Forecastin1g-Spring 2012 [Compatibility Mode]

ETE 329 B i S t E i i Business System Engineering

Part-1: ForecastingPart 1: Forecasting

Presented by Sonia Sultana

Senior Lecturer

Sonia Sultana, Lecturer, Daffodil International University

Senior LecturerDaffodil International University

ForecastingForecasting-- IntroductionIntroduction

• Forecasting is an estimate of what is likely to happen inthe future.

• Forecasts are concerned with determining what thefuture will look like; planning is concerned with what itshould look like.

• Forecasting provides a basis for coordinating activitiesin various parts of the companyin various parts of the company.

• Forecasts are important input to both long-term, strategicdecision-making, as well as for short-term planning fordec s o a g, as we as o s o t te p a g oday-to-day operations.

Forecasting- Importance

• Finance uses long-term forecasts for capitall i d h t t f t f b d tiplanning and short-term forecasts for budgeting.

• Marketing produces sales forecasts for marketl i d k t t tplanning and market strategy.

• Operations develops and uses forecasts forh d li i d lscheduling, inventory management, and long-term

capacity planning.• Human Resource Management uses forecasts to

estimate the need for employees.

Forecasting- Types

1. Demand Forecasts these are estimates of demandfor a company’s goods or services.

2. Technological Forecasts These are forecastsconcerned with the rate of change in technologyconcerned with the rate of change in technologyand the impact on a company’s revenues and/orcosts.

3. Economic Forecasts predict inflation rates,employment rates, money supply, housing starts,and other measures of the performance of aneconomy.

4

Features of Forecasts

Forecasting techniques assume that the same basicor original system that existed in the past will existor original system that existed in the past will existin the future.

Forecasts are rarely perfect.

Forecast accuracy decreases as the time horizonForecast accuracy decreases as the time horizonincreases.

F t f f it tForecasts for groups of items are more accuratethan forecasts for individual items.

5

Forecasting ProcessForecasting Process

1. Identify the purpose of forecast

3. Plot data and identify patterns

2. Collect historical data

6. Check forecast accuracy with one

4. Select a forecast 5. Develop/compute forecast for period

purpose of forecast identify patterns data

accuracy with one or more measures

model that seems appropriate for data

forecast for period of historical data

7.I No 8b. Select new

forecast model or adjust parameters of existing model

Is accuracy of forecast

acceptable?

No

Y

8a. Forecast over planning horizon

9. Adjust forecastbased on additionalqualitative information

10. Monitor results and measure forecast accuracy

Yes

qualitative information y

Forecasts by Time HorizonForecasts by Time Horizon• Short-range forecast

• Up to 1 year; usually less than 3 months• Job scheduling, worker assignments

di f• Medium-range forecast• 3 months to 3 years

Sales & production planning budgeting• Sales & production planning, budgeting

• Long-range forecast• Long range forecast• 3+ years• New product planning, facility locationp p g, y

Demand behaviorDemand behavior• Trend

• A gradual, long-term up or down movement of demand• Linear, exponential, several year duration

• Seasonal pattern• An up-and-down repetitive movement in demand occurring periodically

short term: often annually)D t th h bit t• Due to weather, habits etc.

• Occurs within a predefined period: year, month, week, day• Cycle

• An up-and-down repetitive movement in demand (long term)• An up-and-down repetitive movement in demand (long term)• Repeating up & down movements• Due to interactions of factors influencing economy• Usually 2-10 years durationy y

• Random variations• Movements in demand that do not follow a pattern

Graphical representation of Demand Graphical representation of Demand BehaviorBehavior

ndnd ndnd

Dem

anD

eman

Dem

anD

eman

Random Random movementmovement

TimeTime(a) Trend(a) Trend

TimeTime(b) Cycle(b) Cycle

eman

dem

and

Dem

and

Dem

and

TimeTimeTimeTime

DD DD

(d) Trend with seasonal pattern(d) Trend with seasonal pattern(c) Seasonal pattern(c) Seasonal pattern

Forecasting Techniques Forecasting Techniques

Type I: Qualitative forecastingIt is based on opinion and intuition Generally used when data areIt is based on opinion and intuition. Generally used when data are

limited, unavailable, or not currently relevant. Forecast dependson skill & experience of forecaster & available information.UsedUsed whenwhen situationsituation isis vaguevague andand littlelittle datadata existexist.. ItIt isis appliedappliedgg ppppforfor NewNew productsproducts andand NewNew technologytechnology

1.1 Four Qualitative models are:QJury of executive opinionSales force compositeConsumer surveyConsumer survey Delphi method

Four Qualitative ModelsFour Qualitative Models1.Jury of executive opinion

collect opinions of high-level executives, sometimes augment bystatistical modelsInvolves small group of high-level managersCombines managerial experience with statistical modelsRelatively quick

2.Sales Force CompositeEach salesperson projects his or her salesCombined at district and national levelsTends to be overly optimistic

3.Consumer /Market SurveyA k t b t h i l• Ask customers about purchasing plans

What consumers say, and what they actually do are often differentSometimes difficult to answer

Four Qualitative ModelsFour Qualitative Models

4.Delphi MethodIterative group process, continues until consensus is reachedIterative group process, continues until consensus is reachedSteps involved in Delphi Method:1. Choose the experts to participate.

h h ( l) b f f ll2. Through a questionnaire (or E‐mail), obtain forecasts from allparticipants.

3. Summarize the results and redistribute them to the3participants along with appropriate new questions.

4. Summarize again, refining forecasts and conditions, andagain develop new questionsagain develop new questions.

5. Repeat Step 4 if necessary. Distribute the final results to allparticipants.

Qualitative Qualitative MethodsMethods : : AdvantagesAdvantages & & DisadvantagesDisadvantages

Advantages :• Take intangible factors into consideration• Take intangible factors into consideration.• Useful when there are little data available (new product, new

market, new business unit). )

Disadvantages :g• Long consultation process• High risk of getting a biased forecast• Expensive• Usually not precise

Q i i f i

Type II: Quantitative ForecastingType II: Quantitative forecasting

It is used when situation is ‘stable’ and historical data existExisting productsExisting productsCurrent technologyInvolves mathematical techniques. e.g., forecasting sales of

N i hOverview of Quantitative Forecasting

vo ves at e at ca tec ques. e.g., o ecast g sa es ocolor televisions

1. Naive approach2. Moving averages3 Exponential smoothing

TimeTime--Series ModelsSeries Models3. Exponential smoothing4. Trend projection5. Linear regression Associative ModelAssociative Modelg

Quantitative Methods : Quantitative Methods : Advantages & DisadvantagesAdvantages & Disadvantages

Advantages :• Easy to use once the right

Disadvantages :• Do not take « newmodel has been developed.

• Data collection is quick andi t f th

• Do not take « newinformation » intoconsideration

easy since most of therequired information is alreadyin the business’ systems (ex.previous sales) or readilyprevious sales) or readilyavailable (ex. consumer priceindex).

Realities of ForecastingRealities of Forecasting1. Forecasts are seldom perfect: almost always

wrong by some amountg y

2. Aggregated forecasts are more accurate thanindividual forecastsindividual forecasts

3. More accurate for shorter time periods3. o e accu ate o s o te t e pe ods

4. Most forecasting methods assume that there issome underlying stability in the system: watchout for special events.

Naive ForecastsNaive Forecasts

A forecast that assumes that demand in the next period willbe equal to demand in the most recent period.be equal to demand in the most recent period.

Characteristics:

• Simple to useVirt all no cost• Virtually no cost

• Quick and easy to prepare• Easily understandable• Easily understandable• Can be a standard for accuracy• Cannot provide high accuracyp g y

Naive ForecastsNaive Forecasts

Assumes demand innext period is the sameORDERSORDERS

MONTHMONTH PER MONTHPER MONTH next period is the sameas demand in mostrecent period

JanJan 120120FebFeb 9090MM 100100

MONTHMONTH PER MONTHPER MONTH

--120120

FORECASTFORECAST

If May sales were48, then June sales

ill b 48

MarMar 100100AprApr 7575MayMay 110110JuneJune 5050

1201209090

1001007575 will be 48

Sometimes can be costeffective & efficient

JuneJune 5050JulyJuly 7575AugAug 130130SeptSept 110110

757511011050507575 effective & efficientSeptSept 110110

OctOct 9090 1301301101109090Nov Nov --

Techniques for AveragingTechniques for Averaging

• These are techniques that are useful for data that has onlyrandom variation.

• These techniques smooth fluctuations in a time series.

• Forecasts that are based on an average are more “stable”than the original data.

• There are three popular averaging techniques:Si l iSimple moving averageWeighted moving averageSimple exponential smoothing

Moving Average

• A technique that uses a number of historical data values togenerate a forecast.

l fi di i f i b d i• Involves finding a series of successive averages by droppingthe first data value in the series and adding the last datavalue.

• Useful for data without trend, seasonality, or cycles.

Weekly Patient Arrivals at a Medical Clinic

425

450

475

Arr

ival

s

350

375

400

1 4 10 13 16 19 22 2 28

Pat

ient

Sonia Sultana, Lecturer, Daffodil International University

1 4 7 10 13 16 19 22 25 28

Week

Simple Moving Average Formula• The simple moving average model assumes an average is a goodestimator of future behavior.

• A technique that averages a number of recent actual values,q g ,updated as new values become available

• The formula for the simple moving average is:

F = A + A + A +...+Ant

t-1 t-2 t-3 t-n

n

Ft = Forecast for the coming periodN N b f i d b dN = Number of periods to be averaged

A t-1 = Actual occurrence in the past period for up to “n” periods

Simple Moving AverageA key decision involves selecting the number of periods that will beincluded in the average.

• The larger the number of periods, the greater the smoothing; theThe larger the number of periods, the greater the smoothing; thesmaller the number of periods, the quicker the forecast reacts tochanges in the data.

Example of Three- and Five-Period Moving Average

90

100

d

3-Period 5-Period MA MA

Period Demand Forecast Forecast1 53

50

60

70

80D

eman

d1 532 623 844 78 66.35 95 74.76 75 85.7 74.47 66 82 7 78 8 50

1 2 3 4 5 6 7 8 9 10

Period

Demand 3-Period MA 5-Period MA

7 66 82.7 78.88 82 78.7 79.69 71 74.3 79.210 83 73.0 77.8 78.7 75.4

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Example 1 – Simple Moving Average Illustration

Market Mixer, Inc. sells can openers. Monthly sales for an eight-month period were as follows:

Month Sales Month Sales

Example 1 Simple Moving Average Illustration

1 450 5 4602 425 6 4553 445 7 4304 435 8 420

Forecast next month’s sales using a 3-month moving average.

Solution:Period Sales Moving Average Forecast

1 450Comments:1. Any forecasts beyond Period 9 will

2 4253 4454 435 (450 + 425 + 445) / 3 = 4405 460 (425 + 445 + 435) / 3 = 435

y yhave the same value as the Period 9 forecast; i.e., 435.

2. As a new actual value becomes available, the forecast will be updated by adding the newest value and5 460 (425 445 435) / 3 435

6 455 (445 + 435 + 460) / 3 = 4477 430 (435 + 460 + 455) / 3 = 4508 420 (460 + 455 + 430) /3 = 4489 (455 + 430 + 420) / 3 =

by adding the newest value and dropping the oldest one.

3. SMA gives equal weight to all values in the average. Hence, the oldest value has the same weight, or importance as the newest435

23

9 (455 + 430 + 420) / 3 importance, as the newest.435

Simple Moving Average Problem (2)Simple Moving Average Problem (2)

W eek Demand1 820

• Question: What is the 3 weeki f f1 820

2 7753 680

moving average forecast forthis data?A l h k

4 6555 6206 600

• Assume you only have 3 weeksand 5 weeks of actual demanddata for the respective6 600

7 575

data for the respectiveforecasts

Simple Moving Average Problem (2) Simple Moving Average Problem (2) SolutionSolutionSolutionSolution

W eek Demand 3-W eek 5-W eek1 8202 7753 6804 6555 6206 6007 575

Weighted Moving Average

• A model that applies different “weights” to each value in thepp gmoving average calculation.

The formula for the moving average is:

F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t- n

w = 1i

n

∑wt = weight given to time period “t” occurrence. (Weights must add to one.)

i=1

(Let us continue with the same problem as we had in Example 1.) Market Mixer, Inc. sells Example 1 – Weighted Moving Average Illustration

( p p ) ,can openers. Monthly sales for an eight-month period were as follows:

Month Sales Month Sales1 450 5 4602 425 6 4553 445 7 4304 435 8 420

Forecast next month’s sales using a 3-month weighted moving average, where the weightfor the most recent data value is 0.60; the next most recent, 0.30; and the earliest, 0.10.

Solution:Period Sales Weighted Moving Average Forecast

1 4502 425

Comments:1. Any forecasts beyond 2 425

3 4454 435 (450*.10) + (425*.30) + (445*.60) = 4405 460 (425*.10) + (445*.30) + (435*.60) = 4376 455 (445* 10) + (435* 30) + (460* 60) = 451

y yPeriod 9 will have the same value as the Period 9 forecast, i.e., 427.

3. WMA gives greater weight to more recent values in the6 455 (445 .10) + (435 .30) + (460 .60) = 451

7 430 (435*.10) + (460*.30) + (445*.60) = 4558 420 (460*.10) + (455*.30) + (430*.60) = 4419 (445*.10) + (430*.30) + (420*.60) =

to more recent values in the moving average and is more responsive to recent changes in the data.

427

27

Weighted Moving Average Problem (2) Weighted Moving Average Problem (2)

Question: Given the weekly demand information and weights,what is the weighted moving average forecast of the 5th periodor week?

Weights:t-1 .7

W eek Demand Forecast1 8202 775

t-2 .2t-3 .1

3 6804 6555

Simple Exponential Smoothing

• This is a variation of the weighted moving average model.W i ht d t i d b ti l f ti hi h• Weights are determined by an exponential function whichdeclines as the data gets older.

• The most recent observations might have the highestg gpredictive value.

• Therefore, we should give more weight to the more recenti i d h f itime periods when forecasting.

• The formula: Ft+1 = aAt + (1 – a)Ft

Where  F = forecast for next periodWhere  Ft+1 = forecast for next perioda = smoothing constant (0 < a < 1)At = current period’s actual demand

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Ft = current period’s forecast

Advantages of Simple Exponential Smoothing model over Advantages of Simple Exponential Smoothing model over other forecasting approachesother forecasting approaches

• Exponential models are surprisingly accurate• Formulating Exponential model is relatively easy• The user can understand how the model works• Little computation is required to use the model• Computer storage requirements are small becausep g qof the limited use of historical data

• Tests for accuracy as to how well the model isyperforming are easy to compute

Example 1 – Simple Exponential Smoothing Illustration(Let us continue with the same problem as we had in Example 1.) Market Mixer, Inc. sells can openers. Monthly sales for an eight-month period were as follows:

Month Sales Month Sales1 450 5 4602 425 6 4552 425 6 4553 445 7 4304 435 8 420

Forecast next month’s sales using exponential smoothing with alpha (α) = 0.30 and thefirst (starting) forecast = 450.( g)

Solution:Period Sales Exponential Smoothing Forecast

1 450 4502 425 ( 30*450) + (1 - 30)*450 = 450 Comments:2 425 (.30 450) + (1 - .30) 450 = 4503 445 (.30*425) + (1 - .30)*450 = 4434 435 (.30*445) + (1 - .30)*443 = 4435 460 (.30*435) + (1 - .30)*443 = 4416 455 ( 30*460) + (1 30)*441 447

1. Any forecasts beyond Period 9 will have the same value as the Period 9 forecast, i.e., 436.

3. The higher the value of α, the quicker the reaction to6 455 (.30*460) + (1 - .30)*441 = 447

7 430 (.30*455) + (1 - .30)*447 = 449 8 420 (.30*430) + (1 - .30)*449 = 4439 (.30*420) + (1 - .30)*443 =

quicker the reaction to changes in the data and the less the smoothing.

436

Exponential Smoothing Problem (1)Exponential Smoothing Problem (1)

W eek Demand1 820

• Question: Given the weekly1 8202 7753 680

Q ydemand data, what are theexponential smoothingf f i d i4 655

5 750

forecasts for periods 2‐10 usinga=0.10 and a=0.60?

• Assume F =D6 8027 7988 689

• Assume F1=D1

8 6899 775

10

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783 53 723 236 802 783.53 723.237 798 785.38 770.498 689 786 64 787 008 689 786.64 787.009 775 776.88 728.20

10 776 69 756 2810 776.69 756.28

Exponential Smoothing Problem (1) Exponential Smoothing Problem (1) PlottingPlotting

900

700

800

eman

d Demand

0.1

500600

1 2 3 4 5 6 7 8 9 10

De

0.6

1 2 3 4 5 6 7 8 9 10

Week

Exponential Smoothing Problem (2)Exponential Smoothing Problem (2)Question: What are the exponential smoothingforecasts for periods 2‐5 using a =0.5?AssumeF1=D1

Week Demand1 820

W eek Demand 0.51 820

2 7753 680

2 7753 6804 655

4 6555

5

Picking a Smoothing ConstantPicking a Smoothing Constant

Exponential SmoothingExponential Smoothing

95

100Actual Alpha=0.10 Alpha=0.40

85

90

95

eman

d

75

80

De

702 3 4 5 6 7 8 9 10 11

Period

Problem 1 Problem 1 • National Mixer Inc. sells can openers.

Monthly sales for a seven-month periodwere as follows:• Forecast September sales volume using

h f h f ll i

Month Sales(1000)

each of the following:• A five-month moving average

Exponential smoothing with a smoothing

Feb 19Mar 18Apr 15• Exponential smoothing with a smoothing

constant equal to .20, assuming a Marchforecast of 19.

Apr 15May 20Jun 18

• The naive approach• A weighted average using .60 for August,

30 for July and 10 for June

Jul 22Aug 20

.30 for July, and .10 for June.

Problem 2 Problem 2

• A dry cleaner uses exponential smoothing toforecast equipment usage at its main plant Augustforecast equipment usage at its main plant. Augustusage was forecast to be 88% of capacity. Actualusage was 89 6% A smoothing constant of 0 1 isusage was 89.6%. A smoothing constant of 0.1 isused.

Prepare a forecast for September• Prepare a forecast for September• Assuming actual September usage of 92%, prepare

f t f O t ba forecast of October usage

Problem 3 Problem 3 • An electrical contractor’s records during the last five

weeks indicate the number of job requests:Week: 1 2 3 4 5Requests: 20 22 18 21 22

Predict the number of requests for week 6 using each of these methods:these methods:• Naïve• A four-period moving average• A four period moving average• Exponential smoothing with a smoothing constant of .30.

Use 20 for week 2 forecast.

Forecast AccuracyForecast Accuracy

• Source of forecast errors:• Model may be inadequatey q• Irregular variations• Incorrect use of forecasting technique

R d i ti• Random variation

• Key to validity is randomness• Key to validity is randomness • Accurate models: random errors• Invalid models: nonrandom errors

• Key question: How to determine if forecasting errors are random?errors are random?

Error measuresError measures

• Error - difference between actual value and predicted valuevalue

• Mean Absolute Deviation (MAD)• Average absolute error

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

• Mean Absolute Percent Error (MAPE)• Mean Absolute Percent Error (MAPE)

• Average absolute percent error

MAD, MSE, and MAPEMAD, MSE, and MAPE

MADActual forecast−∑

MAD =n

2

MSE =Actual forecast)

1

2−∑

n

(

-1n

Actual Forecast−∑

Actual Forecast100

ActualMAPEn

×=∑

n

ExampleExample

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 1 904 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0 467 216 217 -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