FORECASTING II

Sep 4th 2008

Lecture 4

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OUTLINE

Forecasting based on time series data Seasonality & Cycles

Associative (causal) forecasting techniques Simple linear regression

Accuracy and control of forecasts Forecast accuracy Controlling forecast

Choosing a forecasting technique

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SEASONALITY What are seasonal variations?

Regular repeating movements in series values that can be tied to recurring events

Examples Sales of gift items during holiday season Sales of winter clothing during winter season Airline ticket sales during summer period Increased vehicles on roads during rush hours

Seasonality in a time series is expressed in terms of the amount that actual values deviate from the average of the series value

There are two seasonal models Additive

The additional value added or subtracted from the series average Multiplicative

Seasonality expressed as percentage of the average value 1.10 of the series average 3

SEASONALITY If average demand during a calendar year =

100 units, months of December and November being seasonal months Additive model = Demand during Dec and

Nov will be 100 + 5 (additional quantity) = 105 units

Multiplicative model = Demand during Dec and Nov 100 * 1.10 (percentage) = 110 units

Seasonal relative or seasonal index Percentage of average or trend

Why do we need to know seasonal index? Helps in planning and scheduling Helps in removing seasonality or also called

as deseasonalizing data Incorporate seasonality to the data

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SEASONALITY

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EXAMPLE 6 A furniture manufacturer wants to predict quarterly

demand for a certain loveseat for periods 15 and 16, which happen to be the second and third quarters of a particular year. The series consists of both trend and seasonality. The trend portion of demand is projected using the equation Ft = 124 + 7.5t. Quarter relatives are Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, and Q4 = 0.95. Use this information to deseasonalize sales for periods 1

through 8. Use this information to predict demand for periods 15 and 16.

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EXAMPLE 6

Period 15: 260.15 Period 16: 183.00

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COMPUTING SEASONAL RELATIVES

Seasonal relatives are computed using centered moving average

What is centered moving average? A moving average positioned at the center of the data

A center moving average is used to obtain the seasonal relative because: It “looks forward” and “looks backward” – closely follow

the data movements, randomness in data, trends, cycle etc.

Centered moving average closely followed the data

Period DemandThree-period

Centered Average1 252 283 26

Average = (25+28+26)/3 = 26.34

26.34

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CENTERED MOVING AVERAGE

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EXAMPLE 7 The manager of a parking lot has computed daily relatives for

the number of cars per day in the lot. The computations are repeated here (about three weeks are shown for illustration). A seven-period centered moving average is used because there are seven days (seasons) per week.

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CYCLES

What are cycles? Upward and downward movement similar to the

seasonal variations but on a long term basis Examples of cycles

Decrease in travel with high gas prices U.S. motorists drove 12.2 billion miles fewer in

June 2008 compared to June 2007 We see a long term decrease in number of miles

driven by the U.S. motorists

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ASSOCIATIVE FORECASTING TECHNIQUES

Associative forecasting techniques rely on identification of: Related variables (predictor variables/factors)

that can be used to predict the variable of interest (predicted variable/response variable)

In the associative techniques an equation is developed which summarizes the effects of predictor variable This approach is also known as regression

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SIMPLE LINEAR REGRESSION It is a linear relationship between two variables The objective is to construct a line that minimizes

the sum of squares of vertical deviation Least squares criterion

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SIMPLE LINEAR REGRESSION

yc = a + b x

whereyc = Predicted (dependent) variable

x = Predictor (independent) variableb = Slope of the linea = Value of yc when x = 0 (i.e., the height of the line

at the y intercept)

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LINEAR REGRESSION ASSUMPTIONS Variations around the line are random Deviations around the line normally distributed Predictions are being made only within the range

of observed values For best results:

Always plot the data to verify linearity Check for data being time-dependent Small correlation may imply that other variables are

important

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EXAMPLE 8 Healthy Hamburgers has a chain of 12 stores in

northern Illinois. Sales figures and profits for the stores are given in the following table. Obtain a regression line for the data, and predict profit for a store assuming sales of $10 million.

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ACCURACY AND CONTROL OF FORECAST Though the forecast are rarely match with the actual

data it is very important to minimize the forecast error Accurate forecasts are necessary for every business

organization : Schedules Production quantity Man power

Forecast Error = Actual – Forecasted value Minimizing forecast error will:

Save additional cost Improve customer satisfaction Smooth flow of process

Improper forecast will lead to: Too little or too much resources allocated Too much or too little production Mismatch in timing of activities 17

MAD, MSE, AND MAPE

MAD (Mean Absolute Deviation)

= Actual forecast

n

MSE (Mean Squared Error)

= Actual forecast)

-1

2

n

(

MAPE(Mean Absolute Percentage Error)

= Actual forecas

t

n

/ Actual*100)

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MAD, MSE AND MAPE

MAD Easy to compute Weights errors linearly

MSE Squares error More weight to large errors

MAPE Puts errors in perspective

Accuracy of one forecast method can be compared with the other using these performance measures

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EXAMPLE 10

Period Actual Forecast(A-F)

(Error) |Error| (Error)^2(|Error|/Actual)*

1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28 20

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

Control limits Upper control limit Lower control limit

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CONCEPTUAL REPRESENTATION OF CONTROL CHART

SOURCES OF FORECAST ERRORS Model may be inadequate

Omission of important variable A change or shift in variable which the model does

not capture Appearance of new variable

Irregular variations Incorrect use of forecasting technique Randomness is the only inherent variation that

should remain in the data after all causes for variation are accounted

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EXAMPLES OF NONRANDOMNESS

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

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OPERATIONS STRATEGY

Forecasts are the basis for many decisions Work to improve short-term forecasts Accurate short-term forecasts improve

Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility

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STEPS IN THE FORECASTING PROCESS

1 Determine purpose of forecast

2 Establish a time horizon & time period

3 Gather and analyze data4 Select a technique & estimate parameters

5 Make forecasts

6 Monitor and update

“The forecast”