To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Forecasting

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Introduction Everyday, managers make decisions without knowing what will happen in the future. Inventory is ordered though no one knows what sales will be, new equipment is purchased though no one knows the demand for products, and investments are made though no one knows what profits will be. Managers are always trying to reduce this uncertainty and to make better estimates of what will happen in the future. Accomplishing this is the main purpose of forecasting. There are many ways to forecast the future. Regardless of the method that is used to make the forecast, the same eight overall procedures that follow are used.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Introduction Eight Steps to Forecasting 1.Determine the use of the forecast-what objective are we trying to obtain? 2.Select the items or quantities that are to be forecasted. 3.Determine the time horizon of the forecast-is it 1 to 30 days (short term), one month to one year (medium term), or more than one year (long term)? 4.Select the forecasting model or models. 5.Gather the data needed to make the forecast. 6.Validate the forecasting model. 7.Make the forecast. 8.Implement the results. These steps present a systematic way of initiating, designing, and implementing a forecasting system.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Introduction There is seldom a single superior forecasting method. One organization may find regression effective, another firm may use several approaches, and a third may combine both quantitative and subjective techniques. Whatever tool works best for a firm is the one that should be used.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Types of Forecasts Forecasting models can be classified into one of the three categories. These categories, shown in the next figure, are time- series models, Causal models, and qualitative models.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Moving Average Exponential Smoothing Trend Projections Time-Series Methods: include historical data over a time interval Forecasting Techniques No single method is superior Delphi Methods Jury of Executive Opinion Sales Force Composite Consumer Market Survey Qualitative Models : attempt to include subjective factors Causal Methods: include a variety of factors Regression Analysis Multiple Regression Decomposition

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Time-Series Models Time-series models attempt to predict the future by using historical data. These models make the assumption that what happens in the future is a function of what has happened in the past. In other words, time-series models look at what has happened over a period of time and use a series of past data to make a forecast. Thus, if we are forecasting weekly sales for lawn mowers, we use the past weekly sales for lawn mowers in making the forecast.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Causal Models Causal models incorporate the variables or factors that might influence the quantity being forecasted into the forecasting model. For example, daily sales of a cola drink might depend on the season, the average temperature, the average humidity, whether it is a weekend or a weekday, and so on. Thus, a causal model would attempt to include factors for temperature, humidity, season, day of the week, and so on. Causal models may also include past sales data as time- series models do.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Qualitative Models Whereas time-series and causal models rely on quantitative data, qualitative models attempt to incorporate judgment or subjective factors into the forecasting mode. Opinions by experts, individual experiences and judgments, and other subjective factors may be considered. Qualitative models are especially useful when subjective factors are expected to be very important or when accurate quantitative data are difficult to obtain.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Qualitative Models\continued Here is a brief overview of four different qualitative forecasting techniques: 1.Delphi method. This iterative group process allows experts, who may be located in different places, to make forecasts. There are three different types of participants in the Delphi process: decision makers, staff personnel, and respondents. The decision making group usually consists of five to ten experts who will be making the actual forecast. The staff personnel assist the decision makers by preparing, distributing, collecting, and summarizing a series of questionnaires and survey results. The respondents are a group of people whose judgments are valued and are being sought. This group provides inputs to the decision makers before the forecast is made.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Qualitative Models\continued 2.Jury of executive opinion. This method takes the opinions of a small group of high level managers, often in combination with statistical models, and results in a group estimate of demand. 3.Sales force composite. In this approach, each salesperson estimates what sales will be in his or her region; these forecasts are reviewed to ensure that they are realistic and are then combined at the district and national levels to reach an overall forecast. 4.Consumer market survey. This method solicits input from customers or potential customers regarding their future purchasing plans. It can help not only in preparing a forecast but also in improving product design and planning for new products.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Time-Series Forecasting Models A time series is based on a sequence of evenly spaced (weekly, monthly, quarterly, and so on) data points. Examples include weekly sales of IBM personal computers, quarterly earnings reports of Microsoft Corp. stock, daily shipments of Everyday batteries, and annual U.S. consumer price indices. Forecasting time-series data implies that future values are predicted only from past values and that other values, no matter how potentially valuable, are ignored. In the next slides, we will study two models of the time- series models, Exponential Smoothing and Trend Projections

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Moving Averages n Simple moving average =  demand in previous n periods Moving average methods consist of computing an average of the most recent n data values for the time series and using this average for the forecast of the next period.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Wallace Garden Supply’s Three-Month Moving Average Month Actual Sales Three-Month Moving Average January10 February12 March13 April16 May19 June23 July26 ( )/3 = 11 2 / 3 ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / 3

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Weighted Moving Averages Weighted moving averages use weights to put more emphasis on recent periods.  (weight for period n) (demand in period n) ∑ weights Weighted moving average =

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Calculating Weighted Moving Averages Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 3*Sales last month + 2*Sales two months ago + 1*Sales three months ago 6 Sum of weights

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Wallace Garden’s Weighted Three- Month Moving Average MonthActual Shed Sales Three-Month Weighted Moving Average January February March April May June July26 [3*13+2*12+1*10]/6 = 12 1 / 6 [3*16+2*13+1*12]/6 =14 1 / 3 [3*19+2*16+1*13]/6 = 17 [3*23+2*19+1*16]/6 = 20 1 / 2

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Exponential Smoothing Exponential smoothing is a forecasting method that is easy to use and is handled efficiently by computers. The basic exponential smoothing formula can be shown as follows: New forecast = previous forecast +  (previous actual – previous forecast) or: F t = F t-1 +  (A t-1 - F t-1 ) F t = new forecast F t-1 = previous forecast  = smoothing constant (that has a value between 0 and 1) A t-1 = previous period actual

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Exponential Smoothing The concept here is not complex. The latest estimate of demand is equal to our old estimate adjusted by a fraction of the difference between the last period's actual demand and the old estimate. Selecting the Smoothing Constant. The exponential smoothing approach is easy to use and has been applied successfully by banks, manufacturing companies, wholesalers, and other organizations. The appropriate value of the smoothing constant, , however, can make the difference between an accurate forecast and an inaccurate forecast. In picking a value for the smoothing constant, the objective is to obtain the most accurate forecast.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Exponential Smoothing The overall accuracy of a forecasting model can be determined by comparing the forecasted values with the actual or observed values. The forecast error is defined as Forecast error = demand – forecast One measure of the overall forecast error for a model is the mean absolute deviation (MAD). This is computed by taking the sum of the absolute values of the individual forecast errors and dividing by the number of periods of data (n): Mean Absolute Deviation = MAD =

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Example Let us apply this concept with a trial-and-error testing of two values of  in the following example. The port of Baltimore has unloaded large quantities of grain from ships during the past eight quarters. The port's operations manager wants to test the use of exponential smoothing to see how well the technique works in predicting tonnage unloaded. He assumes that the forecast of grain unloaded in the first quarter was 175 tons. Two values of  are examined,  =0.10 and  =0.50.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast ?

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using  = = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) 9? 179= ( )

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using  = = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) 9? 184 = ( )

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example To evaluate the accuracy of each smoothing constant, we can compute the absolute deviations and MADs.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Selecting a Smoothing Constant

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example Based on this analysis, a smoothing constant of  =0.10 is preferred to  =0.50 because its MAD is smaller.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Trend Projections Another method for forecasting time series with trend is called trend projection. This technique fits a trend line to a series of historical data points and then projects the line into the future for medium – to long- range forecasts. There are several mathematical trend equations that can be developed (e.g. exponential and quadratic), but in this section we look at linear (straight line) trends only.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Trend Projections A trend line is simply a linear regression equation in which the independent variable (X) is the time period. The form is a = - b

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company Let us consider the case of Midwestern Manufacturing Company. That firm's demand for electrical generators over the period is shown in the table below: YearSales

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company A trend line to predict demand (Y) based on the period can be developed using a regression model. We let 1996 be time period 1 (X = 1) then 1997 is time period 2 (X = 2), and so forth. YearTimeSales

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company Time period Generator demand XY

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company a = (4)=56.7 Hence, the least squares trend equation is Y= X. To project demand in 2003, we first denote the year 2003 in our new coding system as X = 8 (sales in 2003) = (8) = 141 generators (sales in 2004) = (9) = 152 generators