chapter 5 forecasting. eight steps to forecasting 1. determine the use of the forecast—what...

Chapter 5Chapter 5

ForecastingForecasting

Eight Steps to ForecastingEight Steps to Forecasting1. 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), 1 month to 1 year (medium term), or more than 1 year (long term)?4. Select the forecasting model or models.5. Gather the data or information needed to make the forecast.6. Validate the forecasting model.7. Make the forecast.8. Implement the results.

Quantitative Analysis for Management, 9e by Render/Stair/Hanna

5-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Types of ForecastsTypes of Forecasts

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-3 © 2006 by Prentice Hall, Inc.

Upper Saddle River, NJ 07458

Time-Series ModelsTime-Series Models• Time-series models attempt to predict the future by using historical data. • 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. • The time-series models we examine in this chapter are

• Moving average • Exponential smoothing,• Trend projections, and • Decomposition.

Regression analysis can be used in trend projections andis one type of decomposition model. The primary emphasis of this

chapter is time series forecasting.



Causal ModelsCausal 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.

• Causal models may also include past sales data as time-series models do, but they include other factors as well.

• These include• Linear regression analysis• Multiple regression analysis



Qualitative ModelsQualitative Models• Qualitative models attempt to incorporate judgmental or subjective

factors into the forecasting model. • 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.



Delphi method. 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 5 to 10 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.



Jury of executive opinion 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.



Sales force compositeSales 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.



Consumer market surveyConsumer 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.



Scatter Diagrams and Time SeriesScatter Diagrams and Time Series• A scatter diagram helps to obtain ideas about a relationship.



Measures of Forecast AccuracyMeasures of Forecast Accuracy



Forecast error = Actual value - Forecast value

This is computed by taking the sum of the absolute values of the individual forecast errors and dividing by the numbers of errors (n):

Mean Absolute Deviation (MAD).

Mean Squared Error (MSE)Mean Squared Error (MSE), , • It is the average of the squared errors



Mean Absolute Percent Error (MAPE) Mean Absolute Percent Error (MAPE)

• The MAPE is the average of the absolute values of the errors expressed as percentages of the actual values.



Components of a Time SeriesComponents of a Time Series• 1. Trend (T) is the gradual upward or downward movement

of the data over time.• 2. Seasonality (S) is a pattern of the demand fluctuation

above or below the trend line that repeats at regular intervals.• 3. Cycles (C) are patterns in annual data that occur every

several years. They are usually tied into the business cycle.• 4. Random variations (R) are “blips” in the data caused by

chance and unusual situations; they follow no discernible pattern.



Moving AveragesMoving Averages



WEIGHTED MOVING AVERAGEWEIGHTED MOVING AVERAGE



Exponential SmoothingExponential Smoothing• Exponential smoothing is a type of moving

average technique, which involves little record keeping of past data. The exponential smoothing approach has been applied successfully by banks, manufacturing companies, wholesalers, and other organizations. The exponential smoothing formula is as follow:



ExampleExample• In January, a demand for 142 of a certain car

model for February was predicted by a dealer. Actual February demand was 153 autos. Using a smoothing constant of we can forecast the March demand using the exponential smoothing model.



SELECTING THE SMOOTHING SELECTING THE SMOOTHING CONSTANT CONSTANT

• The appropriate value of the smoothing constant 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.

• Several values of the smoothing constant may be tried, and the one with the lowest MAD could be selected.

• This is analogous to how weights are selected for a weighted moving average forecast.

• Some forecasting software automatically select the best smoothing constant.

• QM for Windows displays the MAD that obtains values of ranging from 0 to 1 in increments of 0.01.



ExampleExample



EXPONENTIAL SMOOTHING EXPONENTIAL SMOOTHING WITH TREND ADJUSTMENTWITH TREND ADJUSTMENT

• The averaging or smoothing forecasting techniques are useful when a time series has random component, but these techniques are not suitable to respond trends.

• The idea is to develop an exponential smoothing forecast and then adjust this for trend.

• Two smoothing constants, and are used in this model, and both of these values must be between 0 and 1. The level of the forecast is adjusted by multiplying the first smoothing constant, by the most recent forecast error and adding it to the previous forecast.

• The trend is adjusted by multiplying the second smoothing constant, by the most recent error or excess amount in the trend.

• A higher value gives more weight to recent observations and thus responds more quickly to changes in the patterns.



Example: Midwestern Manufacturing’s DemandExample: Midwestern Manufacturing’s Demand





Trend ProjectionTrend ProjectionTrend projections are used to forecast time-series data that

exhibit a linear trend. Least squares may be used to determine a trend projection

for future forecasts. Least squares determines the trend line forecast by

minimizing the mean squared error between the trend line forecasts and the actual observed values.

The independent variable is the time period and the dependent variable is the actual observed value in the time series.



Trend Projection Trend Projection (continued)(continued)The formula for the trendprojection is:

Y = b + b X

where: Y = predicted value b1 = slope of the trend line b0 = intercept X = time period (1,2,3…n)

0 1



Midwestern Manufacturing Midwestern Manufacturing Trend Projection ExampleTrend Projection Example

Midwestern Manufacturing Company’s demand for electrical generators over the period of 2004 – 2010 is given below.



Midwestern Manufacturing Midwestern Manufacturing Company Trend SolutionCompany Trend Solution

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.89R Square 0.80Adjusted R Square 0.76Standard Error 12.43Observations 7.00

ANOVAdf SS MS F Sign. F

Regression 1.00 3108.04 3108.04 20.11 0.01Residual 5.00 772.82 154.56Total 6.00 3880.86

Coefficients

Standard Error t Stat P-value

Lower 95%

Intercept 56.71 10.51 5.40 0.00 29.70Time 10.54 2.35 4.48 0.01 4.50

Sales = 56.71 + 10.54 (time)



Midwestern ManufacturingMidwestern Manufacturing’’s Trend s Trend



Seasonal VariationsSeasonal Variations Seasonal indices can be used to make adjustments

in the forecast for seasonality.

A seasonal index indicates how a particular season compares with an average season.

The seasonal index can be found by dividing the average value for a particular season by the average of all the data.

• Now suppose we expected the third year’s annual demand for answering machines to be 1,200 units, which is 100 per month. We would not forecast each month to have a demand of 100, but we would adjust these based on the seasonal indices as follows:





Eichler Supplies: Seasonal Index Eichler Supplies: Seasonal Index ExampleExample

Month Sales Demand

AverageTwo-YearDemand

AverageMonthlyDemand

SeasonalIndex

Year 1

Year 2

80 100 90 94 0.95775 85 80 94 0.85180 90 85 94 0.90490 110 100 94 1.064

JanFebMarAprMay 115 131 123 94 1.309

… … … … … …

Total Average Demand 1,128Seasonal Index: = Average 2 -year demand/Average monthly demand



Seasonal Variations with TrendSeasonal Variations with Trend

Steps of Multiplicative Time-Series Model

1. Compute the CMA for each observation.2. Compute seasonal ratio (observation/CMA).3. Average seasonal ratios to get seasonal indices.4. If seasonal indices do not add to the number of seasons,

multiply each index by (number of seasons)/(sum of the indices).

Centered Moving Average (CMA) is an approach that prevents a variation due to trend from being incorrectly interpreted as a variation due to the season.



Turner IndustriesTurner Industries Seasonal Variations Seasonal Variations with Trendwith Trend

Turner Industries’ sales figures are shown below with the CMA and seasonal ratio.Year Quarter Sales CMA

Seasonal Ratio

1 1 1082 1253 150 132 1.1364 141 134.125 1.051

2 1 116 136.375 0.8512 34 138.875 0.9653 159 141.125 1.1274 152 143 1.063

3 1 123 145.125 0.8482 142 147.187 0.963 1684 165

CMA (qtr 3 / yr 1 ) = .5(108) + 125 + 150 + 141+ .5(116)4

Seasonal Ratio = Sales Qtr 3 = 150 CMA 132



Decomposition Method with Trend Decomposition Method with Trend and Seasonal Componentsand Seasonal Components

Decomposition is the process of isolating linear trend and seasonal factors to develop more accurate forecasts.

There are five steps to decomposition:1. Compute the seasonal index for each season.2. Deseasonalize the data by dividing each number by its seasonal

index.3. Compute a trend line with the deseasonalized data.4. Use the trend line to forecast.5. Multiply the forecasts by the seasonal index.



Turner Industries: Turner Industries: Decomposition MethodDecomposition Method

Turner Industries has noticed a trend in quarterly sales figures. There is also a seasonal component. Below is the seasonal index and deseasonalized sales data.

Yr Qtr Sales Seasonal

IndexDesasonalized

Sales1 1 108 0.85 127.059

2 125 0.96 130.2083 150 1.13 132.7434 141 1.06 133.019

2 1 116 0.85 136.4712 134 0.96 139.5833 159 1.13 140.7084 152 1.06 143.396

3 1 123 0.85 144.7062 142 0.96 147.9173 168 1.13 148.6734 165 1.06 155.660

*

•This value is derived by averaging the season rations for each quarter. Refer to slide 5-37.

Seasonal Index for Qtr 1 = 0.851+0.848 = 0.85 2

108 0.85=




Using the deseasonalized data, the following trend line was computed:

Sales = 124.78 + 2.34X

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.98981389R Square 0.97973154Adjusted R Square 0.9777047Standard Error 1.26913895Observations 12

ANOVAdf SS MS F Significance F

Regression 1 778.5826246 778.5826246 483.3774 8.49E-10Residual 10 16.10713664 1.610713664Total 11 794.6897613

Coefficients Standard Error t Stat P-value Lower 95%Intercept 124.78 0.781101025 159.8320597 2.26E-18 123.1046Time 2.34 0.10613073 21.98584604 8.49E-10 2.0969




Using the trend line, the following forecast was computed:

Sales = 124.78 + 2.34XFor period 13 (quarter 1/ year 4):

Sales = 124.78 + 2.34 (13) = 155.2 (before seasonality adjustment)

After seasonality adjustment:

Sales = 155.2 (0.85) = 131.92Seasonal index for quarter 1



Decomposition of Time-Series: Two Decomposition of Time-Series: Two ModelsModels

Additive model assumes demand is the summation of the four components.The underlying level of the series fluctuates but the magnitude of the seasonal spikes remains approximately stable Tool: Regression

demand = T + S + C + R

Decomposition of Time-Series: Two Decomposition of Time-Series: Two ModelsModels

Multiplicative model assumes demandis the product of the four components. As the underlying level of the series changes, the

magnitude of the seasonal fluctuations varies as well.

Tool: Decomposition

demand = T * S * C * R



Multiple Regression with Trend and Multiple Regression with Trend and Seasonal ComponentsSeasonal Components

Multiple regression can be used todevelop an additive decompositionmodel.

One independent variable is time. Seasons are represented by dummy independent variables.

Y = a + b X + b X + b X + b X

Where X = time period X = 1 if quarter 2 = 0 otherwise X = 1 if quarter 3 = 0 otherwise X = 1 if quarter 4 = 0 otherwise

1 1 2 2 3 3 4 4

1

2

3

4



Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

n

|errorsforecast |Σ MAD

MADi) periodin demandforecast i periodin demand Σ(actual

MADRSFEgnalTrackingSi

where

Tracking signals measure how well predictions fit actual data.

+ 2 MADs are the control Limits or 89% Errors 1 MAD is 0.8 St dev.



Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

chapter 5 forecasting. eight steps to forecasting 1. determine the use of the forecast—what...

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