The Importance of Forecasting in POM Chapter 3 The Importance of Forecasting in POM

Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases I see that you will get an A this semester.

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

The Importance of Forecasting in P.O.M

Factors Influencing Demand Business Cycle Product Life Cycle Testing and Introduction Rapid Growth Maturity Decline Phase Out

Factors Influencing Demand Other Factors Competitor’s efforts and prices Customer’s confidence and attitude

Who makes the sales forecast? Sales Personnel 32% Marketing Personnel 29%

Reliance on Forecasting

A Classification of Forecasting Methods:

Judgmental Forecasts Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method Opinions of managers and staff Achieves a consensus forecast

Statistical Forecasting: Time Series Model

Time Series Forecasting -- using the Past to Develop Future Estimates

Time Series Forecasts Trend - long-term movement in data Seasonality - short-term regular variations in data Cycle – wavelike variations of more than one year’s duration Irregular variations - caused by unusual circumstances Random variations - caused by chance

Forecast Variations Trend Cycles Irregular variation 90 89 88 Seasonal variations

Naive Forecasts Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell.... The forecast for any period equals the previous period’s actual value.

Naïve Forecasts Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy

Uses for Naïve Forecasts Stable time series data F(t) = A(t-1) Seasonal variations F(t) = A(t-n) Data with trends F(t) = A(t-1) + (A(t-1) – A(t-2))

Short Run Forecasts Moving Average Method Exponential Smoothing

Moving Average Method This method consists of computing an average of the most recent n data values in the time series. This average is then used as a forecast for the next period. Moving average =  (most recent n data values) n Moving average usually tends to eliminate the seasonal and random components.

Moving Average Method The larger the averaging period, n, the smoother the forecast. The ultimate selection of an averaging period would depend upon management needs.

Simple Moving Average Actual MA5 MA3 High AP forecast has a low impulse response and a high noise dampening ability.

Weighted Moving Average Method Weighted moving average – More recent values in a series are given more weight in computing the forecast.

Exponential Smoothing It is a forecasting technique that uses a smoothed value of time series in one period to forecast the value of time series in the next period. The basic model is as follows: Ft+1 = aYt + (1-a)Ft Where: Ft+1= the forecast of time series for period t+1 Yt = the actual value of the time series in period t Ft = the forecast of time series for period t a = the smoothing constant 0£a£1

Example 3 - Exponential Smoothing F2 = F1+.1(A1-F1) = 42+.1(42-42) = 42 F3 = F2+.1(A2-F2) = 42+.1(40-42) = 41.8

Week 8 102 85.0 17.0 85.0 17.0 9 110 86.7 23.3 88.4 21.6 90.1 19.9 10 90 89.0 1.0 92.7 2.7 96.1 6.1 11 105 89.1 15.9 92.2 12.8 94.3 10.7 12 95 90.7 4.3 94.8 .2 97.5 2.5 13 115 91.1 23.9 94.8 20.2 96.8 18.2 14 120 93.5 26.5 98.8 21.2 102.3 17.7 15 80 96.2 16.2 103. 23. 107.6 27.6 16 94.6 .4 98.4 3.4 99.3 4.3 17 100 94.6 5.4 97.7 2.3 98.0 2.0 Total Errors 133.9 124.4 126 Actual Demand Forecasts a = .1 a = .2 a = .3 Forecast Error Forecast Error Forecast Error MAD=13.39 MAD=12.44 MAD=12.60 The smoothing constant a = .2 gives slightly better accuracy when compared to a = .1, and a = .3.

Picking a Smoothing Constant  .1 .4 Actual

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 Mean Absolute Percent Error (MAPE) Average absolute percent error

MAD, MSE, and MAPE  Actual  forecast MAD = n MSE = Actual forecast) - 1 2   n ( MAPE = Actual forecast  n / Actual*100) (

Example 10

Controlling the Forecast Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are present

Sources of Forecast errors Model may be inadequate Irregular variations Incorrect use of forecasting technique

Tracking Signal  Tracking signal = (Actual - forecast) MAD Ratio of cumulative error to MAD Tracking signal = (Actual - forecast) MAD  Bias – Persistent tendency for forecasts to be Greater or less than actual values.

Common Nonlinear Trends Parabolic Exponential Growth

Trend Projection

Trend Projection  (t – Ft)2 The approach used to determine the linear function that best approximates the trend is the least – squared method. The objective is to determine the value of a and b that minimize:  (t – Ft)2 Where: t = actual value of time series in period Ft = forecast value in period t n = number of period n t=r

Linear Trend Equation Ft = a + bt Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line

Calculating a and b b = n (ty) - t y 2 ( t) a 

Linear Trend Equation Example

Linear Trend Calculation y = 143.5 + 6.3t a = 812 - 6.3(15) 5 b 5 (2499) 15(812) 5(55) 225 12495 12180 275 6.3 143.5

Casual Forecasting Models Regression Correlation Coefficient Coefficient of Determination Multiple Regression Autogressive Model Stepwise Regression

Associative Forecasting Regression - technique for fitting a line to a set of points Least squares line - minimizes sum of squared deviations around the line

Causal Forecasting Models (Regression) Regression analysis is a statistical technique that can be used to develop an equation to estimate mathematically how two or more variables are related. Y = bo + b1x b1 = n xy – x y n x2 – ( x)2 bo = y - b1x     

Linear Model Seems Reasonable Computed relationship A straight line is fitted to a set of sample points.

Correlation Coefficient The coefficient of correlation, r, explains the relative importance of the association between y and x. The range of r is from -1 to +1. r = n xy - x y______________  [ n x2 – ( x)2][n y2 -( y)2] Although the coefficient of correlations is helpful in establishing confidence in our predictive model, terms such as strong, moderate, and weak are not very specific measures of a relationship.       

Coefficient of Determination The coefficient of determination, r2, is the square of the coefficient of correlation. This measure indicates the percent of variation in y that is explained by x.

Multiple Regression Multiregression analysis is used when two or more independent variables are incorporated into the analysis. In forecasting the sale of refrigerators, we might select independent variable such as: Y= annual sales in thousands of units X1 = price in period t X2 = total industry sales in period t-1 X3 = number of building permits for new houses in period t-1

Multiple Regression X4 = population forecast for period t X5 = advertising budget for period t Y = bo +b1X1+b2X2+b3X3+b4X4+b5X5

Autogressive Models Regression models where the independent variables are previous values of the same time series Yt = bo+b1Yt-1+b2Yt-2+b3Yt-3

Stepwise Regression In regular multiple regression analysis, all the independent variables are entered into the analysis concurrently. In stepwise regression analysis, independent variables will be selected for entry into the analysis on the basis of their explanatory (discriminatory) power.

Choosing a Forecasting Technique No single technique works in every situation Two most important factors Cost Accuracy Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon

Exponential Smoothing

Linear Trend Equation

Simple Linear Regression