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Forecasting

I see that you willget an A this semester.

10th ed.

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FORECAST: A statement about the future value of a

variable of interest such as demand. Forecasting is used to make informed

decisions. Long-range Short-range

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Assumes causal systempast ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreases as time horizon increases

Features of ForecastsFeatures of Forecasts

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Uses of ForecastsUses of Forecasts

Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing MIS Operations Product / service design

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Examples of Forecasting UsesExamples of Forecasting Uses

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design Timing of new products and services

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Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

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Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Obtain, clean and analyze data

Step 5 Make the forecast

Step 6 Monitor the forecast

“The forecast”

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Types of ForecastsTypes of Forecasts Judgmental - uses subjective inputs (e.g., sales force

estimates).

Time series - uses historical data assuming the future will be like the past. Time could be in weeks, months, years, etc., and is based on t=1,2,3,…

Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households.

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Judgmental ForecastsJudgmental Forecasts

Executive opinions

Sales force opinions

Consumer surveys

Outside opinion Delphi method

Opinions of managers and staff

Achieves a consensus forecast

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Time Series ForecastsTime 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 that are not random Random variations - caused by chance

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Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Cycles

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Some Common Time Series Techniques Some Common Time Series Techniques or Time Series Forecasting Modelsor Time Series Forecasting Models

Naïve forecasts

Moving average

Weighted moving average

Exponential smoothing

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Naive ForecastsNaive Forecasts

The forecast for any period equals the previous period’s actual value.

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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

Naïve ForecastsNaïve Forecasts

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Ft = At-1

Formula for Naïve ForecastsFormula for Naïve Forecasts

This is the forecasting that is the most responsive to changes in the past actual demand.

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Moving Average FormulaMoving Average Formula

Moving average – A technique that averages a number of recent actual values, updated as new values become available.

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

Ft = MAn= n

At-n + … At-2 + At-1

Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1

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Simple Moving AverageSimple Moving Average

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual Demand

MA3

MA5

Ft = MAn= n

At-1 + At-2 + … At-n

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Exponential SmoothingExponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)

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Exponential Smoothing FormulaExponential Smoothing Formula

• Premise--The most recent observations might have the highest predictive value.

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

The symbol “α” is the Greek letter “alpha.” Alpha is called the smoothing constant. Note that alpha varies from zero to one.

Ft = Ft-1 + (At-1 - Ft-1)

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Exponential SmoothingExponential Smoothing

iti

ttt

ttt

AAAA

FAF

111

1

22

1

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Picking a Smoothing ConstantPicking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

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900

950

1000

1050

1100

1150

1200

1250

1300

1350

1400

April July October January

Demand

F (.05)

F(.2)

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Homework Problem

Referring to page 118 in the text, do problems 2a and 2b, but skip problem 2b(1) which asks for a linear trend equation.

Complete and partial solutions of homework problems are found on the slides at the end of this session.

For this problem and for all homework problems, do not go to the solutions until you have made a strong effort tosolve the problems.

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Linear Trend EquationLinear Trend Equation

Ft = Forecast for period t t = The time period being forecasted a = Value of Ft at t = 0 b = Slope of the line

Ft = Yt = a + bt

0 1 2 3 4 5 t

Ft

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Calculating a and bCalculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

Yt = a + bt

where b and a follow from the following formulae:

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79.55538510

996555958102

22

ttn

YttYnb

78.67

10

5579.5996

n

tbYa

Linear Trend Equation Linear Trend Equation ExampleExample

Calculations of b and a are from the sums given in the table on the left.

Period (t) Sales (Yt) t*Y t squared

1 67 67 12 74 148 43 102 305 94 87 346 165 106 530 256 86 516 367 117 817 498 113 904 649 130 1168 81

10 116 1156 10055 996 5958 385

n = 10 Ft = Yt = a + bt

Ft = Yt = a + bt = 67.78 + 5.79t

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0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Actual

Trend

Plot of Previous SlidePlot of Previous Slide

Y

t

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Homework Problem

Referring to page 118 in the text, do 2b(1), which asks for a linear trend equation. Also,do problem 2c. However, change problem 2c to read as follows:

“Which method seems MOST appropriate?Why?”

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Associative ForecastingAssociative Forecasting

Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households

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Example of an Associative Example of an Associative Forecast: Using x to Predict yForecast: Using x to Predict y

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

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Example of an Associative Forecast Equation for Automobiles(with several variables, and nonlinear)

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Forecast AccuracyForecast Accuracy

Error - difference between actual value and predicted value

Mean Absolute Deviation (MAD) Average absolute error

Mean Squared Error (MSE) Average of squared error

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Some Measures of Some Measures of Forecasting AccuracyForecasting Accuracy

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

Note that the errors are taken for each of the past n periods where the actual demand is known.

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Some Characteristics Some Characteristics of MAD and MSEof MAD and MSE

MAD Easy to compute Weights errors linearly

MSE Squares error More weight to large errors

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Sources of Forecast errorsSources of Forecast errors

Model may be inadequate Irregular variations Incorrect use of forecasting technique

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The next two slides ask some basic questions about forecasting, and give some examples of measuring forecasting error. These slides make up an in-class assignment. You can try to answer thequestions on the slides. However, if you have difficulty with allor some of the questions, we will do them in class. At least become familiar with the questions before the next class.

If you find the next two slides difficult to read, simply magnify the size of the slides. If you can, please try to print a hardcopy of the nexttwo slides and bring them to class. If you can set the resolution of your printer, it is suggested that you set it to a high resolution for the bestprinted copy.

In-class assignment

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Choosing a Forecasting Choosing a Forecasting TechniqueTechnique

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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Good Operations StrategyGood Operations Strategy

Understand that forecasts are the basis for many decisions

Work to improve short-term forecasts Understand that accurate short-term

forecasts have benefits for the following: Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility

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Supply Chain ForecastsSupply Chain Forecasts

Sharing forecasts with suppliers can Improve forecast quality in the supply chain Lower costs Lead to shorter lead times

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Common Nonlinear TrendsCommon Nonlinear Trends

Parabolic

Exponential

Growth

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Exponential SmoothingExponential Smoothing

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Linear Trend EquationLinear Trend Equation

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Simple Linear RegressionSimple Linear Regression

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Homework Problem Solutions

Month

Sales

F M A M J J A S

20

0

2a

3-50

50.)28(28)140(7

)132(28)542(7

)t(tn

YttYnb

22

86.167

)28(50.132

n

tbYa

2b(1)

Hence, n = 7, t = 28, t2 = 140

t Y tY t2

1 19

19

1

2 18

36

4

3 15

45

9

4 20

80

16

5 18

90

25

6 22

132

36

7 20

140

49

28 132

542

140

For the September forecast, t = 8, and Yt = 16.86 + .50(8) = 20.86

Therefore, Yt = 16.86 + .50t

To solve this problem, we need to plugthe appropriate values into the equation Ft = Yt = a + bt

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195

2022182015MA5

2b(2)

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Ft = Ft-1 + (At-1 - Ft-1)2b(3)

Month Forecast = F(old) + .20[Actual – F(old)]

April 18.8 = 19 + .20[ 18 – 19 ]

May 18.04 = 18.8 + .20[ 15 – 18.8 ]

June 18.43 = 18.04 + .20[ 20 – 18.04 ]

July 18.34 = 18.43 + .20[ 18 – 18.43 ]

August 19.07 = 18.34 + .20[ 22 – 18.34 ]

September 19.26 = 19.07 + .20[ 20 – 19.07 ]

Answer is 19.26 (or actually, 19,260 units).

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Ft = At-1

This formula is telling us that the forecast in period t is simply the actual demand for period t-1, or simply, the actual demand of the previous period. For the September forecast, the answer would be the actual demand in August.

Hence, the answer is 20 (or 20,000 units)

2b(4)

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2b(5)2b(5)

Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1

= .6 (20) + .3(22) + .1(18) = 20.4, (or 20,400 units)

Note that the more recent actual demand values are usually given more weight in computing the forecast.

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2c

Change this problem to read “which method seems the most appropriate?”

To logically find the answer, go back to the plot in 2a, and make your best guess as to where the Septemberactual demand might be on the plot or graph. Hence, you need to see a pattern on the plot.

Once you have September on the plot, find the method from part b of the problem which comesthe closest to your guess on the plot.

The answer should be the linear trend equation.

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See you next class