BABS 502 Lecture 1 Feb 24, 2014 (C) Martin L. Puterman1.

BABS 502

Lecture 1Feb 24, 2014

(C) Martin L. Puterman 1

Bookkeeping

• Your instructor• Course guidelines

– Lectures– Assignments– Project – no exam– Contest– Software – R


What is a Forecast?A prediction of the future

fore = before + cast = throwLiterally planning before you throw.

There is some confusion about this pointOften organizations refer to direct outputs of decisions as forecasts. (Sometimes it is easier to use this terminology)

Example – “production forecasts” are not “forecasts”

They are subject to variability but are known to somedegree of accuracy by organization members.


Course Themes

• Forecasts are necessary for effective decision making– Forecasting, planning and control are interrelated

• Forecasts are usually (almost always) wrong– Quantifying forecast variability is as important as

determining the forecast; it is the basis for decision making.

– Rare events happen and can have significant impact on forecasts

• Scientific methods improve forecasting(C) Martin L. Puterman 4

Course Objectives

• To provide a structured and objective approach to forecasting

• To provide hands on experience with several popular forecasting methods and statistical software

• To determine the data requirements for effective forecasting

• To integrate forecasting with management decision making and planning

• To introduce you to some advanced forecasting methods


Why Forecast?• It’s fun• To look smart• But most importantly: To make better decisions

– Investments– Inventory– Staffing levels– Medical treatment timing

• Fact repeated: Forecasts are usually (always?) wrong! – Why do it then? – Because you have to!!

• Effect of bad forecasts– Excess costs – too much staff or stock– Poor service –waiting lines and stockouts


Knowledge Base for Effective Forecasting

• Subject Matter Knowledge– Industry– Market– Demand Sources

• Statistics• Statistical software • Using databases• Interpersonal skills

– acquiring data• Working with IT department

– report writing– presentations– team work


Forecasting Applications

• Demand forecasts – Whistler-Blackcomb - staffing– TELUS – capacity expansion – Worksafe BC – staffing, budgeting and reserve planning– Health Authorities – staffing, scheduling and planning – Mike’s Products - production and inventory decisions

• Price forecasts– Teck- Cominco - production planning, ore purchase– Vancouver Olympic Village – resale value

• New market forecasts; – Webvan, Petfood.com, Napster

• Technology forecasts– Intel; Nortel; TELUS; Microsoft; Google


Forecasting Demand by SKUfor a

Consumer Product Distribution System


The Challenge

• Enhance the performance of the inventory and distribution system for products in the US market

• Highly competitive market with highly seasonal demand patterns

• Client’s Goal - Get the right product in the right quantity to the right customer on time!


The Production/Distribution System


Co-packers

Distribution Centers

Retailers (many)

Products

Modeling• A linear programming based planning tool

• For each SKU it finds for the next 12 months:

- Optimal co-packer production levels- Optimal distribution and transshipment plans- Optimal distribution center (DC) inventory levels

• Developed for operational decisions but first used for tactical/strategic decisions

• Implemented in Excel using Frontline Solver

• User friendly interface


Using the Model in Practice


Month Date Steps to Take

T – 1 20th Provide forecasts for month T to T + 12

T 5th Estimate closing inventory at the end of month T, using- Opening inventory of month T,- Production schedule of month T, and- Actual order from distributors and DC re-order suggestions in month T

Monthly input data check list, including- Unit costs- Production and inventory capacity- Minimum and fixed productionFrom production and distribution personnel. Document the changes to the data.

6-9th - Run the tool with updated data, review the output and re-run if necessary.- Set production plan for month T + 1- Document changes of actual plan from tool output and reasons of changes

10th Provide co-packers with production plan for month T+1

Forecasts drive the model!• Key input – Forecasts by sales region by SKU for next

12 months.– Produced by regional sales representatives– Accuracy declines over 12 month period– Not calibrated but good in aggregate!

• But model is used in a rolling horizon approach


(C) Martin L. Puterman 15Company logo

Model in MS Excel


More on Forecasting


Forecasting is NOT a Statistical Topic

• Primary interest is not in hypothesis tests or confidence intervals.

• Underlying statistical models are often used: – regression– time series – neural networks – dynamic Bayesian systems and state space models

• Forecasts must be assessed on– the quality of the decisions that are produced – their accuracy


Types of Forecasting• Extrapolation

– Based on previous data patterns • Assumes past patterns hold in future

– Exponential Smoothing, Trend Models, ARIMA models

• Causal – Based on factors that might influence the quantity being forecasted

• Assumes past relationships hold in the future– Regression

• Judgemental– Based on individual knowledge– Sales force composites, expert opinion, consensus methods– Surveys and market research

• Collaborative– Based on information available to supply chain partners– Information sharing and partnerships


Forecasting Considerations

• Forecasts vs. Targets• Short Term vs. Medium Term vs. Long term

– Operational or Strategic Decision Making• One Series vs. Many• Seasonal vs. Non-seasonal• Simple vs. Advanced• One-Step Ahead vs. Many Steps Ahead• Automatic vs. Manual• Exceptions• When to update models


Forecasting Horizons· Short term

· a few days or weeks· Medium term

· usually a few months to 1 or 2 years· Long term

· usually more than 2 year· Why distinguish between these?

· Different methods are more suitable in each case.· Different applications require different forecasts.


Some Forecasting Observations

He who lives by the crystal ball soon learns to eat ground glass.– Edgar R. Fiedler in The Three Rs of Economic Forecasting-Irrational, Irrelevant and

Irreverent , June 1977.

Prediction is very difficult, especially if it's about the future. – Nils Bohr, Nobel laureate in Physics – This quote serves as a warning of the importance of testing a forecasting model out-of-sample.

It's often easy to find a model that fits the past data well--perhaps too well!--but quite another matter to find a model that correctly identifies those features of the past data which will be replicated in the future

There is no reason anyone would want a computer in their home.– President, Chairman and founder of Digital Equipment Corp, 1977

640K ought to be enough for anybody.– Bill Gates, 1981

Our sales forecasts are accurate in aggregate– Many marketing directors


Forecasting methods that workBased on conclusions of forecasting competitions

• Naïve: Last Period or Same Period Last Year• Regression

– Extrapolation– Causal

• Exponential Smoothing– Simple– Trend / Damped Trend– Holt-Winters

• Pooled methods


Forecasting methods I don’t recommend

• Crystal balls• Tea leaves• Fortune cookies• Expert Opinion• Complex statistical models

– Box-Jenkins / ARIMA Models– Multivariate Econometric Models– Neural Networks


Forecasting in Organizations

There is no forecasting department!


Forecasting Practice in Organizations

• Surveys have addressed the following questions:– What quantities do organizations need to forecast? – What methods are users familiar with? – What methods have been used? – What are the impediments to using quantitative

techniques?– What factors which make forecasting most difficult?

• Bottom Line – Formal forecasting is not widely used because of the lack of data or knowledge.


What do organizations need to forecast?• Costs

– raw materials– wage rates and overheads – interest rates– exchange rates

• Sales or demand– by region– by SKU– by time of day– for new and existing products – competitive behaviour

• Defect rates


What do organizations need to forecast?

• Technology– new products– new processes– diffusion rates

• Social and Political trends– demographics– wealth profile– welfare and health provisions– impact of technology

• Projects– duration– costs– life cycle needs


Top 10 impediments to effective forecasting

10. Absence of a forecasting function9. Poor data 8. Lack of software7. Lack of technical knowledge6. Poor data5. Lack of trust in forecasts4. Poor data3. Too little time2. Not viewed as important 1. Poor data


Forecasting Challenges• Technical Issues

– What is the best approach• Organizational Issues

– reporting structures– accountability– incentive systems

• Information – historical data not available– timeliness and reliability– what information is required when

• Users – conflicting objectives


Silos and Forecasting


IT

MarketingProduction Forecaster

Scientific Forecasting


Scientific Forecasting

• Requires familiarity with very basic statistical concepts:– Mean, standard deviation, skewness and kurtosis– medians and percentiles– histograms, stem and leaf plots, box plots– scatter plots, correlation, regression


If you’re not keeping score, you are only practicing!

http://en.wikipedia.org/wiki/Skewness

http://en.wikipedia.org/wiki/Kurtosis

The Forecasting Process - I

• Determine what is to be forecasted and at what frequency

• Obtain data• Process the data• PLOT THE DATA• Clean the data• Hold out some data


The Forecasting Process - II

• Obtain candidate forecasts• Assess their quality

– Forecast accuracy on hold out data– Do they make sense?– Do they produce good decisions?

• Revise forecasts• Recalibrate model on full data set• Produce forecasts and adjust as necessary• Produce report• In future - Evaluate accuracy of forecasts


Means and Standard Deviations Means and standard deviations are only useful for

summarizing data when it looks like it comes from a normal distribution


-3 -2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

They especially are not appropriate for summarizing time series data with trends or seasonality.

Some Normal Distribution Properties• Determined completely by its mean and standard deviation • Its skewness is 0 and its kurtosis is 0• 95% of the observations fall within 2 standard deviations (not standard errors!) of

the mean – Useful for determining forecast ranges– Usually forecasts are accurate to 2 standard deviations

• 95% of the observations fall below + 1.645

– Useful for determining service levels of inventory policies• When extreme outliers may occur, the normal distribution may not be appropriate

– Such distributions are said to have long tails – These distributions have positive kurtosis.– The book, The Black Swan, by Nassim Taleb addresses the practical significance of this

issue.


Data Patterns


Diagram 1.2: Seasonal - more or less regular movements

w ithin a year

0

20

40

60

80

100

120

Year 5 10

15

20

25

30

35

40

45

Diagram 1.1: Trend - long-term growth or decline occuring

w ithin a series

0

20

40

60

80

100

Year 3 6 9 12

15

18

21

24

27

30

Diagram 1.3: Cycle - alternating upswings of varied length

and intensity

0

2

4

6

8

10

Year 5 10

15

20

25

30

35

40

45

Diagram 1.4: Irregular - random movements and those which

reflect unusual events

0

50

100

150

200

250

300

350

1 10

19

28

37

46

55

64

73

82

Basic Modeling Concept


An observed measurementis made up of a systematic part

and a random part

Unfortunately we cannot observe either of these.Forecasting methods try to isolate the systematic part.

Forecasts are based on the systematic part.The random part determines the distribution shape and

forecast accuracy.

Basic Concept Again


Observed Value = Signal “+” Noise• In non-normal (or non-additive) models the “+” may be

inappropriate and we can regard the observed value as an observation drawn from a probability distribution.

• In this case the goal is to determine an appropriate probability distribution and model the time series behavior of its parameters.

• For example, if the data consists of low counts (such as number of tanker accidents), then clearly a normal distribution won’t fit well.

• What might you suggest?

Forecasting Notation


t a specific time period

T total number of observations

yt observed value at time t

yt+h|t forecasted value k periods ahead at time t^

Correlation

• Measures the strength of the (linear) relationship between two measurements

• Often denoted by rXY

• A number between -1 and +1• Answers question: Does one measurement contain

information about another measurement?• Theoretically rXY = Cov(X,Y)/X Y

• From a sample,


Autocorrelation - What is it?

• Correlation between observations at different time points in a time series - estimated by rk

– Lag 1 autocorrelation measures the correlation between yt and yt-1

– Lag k autocorrelation measures the correlation between yt and yt-k

• Summarized in terms of an autocorrelation function (ACF) which give the autocorrelations between observations at all lags.– It is often represented graphically as a plot of autocorrelation vs. lag– acf() in R – Note formula is different than that for simple correlation between yt

and yt-1


Autocorrelation - Why is it useful?

• Can the past help predict the future?– if autocorrelations at all lags are near zero then best

predictor is historical mean– if all autocorrelations of differences of series are near

zero then best predictor of the future is the current value– if autocorrelations at seasonal lags are large - suggests

seasonality in data

• An important component of the ARIMA or Box-Jenkins’ method


Autocorrelation Example 1


-1.0

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-0.5

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0.0

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0.5

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1.0

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Autocorrelations of C2 (0,0,12,1,0)

Time

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toco

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latio

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-2.0

-0.8

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1.8

3.0

1 17 34 50 67

Plot of C2

Time

C2

Autocorrelation Example 2


4.8

5.1

5.4

5.7

6.0

1 19 37 55 73

Plot of Wages

Time

Wa

ge

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-1.0

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-0.5

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Autocorrelations of Wages (0,0,12,1,0)

Time

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-1.0

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Autocorrelations of Wages (1,0,12,1,0)

Time

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toco

rre

latio

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