Expensive and time-consuming. • Possible existence of irrational patterns. • Low response rates. Opinions of managers and staff. Delphi method (Rand Corp., 1948): Managers and staff complete a series of questionnaires, each developed from the previous one, to achieve a consensus forecast. Technological forecasting. Long-term single-time forecasting. Data are costly to obtain.

10. Statistical (Time Series) Forecast • It is extremely important to plot data and examine them before doing any analysis or forecast. A demand forecast should be based on a time series of past demand rather than sales or shipment. Data patterns: Trend A long term upward or downward movement in data. Seasonality Short-term regular variations related to weather, holiday, or other factors. Cycle Wavelike variation lasting more than one year. Irregular Variation Caused by unusual circumstances, not reflective of typical behavior. Random variation Residual variation after all other behaviors are accounted for.

11. Data Patterns Irregularvariation Trend Cycles 90 89 88 Seasonal variations

12. Simple Naive Forecast • No cost. • Quick and easy to prepare. • Easy to understand. • Can be applied to data with seasonality and trend

13. General Naive Forecast

14. Weighted Moving Average

15. 39 Moving Average Example • Compute a 3-period moving average forecast given demand for shopping carts for the last five periods. • If the actual demand in period 6 turns out to be 39, what would be the moving average forecast for period 7? 41.33 40.00

16. 39 Weighted Moving Average Example • Compute a weighted average forecast using a weight of .40 for the most recent period, .30 for the next most recent, .20 for the next, and .10 for the next. • If the actual demand in period 6 turns out to be 39, what would be the weighted moving average forecast for period 7? 41.0 40.2

17. Properties of Weighted Moving Average • Easy to compute and understand. • Moving average forecast lags and smoothens the actual forecast. • The number of data points in the average determines its sensitivity to each new data point: the fewer the data points in an average, the more responsive the average tends to be. • Weights can be added to values in the average to make the resulting average more responsive to some recent data points. However, weights involve the use of trial-and-error to find suitable weights.

18. Exponential Smoothing • Exponential smoothing is a weighted averaging method based on previous forecast plus a percentage of its forecast error.

19. Properties of Exponential Smoothing • Commonly used values of alpha range from 0.05 to 0.50. Low values are used when the underlying average tends to be stable; higher values are used when the underlying average is susceptible to change. • Moving average or naive forecast can be used to generate starting forecast for exponential smoothing.

20. Picking A Smooth Constant

21. Exponential Smoothing Example Use exponential smoothing to develop a series of forecasts for the data, and compute (actual-forecast)=error for each period. • Use a smoothing factor of .10. • Use a smoothing factor of .40. • Plot the actual data and both sets of forecasts on a single graph.

22. Exponential Smoothing Example

23. Forecasting Method Extension • Trend • Linear Trend • Trend-Adjusted Exponential Smoothing • Seasonality • Cycle • Association

24. Linear Trend

25. Linear Trend Coefficients

26. Linear Trend Example Calculate sales for a California-based firm over the last 10 weeks are shown in the table. Plot the data and visually check to see if a linear trend line would be appropriate. Then, determine the equation of the trend line, and predict sales for weeks 11 and 12.

27. Linear Trend Example Solution a. A plot suggests that a linear trend line would be appropriate. b. For n=10, we have Thus, the trend line is yt=699.40+7.51t, where t=0 for period 0. c. By letting t=11 and t=12, we have

28. Seasonality

29. Cycle • Cycles are similar to seasonal variations but of longer duration, e.g., two to six years between peaks. • It is difficult to project cycles from past data, because turning points are difficult to identify. • A short moving average or a naive approach may be of some value.

30. Associative Forecasts • High correlation of a forecast with leading variables can be useful in computing the forecast. • The simple linear regression is the simplest and most widely used method.

31. Simple Linear Regression Coefficients

32. Simple Linear Regression Example Healthy Hamburgers has a chain of 12 stores in northern Illinois. Sales figures and profits for the stores are given in the following table. Obtain a regression line for the data and predict profit for a store assuming sales of $10 million.

33. Simple Linear Regression Example: Data Plot

34. Simple Linear Regression Example: Solution

35. An Important Measure of Simple Linear Regression • Correlation measures the strength and direction of the relationship between two variables. • +1, positive correlation. • -1, negative correlation. • 0, zero correlation. • The square of the correlation coefficient provides a measure of how well a regression line “fits” the data. The values ranges from 0 to 1.00. • [0.80,1.00], good fit. • [0.25,0.80), moderate fit. • [0.00,0.25), poor fit.

36. Simple Linear Regression and Correlation Example Sales of 19-inch color television sets and 3-month lagged unemployment are shown in the table below. Determine if unemployment levels can be used to predict demand for 19-inch color TVs and, if so, derive a predictive equation.

37. Simple Linear Regression and Correlation Example: Data Plot

38. Simple Linear Regression and Correlation Example: Solution

39. Linear Regression Assumptions • No patterns such as cycles or trends should be apparent. • Deviations around the line should be normally distributed. • Predictions are best being made within the range of observed values.

40. Linear Regression Usage Guidelines • Always plot the data to verify that a linear relationship is appropriate. • The data may be time-dependent. If patterns appear, use analysis of time series or use time as an independent variable as part of a multiple regression analysis. • A small correlation may imply that other variables are important.

41. Linear Regression Summary • Simple linear regression applies only to linear relationship with one independent variable. • One needs a considerable amount of data to establish the relationship --- in practice, 20 or more observations. • All observations are weighted equally.

42. Forecast Accuracy • Error - difference between actual value and predicted value • Mean absolute deviation (MAD) • Average absolute error • Mean squared error (MSE) • Average of squared error

43.   Actual forecast MAD = n 2 ( Actual  forecast)  MSE = n - 1 Forecast Accuracy:MAD & MSE Example 10 (page 97).

44. Forecast Control It is necessary to monitor forecast errors to ensure that the forecast is performing adequately over time. This is generally accomplished by comparing forecast errors to predefined values, or action limits.

45. Why Do We Need Forecast Control? • The omission of an important variable. • Appearance of a new variable. • A sudden or unexpected change in the variable (causing by severe weather or other nature phenomena, temporary shortage or breakdown, catastrophe, or similar events). • Being used incorrectly. • Data being misinterpreted. • Random variation.

46. Forecasting Control Methods • Tracking Signal • Control Chart

47. Forecast Control: Tracking Signal

48. Forecast Control: Control Chart • The control chart sets the limits as multiples of the squared root of MSE.

49. Forecast Control: Control Chart • For a normal distribution, 95% of the errors fall within +/-2s, and approximately 99.7% of the errors fall within +/-3s. Errors fall outside these limits should be regarded as evidence that corrective action is needed. Example 11 (Page 93).

50. Most important Cost Accuracy Need to consider Historical performance Ability to respond to change Forecast Method Selection