Forecasting

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Forecast

• OM is mostly proactive not reactive
• It involves structured planning activities
• Planning requires data pertaining to the feature
• Forecast: A statement about the future
• Not necessarily numerical
• Weather forecasts

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Forecasts are a basic input in the decision processes of operations management because they provide information on future demand. The importance of forecasting to operations management cannot be overstated. The primary goal of operations management is to match supply to demand. Having a forecast of demand is essential for determining how much capacity or supply will be needed to meet demand.

Uses of Forecasts

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1. Forecasting techniques generally assume that the same underlying causal system that existed in the past will continue to exist in the future.
2. Forecasts are not perfect; actual results usually differ from predicted values; the presence of randomness precludes a perfect forecast. Allowances should be made for forecast errors.
3. Forecasts for groups of items tend to be more accurate than forecasts for individual items because forecasting errors among items in a group usually have a canceling effect.
4. Opportunities for grouping may arise if parts or raw materials are used for multiple products or if a product or service is demanded by a number of independent sources.
5. Forecast accuracy decreases as the time period covered by the forecast—the time horizon —increases. Generally speaking, short-range forecasts must contend with fewer uncertainties than longer-range forecasts, so they tend to be more accurate.

REMARKS

• Assume a causal system
• Future resembles the past
• Forecasts rarely perfect because of randomness
• Forecasts more accurate for groups vs. individuals.
• Forecasting errors among items in a group usually have a canceling effect.
• Extremes in a group cancel each other
• Ex. I can forecast the class average from the midterm better than Mrs. X’s individual grade.
• Sample variance of {-1,1,-1,1} is 1.
• Sample variance of {(-1+1)/2, {(-1+1)/2} is 0.
• Forecast accuracy decreases as time horizon for forecasts increases
• Ex. I can forecast this year’s class average better than next year’s class average

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Elements of a Good Forecast

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Steps in the Forecasting Process

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Step 1 Determine the purpose of the forecast.

Step 3 Obtain, clean, & analyze appropriate data

FORECAST ACCURACY

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FORECASTS BASED ON TIME-SERIES DATA

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Naive Methods

A naive forecast uses a single previous value of a time series as the basis of a forecast. The naive approach can be used with a stable series (variations around an average), with seasonal variations, or with trend.

Types of Forecasts

• Judgmental - Subjective analysis of subjective inputs
• Associative models – Analyzes historical data to reveal relationships between (easily or in advance) observable quantities and forecast quantities. Uses this relationship to make predictions.
• Time series – Objective analysis historical data assuming the future will be like the past

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Judgmental Forecasts

• Executive opinions (long-range planning)
• There are factors hard to quantify
• Ex: Effects of November 2004 election on new houses built in 2005
• Sales force composite
• Retailer forecasts for the manufacturer
• Consumer surveys
• The guy at the mall who asks if you like cherry flavor in your shampoo
• Outside opinion
• Financial and consulting gurus and companies
• Opinions of managers and staff
• Delphi method: A series of questionnaires developed sequentially

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Associative Forecasting

• Based on identification of related variables that can be used to predict values of the variable of interest.
• Sales of mountain bikes in an area may be related to the percentage of the young population living in that area.
• Sales of Harley-Davidson motorbikes is related to mid-aged men population. Average age of H-D owners is 46.
• Ice cream sales can be related to temperature
• Home depot bases sales forecasts on mortgage refinancing rates, smaller rates imply higher sales.
• Changes in Federal Reserve Board’s interest rate leads to certain business activities
• House sales
• Industrial investments
• Increase in energy cost leads to price increases in products and services

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Associative Forecasting

• Find an association between the predictor and the predicted
• Predictor variables - used to predict values of variable interest, sometimes called independent variables
• Predicted variable = Dependent variable
• Regression - technique for fitting a line to a set of points
• Linear regression is the most widely used form of regression
• The objective is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations of data points from the line.

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Linear Regression (cont.)

y = a + bx

Where

y = predicted (dependent) variable

x = predictor (independent) variable

b = slope of the line

a = value of y when x = 0 (the height of line at the y intercept)

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Computing a and b

Given n data points, find the intercept a and the slope b to

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Linear Model Seems Reasonable

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Another Linear Regression Example�Variables: Weeks and Sales

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Linear Trend Calculation

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y = 143.5 + 6.3 t

Sales in week t = 143.5 + 6.3 t

a

=

812

-

6.3(15)

5

=

143.5

Linear Trend Calculation

y = 143.5 + 6.3t

When t = 0, the value of y is 143.45 and the slope of the line is 6.3. meaning that the value of of y will increase by 6.3 units for each time period. If t = 10, the forecast is 143.5 + 6.3(10) = 206.5

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Excel example

regression.xls

Linear Regression

• Correlation (r) between variables: The strength and direction of relationships between two variables
• 1.00 means changes in one variable are always matched by changes in the other, vice versa.
• A correlation close to zero means little linear relationship
• The square of the correlation coefficient provides a measure of the percentage of variability in the values of y that is explained by the independent variable.(80% or more: the independent variable is a good predictor of the values of dependent variable)

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Time series

• Time-ordered sequence of observations taken at regular intervals over a period of time
• Future values of the series can be estimated from past values.

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Types of Variations in Time Series Data

• Trend - long-term movement in data
• Seasonality - short-term regular variations in data
• Cycles – wavelike variations of long-term
• Irregular variations - caused by unusual circumstances
• Random variations - caused by chance

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Forecast Variations

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Trend

Irregular�variation

Cycles

Seasonal variations

Year 01

00

99

Figure 3-1

Cyclical

Naïve Forecasts

• Uses a single previous value of a time series as the basis of a forecast.
• Virtually no cost
• Data analysis is nonexistent
• Easily understandable
• Cannot provide high accuracy
• If it were true, future will always be the same as the past

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Some notation: Forecast at time t is F(t)

Actual observation at time t is A(t)

Today is temperature is 98 F, A(Today)=98

F(Tomorrow)=98

F(Day after)=98

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Uses for Naïve Forecasts

• Stable time series data
• Forecast is the same as the last actual observation
• F(t) = A(t-1)
• Seasonal variations
• Forecast is the same as the last actual observation when we were in the same point in the cycle, where a cycle lasts n periods.
• F(t) = A(t-n)
• Data with trends
• There is constant trend, the change from (t-2) to (t-1) will be exactly as the change from (t-1) to (t)
• F(t) = A(t-1) + (A(t-1) – A(t-2))

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Naive Forecasts

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Naïve (Cont.)

• Check if the resulting accuracy is acceptable
• The higher the accuracy, often the higher the cost.
• Do we really need our forecast that accurate? Is it worth the additional resources?
• Why do you need forecasts for? How critical they are for operations?

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Time Series Models: Variations�What is random and what is not?

• Historical data contain random variations or noise
• Random variations are caused by relatively unimportant factors.
• What is random? Can we not study everything to negligible detail? “God does not roll dices” –A.E.
• The objective is to remove all randomness and have real variations.
• Minor variations are random and large ones are real.

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Techniques for Averaging

• Moving averages (MA)
• Naïve methods just trace the actual data with a lag of one period, F(t)=A(t-1)
• They don’t smooth
• MA uses a number of the most recent actual data to smooth
• Weighted moving averages
• Exponential smoothing

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Simple Moving Average�Note the sensitivity of forecasts

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Actual

MA(t,3)

MA(t,5)

Averaging (over time) techniques are used to smooth variations in the data.

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Ex: Three period moving average forecast

Month Demand

1 42 MA(6,3) = (43 + 40 + 41) / 3

2 40 = 41.33.

3 43 If A(6) = 39, then

4 40 MA(7,3) = (40 + 41 + 39) / 3

5 41 = 40.00

6 39

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Weighted average

Moving Average

• Advantage=Easy to compute and easy to understand
• Disadvantage=All values in the average are weighted equally

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Weighted Moving Average

• Similar to moving average
• It assigns more weight to the most recent values in a time series
• Idea: most recent observations must be better indicators of the future than older observations

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Weighted average

Compute a weighted average forecast using a weight of 0.4 for the most recent period, 0.3 for the next most recent, 0.2 for the next and 0.1 for the next.

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Continuing with the data on the left

F(6) = .40(41)+.30(40)+.20(43)+.10(40)=41.0

If the actual demand for period 6 is 39,

F(7) = .40(39)+.30(41)+.20(40)+.10(43)=40.2

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• The weighted average is more reflective of the most recent occurrences.

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Month Demand

1 42

2 40

3 43

4 40

5 41

6 39

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Exponential Smoothing

Forecast today=Forecast yesterday+(alpha)*(Forecast error yesterday)

Each new forecast is equal to the previous forecast plus a percentage of the previous error.

Today’s forecast

Depends on yesterday’s (time-wise dependence, strong memory)

But it has to be corrected by forecast error

Therefore, we should give more weight to the more recent time periods when forecasting.

• Alpha = smoothing constant = percentage of the forecast error.

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Forecast error:=Actual – Forecast =A(t-1)-F(t-1)

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Exponential Smoothing �as an Weighted Average

Idea--The most recent observations might have the highest predictive value along with the most recent forecast errors. Let us balance them:

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Example of Exponential Smoothing

Forecasts made in a period and the period has the same color

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Picking a Smoothing Constant:�Responsiveness vs. Smoothing

• The quickness of forecast adjustment to error is determined by the smoothing constant.
• The closer the alpha is to zero, the slower the forecast will be to adjust to forecast errors.
• Conversely, the closer the value of alpha is to 1.00, the greater the responsiveness to the actual observations and the less the smoothing
• Select a smoothing constant that balances the benefits of responding to real changes if and when they occur.

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Picking a Smoothing Constant�Sensitivity of Forecasts

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α = 0.1

α = 0.4

Actual

Excel example

exponential-smoothing.xls

Techniques for trend

• Develop an equation that will describe trend
• The trend component may be linear or it may not
• Linear trend:

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Y_t = a + bt

b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.

Common Nonlinear Trends

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Figure 3-5

Adjusting for Trend with Double Exponential Smoothing

• Simple exponential smoothing with no trend

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• Add forecasted trend

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• This time trend is

also smoothed,

note that previous

trend (of t-1) and

current trend (of t)

appear in the

smoothing formula

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Techniques for seasonality

• Regularly repeating upward or downward movements in time series values
• Seasonality: weather variations, vacations and holidays
• Seasonality: Expressed in terms of the amount that actual values deviate from the average value of the series
• Seasonality is expressed as a percentage of the average amount

seasonal percentages = seasonal relatives = seasonal indices

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Different models of seasonality

• Seasonal relative = 1.45 for the quantity of television sold in August at Circuit City, meaning that TV sales for that month are 45% above the monthly average.
• Seasonal factor=0.60 for the number of notebooks sold at the UTD bookstore in April, meaning that notebook sales are 40% below the monthly average.

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• Seasonal indices are your vehicle to travel between the seasonal and deseasonal worlds.

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Use Seasonality Indices �to Deseasonalize and Seasonalize

• Deseasonalize historical observations
• Divide them by seasonal indices
• Make the analysis = Generate forecasts
• Seasonalize forecasts
• Multiply them by seasonal indices

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t

t

t

Inputs

Analyze

Output

Excel example

seasonalforecast.xls

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Forecast Accuracy

• Measurement is the first step to improve an activity
• What value of smoothing constant is good?
• Accuracy measurement is a vital aspect of forecasting
• Impossible to correctly predict future values
• Important to include an indication of how big the forecast deviate from the actual values

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Forecast Accuracy

• Error - difference between actual value and predicted value
• Mean absolute deviation (MAD)
• Average absolute error (weights all errors evenly)
• Mean squared error (MSE)
• Average of squared error (weights errors according to their squared values)
• Tracking signal
• Ratio of cumulative error and MAD

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MAD & MSE

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Use for MAD & MSE

• Compare the accuracy of alternative
• forecasting methods using MAD and MSE.
• parameter (such as alpha) values used in forecasting

by using MAD and MSE

• Determine which method yields the lowest MAD or MSE for a given set of data.

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Controlling the quality of forecast

• Necessary to monitor forecast to ensure that the forecast is performing adequately
• This is accomplished by comparing forecast errors to predetermined values
• Errors that fall within the limits are considered acceptable
• Errors outside either limit indicates that corrective action is needed.
• Tracking signal values are compared to predetermined limits (+4,-4) based on judgment and experience
• Upper and lower limits for individual forecast errors are calculated using control chart techniques. We will learn about control charts in quality chapters.

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Choosing a forecasting technique� No single technique works best in every situation

No single technique works best in every situation

• The forecast horizon
• Forecasting frequency
• Forecasting is not free
• Consider cost and accuracy
• Weigh cost-accuracy trade-offs carefully
• Forecast detail, part / product level?
• Availability of
• historical data
• computers
• able users / decision makers

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Choosing a forecasting technique (cont.)

• Moving Averages and Exponential Smoothing are short range techniques. They produce forecast for the next period
• Trend equations are used for much longer time horizons.
• More than one forecasting techniques might be used to increase confidence.

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Summary

• We studied the steps of forecasting
• We examined three forecasting techniques:
• Judgmental
• Associative
• Time Series
• We learned about seasonality, trend, cyclical data
• Discussed monitoring forecast accuracy

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