Chapter 13 Forecasting Topics Components of Forecasting Time

Chapter 13 Forecasting

Topics § Components of Forecasting § Time Series Methods § Accuracy of Forecast § Regression Methods

Components of Forecasting § Many forecasting methods are available for use § Depends on the time frame and the patterns § Time Frames: § § § Short-range (one to two months) Medium-range (two months to one or two years) Long-range (more than one or two years) § Patterns: § § Trend Random variations Cycles Seasonal pattern

Forecasting Components: Patterns • Trend: A long-term movement of the item being forecast • Random variations: movements that are not predictable and follow no pattern • Cycle: A movement, up or down, that repeats itself over a time span • Seasonal pattern: Oscillating movement in demand that occurs periodically and is repetitive

Forecasting Components: Forecasting Methods • Times Series (Statistical techniques) – Uses historical data to predict future pattern – Assume that what has occurred in the past will continue to occur in the future – Based on only one factor - time. • Regression Methods – Attempts to develop a mathematical relationship between the item being forecast and the involved factors • Qualitative Methods – Uses judgment, expertise and opinion to make forecasts

Forecasting Components: Qualitative Methods • Called jury of executive opinion • Most common type of forecasting method for long-term • Performed by individuals within an organization, whose judgments and opinion are considered valid • Includes functions such as marketing, engineering, purchasing, etc. • Supported by techniques such as the Delphi Method, market research, surveys, etc.

Time Series: Techniques • • • Moving Average Weighted Moving Average Exponential Smoothing Adjusted Exponential Smoothing Linear Trend

Moving Average • Uses values from the recent past to develop forecasts • Smoothes out random increases and decreases • Useful for stable items (not possess any trend or seasonal pattern • Formula for:

Revisit of 3 -Month and 5 -Month • Longer-period moving averages react more slowly to changes in demand • Number of periods to use often requires trial-and-error experimentation • Moving average does not react well to changes (trends, seasonal effects, etc. ) • Good for short-term forecasting.

Weighted Moving Average • Weights are assigned to the most recent data. • Determining precise weights and number of periods requires trial-and-error experimentation • Formula:

Exponential Smoothing: Simple Exponential Smoothing • Weights recent past data more strongly • Formula: Ft + 1 = Dt + (1 - )Ft where: Ft + 1 = the forecast for the next period Dt = actual demand in the present period Ft = the previously determined forecast for the present period = a weighting factor (smoothing constant) • Commonly used values of are between. 10 and. 50 • Determination of is usually judgmental and subjective

Comparing Different Smoothing Constants • Forecast that uses the higher smoothing constant (. 50) reacts more strongly to changes in demand • Both forecasts lag behind actual demand • Both forecasts tend to be lower than actual demand • Recommend low smoothing constants for stable data without trend; higher constants for data with trends

Exponential Smoothing: Adjusted § Exponential smoothing with a trend adjustment factor added § Formula: A Ft + 1 = Ft + 1 + Tt+1 where: T = an exponentially smoothed trend factor Tt + 1 + (Ft + 1 - Ft) + (1 - )Tt Tt = the last period trend factor = smoothing constant for trend (between zero and one) § Weights are given to the most recent trend data and determined subjectively § Forecast is higher than the simple exponentially smooth § Useful for increasing trend of the data

Linear Trend Line § When demand displays an obvious trend over time, a linear trend line, can be used to forecast § Does not adjust to a change in the trend § Formula: Y= a+ b x

Seasonal Adjustments § Seasonal pattern is a repetitive up-and-down movement in demand § Can occur on a monthly, weekly, or daily basis. § Forecast can be developed by multiplying the normal forecast by a seasonal factor § Seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand: § lies between zero and one Si =Di/ D

Forecast Accuracy Overview § Forecasts will always deviate from actual values § Difference between forecasts and actual values referred to as forecast error § Like forecast error to be as small as possible § If error is large, either technique being used is the wrong one, or parameters need adjusting § Measures of forecast errors: § § Mean Absolute deviation (MAD) Mean absolute percentage deviation (MAPD) Cumulative error (E bar) Average error, or bias (E)

Forecast Accuracy: Mean Absolute Deviation § MAD is the average absolute difference between the forecast and actual demand. § Most popular and simplest-to-use measures of forecast error. § Formula: § The lower the value of MAD, the more accurate the forecast § MAD is difficult to assess by itself § Must have magnitude of the data

Mean Absolute Deviation § A variation on MAD § Measures absolute error as a percentage of demand rather than period § Formula:

Cumulative Error § § § Sum of the forecast errors (E = et). A large positive value indicates forecast is biased low A large negative value indicates forecast is biased high Cumulative error for trend line is always almost zero Not a good measure for this method

Regression Methods Overview § Time series techniques relate a single variable being forecast to time. § Regression is a forecasting technique that measures the relationship of one variable to one or more other variables. § Simplest form of regression is linear regression.

Regression Methods Linear Regression § Linear regression relates demand (dependent variable ) to an independent variable.

Regression Methods: Correlation § Measure of the strength of the relationship between independent and dependent variables § Formula: § Value lies between +1 and -1. § Value of zero indicates little or no relationship between variables. § Values near 1. 00 and -1. 00 indicate strong linear relationship.

Regression Methods: Coefficient of Determination § Percentage of the variation in the dependent variable that results from the independent variable. § Computed by squaring the correlation coefficient, r. § If r =. 948, r 2 =. 899 § Indicates that 89. 9% of the amount of variation in the dependent variable can be attributed to the independent variable, with the remaining 10. 1% due to other, unexplained, factors.

Multiple Regression § Multiple regression relates demand to two or more independent variables. General form: y = 0 + 1 x 1 + 2 x 2 +. . . + kxk where 0 = the intercept 1. . . k = parameters representing contributions of the independent variables x 1. . . xk = independent variables