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Forecasting

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Learning Objectives

• List the elements of a good forecast.

• Outline the steps in the forecasting process.

• Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each.

• Compare and contrast qualitative and quantitative approaches to forecasting.

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Learning Objectives

• Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.

• Describe two measures of forecast accuracy.

• Describe two ways of evaluating and controlling forecasts.

• Identify the major factors to consider when choosing a forecasting technique.

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FORECAST:• The art and science of predicting future (It may

involve using statistics and mathematical model, or may be a subjective prediction).

• Forecasting is used to make informed decisions.

• Short-range (up to 1 Yr): planning purchasing, job scheduling, workforce levels, job assignment.

• Medium-rang (3 Mth – 3 Yr): sales planning, production planning and budgeting.

• Long-range (more than 3 Yr): planning for new products, facility location or expansion, and R&D.

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Forecasts• Forecasts affect decisions and activities

throughout an organization– Accounting, finance

– Human resources

– Marketing

– MIS

– Operations

– Product / service design

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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 New products and services

Uses of Forecasts

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• Assumes causal systempast ==> future

• Forecasts rarely perfect because of randomness

• Forecasts more accurate forgroups cf. (compared to) individuals

• Forecast accuracy decreases as time horizon increases

I see that you willget an A this semester.

Features of Forecasts

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Elements of a Good Forecast

Timely

AccurateReliable

Be Writ

ten

Easy

to u

se

Mea

ningfu

l Units

Cost-e

ffect

ive

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6 Steps in the Forecasting Process

Step 1 Determine purpose of forecast (How/when it will be used?, Resources)

Step 2 Establish a time horizon (How long?)

Step 3 Select a forecasting technique (Moving AVG, Weighted AVG, etc)

Step 4 Obtain, clean and analyze data (eliminate outliers, incorrect data)

Step 5 Make the forecast

Step 6 Monitor the forecast (modify, revise)

“The forecast”

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Forecast Accuracy• Error - difference between actual value and

predicted value

• Mean Absolute Deviation (MAD)– Average absolute error

• Mean Squared Error (MSE)– Average of squared error

• Mean Absolute Percent Error (MAPE)

– Average absolute percent error

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MAD, MSE, and MAPE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE = 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 (the errors are

presented as percentage)

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Example 1

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 2152 213 2163 216 2154 210 2145 213 2116 219 2147 216 2178 212 216

MAD=MSE=

MAPE=

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Ans: Example 1

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/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

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Types of Forecasts

• Judgmental - uses subjective inputs

• Time series - uses historical data assuming the future will be like the past

• Associative models - uses explanatory variables to predict the future

Qualitative method

Quantitative method

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Qualitative method (Judgmental forecast)

• Executive opinions (long-range planning, new product development)

• Sales force opinions (direct contact with customers; however, sales staff are overly influenced by recent experience)

• Consumer surveys (specific information; but money and time-consuming)

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Quantitative method

• Naïve approach

• Moving average

• Exponential smoothing

• Trend projection

• Linear regression

Time series models

Associative model

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Time 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

• Random variations - caused by chance and unusual circumstances

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Forecast Variations

Seasonal variations

Year 1Year 2Year 3

Trend

Randomvariation

Time

Cycles

Time

Month

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Naive ForecastsUh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

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 Forecasts

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• Stable time series data– F(t) = A(t-1)

• Seasonal variations– F(t) = A(t-n)

• Data with trends– F(t) = A(t-1) + (A(t-1) – A(t-2))

Uses for Naïve Forecasts

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Techniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothing

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Moving Averages• 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= n

wnAt-n + … wn-1At-2 + w1At-1

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Simple Moving Average

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43

45

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

Actual

MA3

MA5

Ft = MAn= n

At-n + … At-2 + At-1

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Exponential Smoothing

• 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.

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

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Exponential 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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Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing

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Picking a Smoothing Constant

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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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Period Actual 0.05 Error 0.7 Error1 422 40 42 -2.00 42 -23 43 41.90 1.10 40.60 2.44 40 41.96 -1.96 42.28 -2.285 41 41.86 -0.86 40.68 0.326 39 41.81 -2.81 40.91 -1.917 46 41.67 4.33 39.57 6.438 44 41.89 2.11 44.07 -0.079 45 42.00 3.00 44.02 0.98

10 38 42.15 -4.15 44.71 -6.7111 40 41.94 -1.94 40.01 -0.0112 41.84 40.00

Alpha = Alpha =

Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing

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Common Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

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Linear Trend Equation

• Ft = Forecast for period t• t = Specified number of time periods• a = Value of Ft at t = 0• b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

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Calculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

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Linear Trend Equation Examplet y

W e e k t 2 S a l e s t y1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

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Linear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

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Techniques for Seasonality

• Seasonal variations– Regularly repeating movements in series

values that can be tied to recurring events.

• Seasonal relative– Percentage of average or trend

• Centered moving average– A moving average positioned at the center of

the data that were used to compute it.

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Associative Forecasting

• Predictor variables - used to predict values of variable interest

• Regression - technique for fitting a line to a set of points

• Least squares line - minimizes sum of squared deviations around the line

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Linear Model Seems Reasonable

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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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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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

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Sources of Forecast errors• Model may be inadequate

• Irregular variations

• Incorrect use of forecasting technique

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Tracking Signal

Tracking signal = (Actual-forecast)

MAD

•Tracking signal

–Ratio of cumulative error to MAD

Bias – Persistent tendency for forecasts to beGreater or less than actual values.

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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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Supply Chain Forecasts

• Sharing forecasts with supply can– Improve forecast quality in the supply chain– Lower costs– Shorter lead times

• Gazing at the Crystal Ball (reading in text)

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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