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3. Forecasting

3. Forecasting. Homework problems : 2,4,5,6,7,11,12,14. . 3.1. Providing Appropriate Forecast Information.

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3. Forecasting

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  1. 3. Forecasting Homework problems: 2,4,5,6,7,11,12,14.

  2. 3.1. Providing Appropriate Forecast Information • The forecasting process involves much more than just the estimation of future demand. The forecast also needs to take into consideration the intended use of the forecast, the methodology for aggregating and disaggregating the forecast, and assumptions about future conditions. • Selection of an appropriate forecast method is determined by different levels of aggregation, cost of data acquisition and processing, length of forecast (timeframe), top management involvement, forecast frequency, etc. Figure 3.1

  3. 3.1. Forecast Information • The forecast information and technique must match the intended application: • For strategic decisions such as capacity or market expansion highly aggregated estimates of general trends are necessary. • Sales and operations planning (SOP) activities require more detailed forecasts in terms of product families and time periods. • Master production scheduling (MPS) and control demand highly detailed forecasts, which only need to cover a short period of time.

  4. 3.1.1 Forecasting for Strategic Business Planning • Forecast is presented in general terms (sales dollars, tons, hours) • Aggregation level may be related to broad indicators (gross national product (GNP), income) • Causal models and regression/correlation analysis are typical tools • Managerial insight is critical and top management involvement is intense • Forecast is generally prepared annually and covers a period of years

  5. 3.1.2 Forecasting for Sales and Operations Planning • Forecast is presented in aggregate measures (dollars, units) • Aggregation level is related to product families (common family measurement) • Forecast is typically generated by summing forecasts for individual products. • Managerial involvement is moderate, and limited to adjustment of aggregate values • Forecast is generally prepared several times each year and covers a period of several months to a year.

  6. 3.1.3 Forecasting for MPS and Control • Forecast is presented in terms of individual products (units, not dollars) • Forecast is typically generated by mathematical procedures, often using software • Projection techniques are common • Assumption is that the past is a valid predictor of the future • Managerial involvement is minimal. • Forecast is updated almost constantly and covers a period of days or weeks.

  7. 3.2. Regression Analysis & Decomposition • Regression identifies a relationship between two or more correlated variables. • Linear regression is a special case where the relationship is defined by a straight line, used for both time series and causal forecasting. • Data should be plotted to see if they appear linear before using linear regression. • Y = a + bX • Y is value of dependent variable, a is the y-intercept of the line, b is the slope, and X is the value of the independent variable.

  8. 3.2 Least Squares Method Y – calculated dependent variable value yi – actual dependent variable point a – y intercept b – slope of the line x – time period • Objective–find the line that minimizes the sum of the squares of the vertical distance between each data point and the line Y = a + bx See Fig. 3.2

  9. Least Squares Regression Line (Fig.3.2) Regression errors are the vertical distance from the point to the line

  10. Least Squares Equation (3.3) Or

  11. Least Squares Example (Fig. 3.3)

  12. Least Squares Example (Fig. 3.2)

  13. Least Squares Example Standard Error of Estimate (Syx) – how well the line fits the data =363.9

  14. Regression Using Excel

  15. Time Series Decomposition

  16. Seasonality • Seasonality may or may not be relative to the general demand trend • Additive seasonal variation is constant regardless of changes in average demand • Multiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case)

  17. Seasonality • Additive seasonal variation is constant regardless of changes in average demand • Forecast=Trend + Seasonal • Multiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case) • Forecast= Trend x Seasonal factors

  18. Seasonal Factor/Index • To account for seasonality within the forecast, the seasonal factor/index is calculated. • The amount of correction needed in a time series to adjust for the season of the year

  19. Seasonal Factor/Index • If we expect (forecast) next year’s sales to be 1,100 units, the seasonal forecast is calculated using the seasonal factors:

  20. Seasonality–Trend and Seasonal Factor Estimate of trend, use linear regression software to obtain more precise results Trend = 170 +55t

  21. Seasonality–Trend and Seasonal Factor • Seasonal factors are calculated for each season, then averaged for similar seasons • Seasonal Factor = Actual/Trend

  22. Seasonality–Trend and Seasonal Factor • Forecasts for 2010 are calculated by extending the linear regression and then adjusting by the appropriate seasonal factor • FITS–Forecast Including Trend and Seasonal Factors

  23. Decomposition Using Least Squares Regression • Decompose the time series into its components • Find seasonal component • Deseasonalize the demand • Find trend component • Forecast future values for each component • Project trend component into future • Multiply trend component by seasonal component

  24. Decomposition Using Least Squares Regression Calculate average of same period values

  25. Decomposition Using Least Squares Regression Calculate seasonal factor for each period

  26. Decomposition Using Least Squares Regression Use linear regression to fit trend line to deseasonalized data Y= 555.0 + 342.2x

  27. Create Forecast by Projecting Trend and Reseasonalizing Project Linear Trend Project Seasonality Y= 555.0 + 342.2x

  28. 3.3. Short-term Forecasting Technique Some basic concepts: • dependent/independent demand • aggregate/disaggregate demand • long-term/short-termforecast (regression and correlation vs. smoothing out the random fluctuations) The underlying assumption of time series models is that the future values of the time series can be predicted based upon previous time series values (i.e., past conditions that produced the historical data won’t change !) The need for some forecasting techniques (Fig. 3.11) What’s wrong with drawing a line (i.e., use the regular averaging process)?

  29. 3.3. Short-term Forecasting Techniques Moving Average: Q: what n to use? large or small (longer or shorter)? Q: Drawback of (simple) moving average? Weighted Moving Average: Example. Use weighted moving average with weights of 0.1, 0.2, and 0.3 to forecast demand for period 33. Sol:

  30. 3.3. Short-term Forecasting Techniques Exponential Smoothing Forecasting (ESF): ESFt = ESFt-1+ α(actual demand t – ESFt-1) …….. (3.6) =α(actual demand t ) + (1- α) ESFt-1 …….. (3.7) where: α= the proportion of the forecast error, under or over estimate, that will be incorporated into (next) forecast (i.e., smoothing constant). ESFt-1 = Exp. smoothing forecast made at the end of period t-1 = Exp. smoothing forecast for period t

  31. 3.3. Short-term Forecasting Techniques Exponential Smoothing Forecasting (ESF): Q: Why is it called “exponential” smoothing? Proof Q: What happens when α=0 or α=1? Q: what αvalue to use? Small or large and the effects.

  32. 3.3. Short-term Forecasting Techniques Bias = Σ(actual demandi – forecast demand i) /n • Bias (mean error) measures consistently high or low forecast MAD = Σ|actual demandi – forecast demand i| /n MSE= • MAD (mean absolute deviation) measures the magnitude of forecast error • What is a good (ideal) forecast? • Which (Bias or MAD) is more critical? • When the forecast errors are normally distributed, the standard deviation of forecast errors = 1.25 MAD

  33. 3.3. Some Insights • Focus forecasting: uses the one forecasting model that would have performed the best in the recent past to make the next forecast. • Simple models usually outperform more complex methods, especially for short-term forecasting. • There is no one model that would consistently outperform all the others. • It might be a good idea to average the forecasts from several models used in each period (combination technique).

  34. 3.4. Using the Forecasts Aggregating Forecasts: • Long-term or product-line forecasts are more accurate than short-term or detailed forecasts. • Theorem: Suppose that X and Y are independent random variables with normal distribution N(μ1, σ12) and N(μ2, σ22), respectively. Let Z=X + Y, then Z is a normal distribution N(μ1+ μ2,σ12+σ22). • Application: Figure 3.17

  35. 3.4. Using the Forecasts Pyramid Forecasting: • To coordinate, integrate, and assure (force) consistency between forecasts prepared in different parts/levels of the organization and company goals or constraints. Figs. 18~20. Incorporating External Information: • Change the forecast directly, if we know the activities that will influence demand for sure. e.g., promotions, product changes, competitor’s action, etc. • Change the forecast model, if we are not sure of the impact of the activities. e.g., use larger α to be more responsive to demand change.

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