4-1 operations management forecasting chapter 4. 4-2 examples predict the next number in the...

4-1

Operations Operations ManagementManagement

ForecastingForecastingChapter 4Chapter 4

4-2

ExamplesExamples Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7, ?

b) 2.5, 4.5, 6.5, 8.5, 10.5, ?

c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?

4-3

ExamplesExamples Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7, y = 3.7

b) 2.5, 4.5, 6.5, 8.5, 10.5, y = 0.5 + 2x

c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5,

y = 4.5 + 0.5x + ci

c1 = 0; c2 = 2; c3 = 0; c4 = -2; etc

4-4

OutlineOutline What is Forecasting?

Time horizons. Life cycle.

Types of Forecasts.

Eight Steps in the Forecasting System. Forecasting Approaches:

Overview of Qualitative Methods. Overview of Quantitative Methods.

4-5

Outline - ContinuedOutline - Continued Time-Series Forecasting:

Moving Averages.

Exponential Smoothing.

Trend Projection.

Associative Forecasting Methods: Regression and Correlation Analysis.

Monitoring and Controlling Forecasts.

Forecasting in the Service Sector.

4-6

What is Forecasting?What is Forecasting?

Art and science of predicting future events.

Underlying basis of all business decisions. Production & Inventory.

Personnel & Facilities.

Focus on forecasting demand.

Sales will be $200 Million!

4-7

Short-range forecast: Usually < 3 months. Job scheduling, worker assignments.

Medium-range forecast: 3 months to 3 years. Sales & production planning, budgeting.

Long-range forecast: > 3 years. New product planning, facility location.

Types of Forecasts by Time HorizonTypes of Forecasts by Time Horizon

4-8

Short- vs. Long-term ForecastingShort- vs. Long-term Forecasting

Medium & Long range forecasts: Long range for design of system. Deal with comprehensive issues. Support management decisions regarding planning.

Short-term forecasts: To plan detailed use of system. Usually use quantitative techniques. More accurate than longer-term forecasts.

4-9

Influence of Product Life CycleInfluence of Product Life Cycle

Stages of introduction and growth require longer forecasts than maturity and decline.

Forecasts useful in projecting: staffing levels,

inventory levels, and

factory capacity (expansion and contraction),

as product passes through life cycle stages.

4-10

Forecasting During the Life CycleForecasting During the Life Cycle

Hard to forecast.

Need long-range forecasts.

Often use qualitative models.

Introduction Growth Maturity Decline

Sales

Forecasting critical, both for future magnitude and growth rate.

Long-range forecasts still important.

Easier to forecast.

Use quantitative models.

Hard to forecast, but forecasting is less important.

Time

4-11

Eight Steps in ForecastingEight Steps in Forecasting Determine the use of the forecast.

Select the items to be forecast.

Determine the time horizon of the forecast.

Select the forecasting model(s).

Gather the data.

Make the forecast.

Validate and implement results.

Monitor forecasts and adjust when needed.

4-12

Realities of ForecastingRealities of Forecasting

Assumes future will be like the past (causal factors will be the same).

Forecasts are imperfect.

Forecasts for groups of product are more accurate than forecasts for individual products.

Accuracy decreases with length of forecast.

4-13

Forecasting ApproachesForecasting Approaches

Used when situation is ‘stable’ & historical data exist. Existing products &

current technology. No significant changes

expected.

Involves mathematical techniques. Example: forecasting sales

of color televisions.

Quantitative Methods Used when little data or time

exist. New products & technology. Long time horizon. Major changes expected.

Involves intuition, experience. Example: forecasting for

e-commerce sales.

Qualitative Methods

4-14

Overview of Qualitative MethodsOverview of Qualitative Methods

Jury of executive opinion. Combine opinions from executives.

Sales force composite. Aggregate estimates from salespersons.

Delphi method. Query experts interatively.

Consumer market survey. Survey current and potential customers.

4-15

Seek opinions/estimates from small group of high-level managers working together.

Combines managerial experience with statistical models.

+ Relatively quick.

- ‘Group-think’.- Leader may dominate.

Jury of Executive OpinionJury of Executive Opinion

4-16

Sales Force CompositeSales Force Composite Each salesperson projects their

sales. Aggregate projections at district

& national levels.

+ Sales rep’s know customers.

- Must not reward inaccurate forecasts. May over- or under-forecast to

acquire more resources.

SalesSales

4-17

Delphi MethodDelphi Method

Iterative group process. 3 types of people:

Decision makers. Staff. Respondents.

+ Reduces ‘group-think’.- Takes time.

Respondents Respondents

Staff Staff

(Make forecast)

(Provide input to decision makers)

Decision MakersDecision Makers

(Administer)

4-18

Consumer Market SurveyConsumer Market Survey

Ask customers about purchasing plans.

+ Relatively simple.- What consumers say, and

what they actually do are often different.

How many hours will you use the Internet

next week?

How many hours will you use the Internet

next week?

4-19

Quantitative Forecasting MethodsQuantitative Forecasting Methods

QuantitativeForecasting

LinearRegression

AssociativeModels

ExponentialSmoothing

MovingAverage

Time SeriesModels

TrendProjection

4-20

Set of evenly spaced numerical data. From observing response variable at regular time

periods.

Forecast based only on past values. Assumes that factors influencing past will continue

influence in future.

Example:Year: 1 2 3 4 5

Sales: 78.7 63.5 89.7 93.2 92.1

What is a Time Series?What is a Time Series?

4-21

TrendTrend

SeasonalSeasonal

CyclicalCyclical

RandomRandom

Time Series ComponentsTime Series Components

4-22

Product Demand over 4 YearsProduct Demand over 4 Years

Year1

Year2

Year3

Year4

Dem

and

for p

rodu

ct o

r ser

vice

4-23

Product Demand over 4 YearsProduct Demand over 4 Years

Actual demand line

Year1

Year2

Year3

Year4

Seasonal peaksTrend component

Dem

and

for p

rodu

ct o

r ser

vice

Random variation

Cyclic component

4-24

Persistent, overall upward or downward pattern.

Due to population, technology etc. Several years duration.

Time

Trend ComponentTrend Component

4-25

Regular pattern of up & down fluctuations. Due to weather, customs etc. Occurs within 1 year. Quarterly, monthly, weekly, etc.

Time

Demand

Summer

Seasonal ComponentSeasonal Component

4-26

Repeating up & down movements. Due to interactions of factors influencing

economy.

Usually 2-10 years duration.

YearYear

DemandDemandCycle

Cyclical ComponentCyclical Component

4-27

Erratic, unsystematic, ‘residual’ fluctuations.

Due to random variation or unforeseen events. Union strike

Tornado

Short duration & non-repeating.

Random ComponentRandom Component

4-28

Any value in a time series is a combination of the trend, seasonal, cyclic, and random components.

Multiplicative model: Yi = Ti · Si · Ci · Ri

Additive model: Yi = Ti + Si + Ci + Ri

General Time Series ModelsGeneral Time Series Models

4-29

Naive ApproachNaive Approach

Demand in next period is the same as demand in most recent period. e.g., If May sales were 48, then June

sales will be 48.

Sometimes cost effective & efficient.

Usually not good.

4-30

MA is a series of arithmetic means.

Used if little or no trend.

Used often for smoothing.

MAMAnn

nn Demand inDemand in previousprevious periodsperiods

Moving Average MethodMoving Average Method

4-31

You’re manager of a museum store that sells historical replicas. You want to forecast sales (in thousands) for months 4 and 5 using a 3-period moving average.

Month 1 4Month 2 6Month 3 5Month 4 ?Month 5 ?

Moving Average ExampleMoving Average Example

4-32

Moving Average ForecastMoving Average Forecast

Month ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1 4 NA NA2 6 NA NA3 5 NA NA4 ?5 ?

4+6+5=15 15/3=5

6 ?

4-33

Month

Moving Average GraphMoving Average Graph

95 96 97 98 99 00

Sales

2

4

8Actual

Forecast

4 5 3 2 1 6

4

2

6

4-34

Actual Demand for Month 4 = 3Actual Demand for Month 4 = 3

Month ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1 4 NA NA2 6 NA NA3 5 NA NA4 3 4+6+5=15 15/3 = 55 ?6 ?

4-35

Month

Moving Average GraphMoving Average Graph

95 96 97 98 99 00

Sales

2

4

8Actual

Forecast

4 5 3 2 1 6

4

2

6

4-36

Moving Average ForecastMoving Average Forecast

Month ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1 4 NA NA2 6 NA NA3 5 NA NA4 3 15 55 7 6+5+3=14 14/3=4.6676 ?

4-37

Month

Moving Average GraphMoving Average Graph

95 96 97 98 99 00

Sales

2

4

8Actual

Forecast

4 5 3 2 1 6

4

2

6

4-38

Actual Demand for Month 5 = 7Actual Demand for Month 5 = 7

Month ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1 4 NA NA2 6 NA NA3 5 NA NA4 3 15 55 7 6+5+3=14 14/3=4.6676 ?

4-39

Month

Moving Average GraphMoving Average Graph

95 96 97 98 99 00

Sales

2

4

8Actual

Forecast

4 5 3 2 1 6

4

2

6

4-40

Moving Average ForecastsMoving Average Forecasts

Month ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1 4 NA NA2 6 NA NA3 5 NA NA4 3 4+6+5=15 15/3=5.05 7 6+5+3=14 14/3=4.6676 ? 5+3+7=15 15/3=5.0

4-41

Month

Moving Average GraphMoving Average Graph

95 96 97 98 99 00

Sales

2

4

8Actual

Forecast

4 5321 6

4

2

6

4-42

Gives more emphasis to recent data. Weights decrease for older data. Weights sum to 1.0.

May be based on intuition. Sum of digits weights: numerators are consecutive.

3/6, 2/6, 1/6 4/10, 3/10, 2/10, 1/10

WMA =WMA =ΣΣ [(Weight for period [(Weight for period nn)) (Demand in period (Demand in period nn)])]

ΣΣWeightsWeights

Weighted Moving Average MethodWeighted Moving Average Method

4-43

Weighted Moving Average: 3/6, Weighted Moving Average: 3/6, 2/6, 1/62/6, 1/6

Month ResponseYi

WeightedMoving Average

1 4 NA2 6 NA3 5 NA4 31/6 = 5.16756 ?

??

4-44

Weighted Moving Average: 3/6, Weighted Moving Average: 3/6, 2/6, 1/62/6, 1/6

Month ResponseYi

WeightedMoving Average

1 4 NA2 6 NA3 5 NA4 3 31/6 = 5.1675 76 ?

25/6 = 4.16732/6 = 5.333

4-45

Increasing n makes forecast: Less sensitive to changes.

Less sensitive to recent data.

Weights control emphasis on recent data.

Do not forecast trend well.

Require historical data.

Moving Average MethodsMoving Average Methods

4-46

Moving Average GraphMoving Average Graph

Time

Demand

Actual

4-47

Moving Average GraphMoving Average Graph

Time

Demand

Actual

Small nSmall n

Large nLarge n

4-48

Weighted Moving Average GraphWeighted Moving Average Graph

Time

Demand

Actual

Large weight Large weight on recent dataon recent data

Small weight Small weight on recent dataon recent data

4-49

Form of weighted moving average. Weights decline exponentially.

Most recent data weighted most.

Requires smoothing constant (). Usually ranges from 0.05 to 0.5

Should be chosen to give good forecast.

Involves little record keeping of past data.

Exponential Smoothing MethodExponential Smoothing Method

4-50

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

Ft = Forecast value for time t

At-1 = Actual value at time t-1 = Smoothing constant

Need initial forecast Ft-1 to start. Could be given or use moving average.

Exponential Smoothing EquationExponential Smoothing Equation

4-51

You want to forecast product demand using exponential smoothing with = .10. Suppose in the most recent month (month 6) the forecast was 175 and the actual demand was 180.

Month 6 180Month 7 ?Month 8 ?Month 9 ?Month 10 ?

Exponential Smoothing ExampleExponential Smoothing Example

4-52

Ft = Ft-1 + αα (At-1 - Ft-1)

MonthMonth ActualActualForecast, Forecast, FF tt

((αα = = .10.10))

66 180180 175.00 (Given)175.00 (Given)

77 ?? 175.00 +175.00 + .10.10((180 180 - 175.00) = 175.50- 175.00) = 175.50

88 ??

99 ??

1010 ??

1111 ??

Exponential Smoothing - Month 7Exponential Smoothing - Month 7

4-53

Exponential Smoothing - Month 8Exponential Smoothing - Month 8Ft = Ft-1 + αα (At-1 - Ft-1)

ActualForecast, F t

(αα = = .10.10))

180 175.00 (Given)

168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

?? 175.50 +175.50 + .10.10((168 168 - 175.50) = 174.75- 175.50) = 174.75

??

??

??

MonthMonth

66

77

88

99

1010

1111

4-54

Exponential Smoothing SolutionExponential Smoothing SolutionFt = Ft-1 + αα (At-1 - Ft-1)

ActualForecast, F t

(α = .10)

180180 175.00 (Given)175.00 (Given)

168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

?? 174.75 + 174.75 + .10.10((159159 - 174.75) = 173.18 - 174.75) = 173.18

??

??

MonthMonth

66

77

88

99

1010

1111

4-55

173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36

Exponential Smoothing SolutionExponential Smoothing SolutionFt = Ft-1 + αα (At-1 - Ft-1)

ActualForecast, F t

(α = .10)

180180 175.00 (Given)175.00 (Given)

168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18

190190

?? 173.36 +173.36 + .10.10((190190 - 173.36) = 175.02- 173.36) = 175.02

MonthMonth

66

77

88

99

1010

1111

4-56

Month

Sales

140150160170180190

6 7 8 9 10 11

Actual

Forecast

Exponential Smoothing GraphExponential Smoothing Graph

4-57

Increasing αα makes forecast: More sensitive to changes. More sensitive to recent data.

αα controls emphasis on recent data.

Do not forecast trend well. Trend adjusted exponential smoothing - p. 90-93

Exponential Smoothing MethodsExponential Smoothing Methods

4-58

Exponential Smoothing GraphExponential Smoothing Graph

Time

Demand

Actual

4-59

Exponential Smoothing GraphExponential Smoothing Graph

Time

Demand

Actual

Large αLarge α

Small αSmall α

4-60

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

Forecast Effects ofForecast Effects of Smoothing Constant Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90% 9% 0.9%

4-61

Choosing Choosing - Comparing Forecasts - Comparing ForecastsA good method has a small error. Choose to produce a small error.

Error = Demand - Forecast Error > 0 if forecast is too low Error < 0 if forecast is too high

MAD = Mean Absolute Deviation: Average of absolute values of errors.

MSE = Mean Squared Error: Average of squared errors. MAPE = Mean Absolute Percentage Error: Average of

absolute value of percentage errors.

4-62

Mean Absolute Deviation (MAD)

Mean Squared Error (MSE)

Forecast Error EquationsForecast Error Equations

2

n

1i

2ii

nerrors forecast

n

)y(yMSE

ˆ

n| errorsforecast|

n

|yy|MAD

n

1iii

ˆ

4-63

Mean Absolute Percentage Error (MAPE)

Forecast Error EquationsForecast Error Equations

nActual

| errorsforecast|

ny

|yy|

MAPE

n

1i i

ii

ˆ

4-64

MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5

MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5

MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6%

Forecast Error ExampleForecast Error Example

Actual F1 F1 error 20 19 1 18 2

10 15 -5 13 -3

24 22 2 21 3

20 21 -1 18 2

F2 F2 error

4-65

MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5

MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5

MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6%

Which Forecast is Best?Which Forecast is Best?