Introduction to Operations Management

Forecasting (Ch.3)Forecasting (Ch.3)

Hansoo Kim ( 金翰秀 )Dept. of Management Information

Systems, YUST

OM Overview

Class Overview(Ch. 0)

Project Management

(Ch. 17)

Strategic Capacity Planning(Ch. 5, 5S)

Operations, Productivity, and Strategy

(Ch. 1, 2)

Mgmt of Quality/Six Sigma Quality

(Ch. 9, 10)

Supply Chain Management

(Ch 11)

Location Planning and Analysis

(Ch. 8)

Demand MgmtForecasting

(Ch 3)

Inventory Management

(Ch. 12)

Aggregated Planning

(Ch. 13)

Queueing/ Simulation

(Ch. 18)

MRP & ERP (Ch 14)

JIT & Lean Mfg System

(Ch. 15)

Term Project

Process Selection/

Facility Layout; LP(Ch. 6, 6S)X X X X X

XX X X

Today’s Outline What is Forecasting? 수요예측이란 ? Types of Forecasting 종류 Seven Steps of Forecasting 절차 Qualitative vs. Quantitative Forecasts

정성적 /정량적 방법 Various Forecasting Methods

여러 가지 수요예측 방법들 Evaluation Measures 평가방법

Terms( 용어 ) Associative models （联合模型） Bias （偏差） Centered moving average （中心

滑动平均数） Control chart （控制图） Correlation （想关系数） Cycles （循环变动） Delphi method （德尔菲法） Error （误差） Exponential smoothing （指数平滑

法） Forecast  ( 预册 ) Irregular variation （不规则变化） Judgmental forecasts （通过判断作

出预测） Least square line （最小二乘直线）

Linear trend equation （线形趋势模型）

Mean absolute deviation, MAD （绝对平均偏差）

Mean squared error, MSE （标准偏差）

Moving average （滑动平均法） Naive forecast （简单预测法） Predictor variable （预测变动） Random variations （随机变量） Regression （回归分析） Seasonal variations （季节性变

动） Time series （时间序列） Tracking signal （跟踪信号） Trend （长期趋势变动） Trend-adjusted exponential

smoothing （调整长期趋势后的指数平滑法）

Example: ForecastingPast Demand for Chairs, Smart Furniture

0

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Week

Dem

and

Demand > Products --- Lost SalesDemand < Products --- Inventory cost

What is demand in 21st week?

Week Demand1 8002 14003 10004 15005 15006 15007 13008 18009 1700

10 130011 170012 170013 150014 230015 230016 200017 170018 180019 220020 190021 ???

What is Forecasting?

The art and science of predicting future events, Using historical data

Underlying basis of all business decisions Production Inventory Personnel Facilities

Sales will be $200 Million!

CRM: Customer Relation Management

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

Types of Forecasts by Time Horizon

Short-range forecast ( 단기 예측 ) Up to 1 year; usually less than 3 months Job scheduling, worker assignments

Medium-range forecast ( 중기 예측 ) 3 months to 3 years Sales & production planning, budgeting

Long-range forecast ( 장기 예측 ) 3+ years New product planning, facility location, R&D

Influence 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

as product passes through life cycle stages

Introduction, Growth, Maturity, Decline( 도입기 , 성장기 , 성숙기 , 쇠퇴기 )

Strategy and Issues During a Product’s Life

Steps 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”

Realities of Forecasting

Forecasts are seldom perfect Forecasts are seldom perfect (( 수요예측은 잘 맞지 않는다수요예측은 잘 맞지 않는다 !!)!!)

Most forecasting methods assume that there is some underlying stabilitystability in the system ( 신제품 보다는 성숙기에 도달한 제품 )

Both product family and aggregated product family and aggregated product product forecasts are more accurate than individual product forecasts ( 단일제품 보다는 제품群으로 예측하는 것이 더 정확하다 )

Forecasting Approaches

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

Involves mathematical techniques e.g., forecasting sales of

color televisions

Quantitative Methods( 정량적방법 )

Used when situation is vague & little data exist New products New technology

Involves intuition, experience e.g., forecasting sales on

Internet

Qualitative Methods( 정성적방법 )

Overview of Qualitative Methods ( 정성적인 방법들 ) Jury of executive opinion

Pool opinions of high-level executives, sometimes augment by statistical models

Delphi method ( 델파이 기법 )** Panel of experts, queried iteratively

Sales force composite Estimates from individual salespersons are

reviewed for reasonableness, then aggregated

Consumer Market Survey Ask the customer

Overview of Quantitative Approaches

Naïve approach Moving averages Exponential

smoothing Trend projection

Linear regression

Time-series Models

Associative models

What is a Time Series?

Set of evenly spaced numerical data Obtained by observing response variable at

regular time periods Forecast based only on past values

Assumes that factors influencing past and present will continue influence in future

Example Year: 2000 2001 2002 2003 2004 Sales: 78.7 63.5 89.7 93.2 92.1

Product Demand Charted over 4 Years with Trend and Seasonality

Year1

Year2

Year3

Year4

Seasonal peaks Trend component

Actual demand line

Average demand over four years

Dem

and

for p

rodu

ct o

r ser

vice

Random variation

Time Series Components

TrendTrend

SeasonalSeasonal

CyclicalCyclical

RandomRandom

Overview of Qualitative Methods ( 정량적인 방법들 )

Naïve Approach Moving Average (MA) 滑动平均法 Weighted Moving Average Exponential Smoothing Method

(指数平滑法 ) Exponential Smoothing with Trend

Adjustment (调整长期趋势后的指数平滑法 )

Naive Approach (简单预测法 )

Assumes 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

© 1995 Corel Corp.

Moving Average (MA) Method滑动平均法

MA is a series of arithmetic means Used if little or no trend Used often for smoothing

Provides overall impression of data over time

Equation

MAMAnn

nn Demand inDemand in PreviousPrevious PeriodsPeriods

Moving Average

whereFt = Forecast for time period tMAn = n period moving averageAt – 1 = Actual value in period t – 1n = Number of periods (data points) in the moving averageFor example, MA3 would refer to a three-period moving average forecast, and MA5 would refer to a five-period moving average forecast.

Moving Average Example

You’re manager of a museum store that sells historical replicas. You want to forecast sales for 2008 using a 3-period moving average.

2003 42004 62005 52006 32007 7

© 1995 Corel Corp.

Moving Average Solution

Time Response Yi

Moving Total (n=3)

Moving Average

(n=3) 2003 4 NA NA 2004 6 NA NA 2005 5 NA NA 2006 3 4+6+5=15 15/3=5.0 2007 7 6+5+3=14 14/3=4.7 2008 NA 5+3+7=15 15/3=5.0

Weighted Moving Average Method

Used when trend is present Older data usually less important

Weights based on intuitionOften lay between 0 & 1, & sum to 1.0

Equation

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

ΣΣWeightsWeights

Actual Demand, Moving Average, Weighted Moving Average

0

5

10

15

20

25

30

35

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Sal

es D

eman

d

Actual sales

Moving average

Weighted moving average

Disadvantages of Moving Average Methods

Increasing n makes forecast less sensitive to changes

Do not forecast trend well Require much historical

data

Measure for Forecasting Error

Mean Square Error (MSE,标准偏差 )

Mean Absolute Deviation (MAD,绝对平均偏差 )

Mean Absolute Percent Error (MAPE)

2

n

1i

2ii

n

errorsforecast

n

)y(yMSE

nn

yyMAD

n

iii

|errorsforecast |

|ˆ|1

n

actual

forecastactual

100MAPE

n

1i i

ii

Exponential Smoothing Method (指数平滑法 )

Form of weighted moving average Weights decline exponentially Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen

Involves little record keeping of past data

Exponential Smoothing Equations

Ft = At -1 + (1- )At -2 + (1- )2·At - 3 + (1- )3At - 4 + ... + (1- )t-1·A0

Ft = Forecast value

At = Actual value

= Smoothing constant

FFtt = = FFtt-1-1 + + ((AAtt-1-1 - - FFtt-1-1) = ) = AAtt-1-1+(1- +(1- ) ) FFtt-1-1

Use for computing forecast

1

1

0

)1(

it

t

i

iA

Exponential Smoothing ExampleDuring the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. ( = .10). The first quarter forecast was 175..

Quarter Actual1 180

2 1683 1594 1755 190

6 2057 1808 1829 ?

Find the forecast for the 9th quarter.

Exponential Smoothing SolutionFt = Ft-1 + 0.1(At-1 - Ft-1)

QuarterQuarter ActualActualForecast, F t

( αα = = .10.10))

1 180 175.00 (Given)

22 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

33 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

44 175175

55 190190

66 205205

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

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

173.36 + .10(190 - 173.36) = 175.02

Exponential Smoothing SolutionFt = Ft-1 + 0.1(At-1 - Ft-1)

Time ActualForecast, F t

(α = .10)

44 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18

55 190190 173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36

66 205205 173.36 + .10(190 - 173.36) = 175.02173.36 + .10(190 - 173.36) = 175.0277 180180

88

175.02 + .10(205 - 175.02) = 178.02175.02 + .10(205 - 175.02) = 178.02

99 178.22 +178.22 + .10.10(182(182 - 178.22- 178.22)) = = 178.58 178.58

182182 178.02 + .10(180 - 178.02) = 178.22178.02 + .10(180 - 178.02) = 178.22

??

Forecast Effects of Smoothing Constant

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

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90% 9% 0.9%

= = AAtt-1-1+(1- +(1- ) ) FFtt-1-1

Impact of

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9

Quarter

Actu

al To

nage Actual

Forecast (0.1)

Forecast (0.5)

Choosing

Seek to minimize the Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)

If: Forecast error = demand - forecast

Then:n

errorForecast MAD

Using MS-Excel

Naïve MA WMA Exponential Smoothing Method

Associative Model:Regression ( 회기분석 ,回归分析 )

Deviation

Deviation

Deviation

Deviation

Deviation

Deviation

Deviation

Time

Valu

es o

f Dep

ende

nt V

aria

ble

bxaY ˆ

Actual observation

Point on regression line

Actual and the Least Squares Line

0

20

40

60

80

100

120

140

160

1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Regression Line

Actual Demand

Linear Trend Projection

Used for forecasting linear trend lineAssumes relationship between

response variable, Y, and time, X, is a linear function

Estimated by least squares methodMinimizes sum of squared errors

iY a bX i

Linear Trend Projection Model

Y a bXi i b > 0

b < 0

a

a

Y

Time, X

Least Squares Equations

Equation: ii bxaY

Slope:

xnx

yxnyxb

i

n

i

ii

n

i

Y-Intercept: xbya

X i Y i X i2 Y i

2 X iY i

X 1 Y 1 X 12 Y 1

2 X 1Y 1

X 2 Y 2 X 22 Y 2

2 X 2Y 2

: : : : :

X n Y n X n2 Y n

2 X nY n

ΣX i ΣY i ΣX i2 ΣY i

2 ΣX iY i

Computation Table ( 계산표 )

Using Regression Model

Year Demand 2000 74 2001 79 2002 80 2003 90 2004 105 2005 142 2006 122

The demand for electrical power at N.Y.Edison over the years 2000 – 2006 is given at the left. Find the overall trend.

Calculation for finding a and b

Year Time Period

Power Demand

x2 xy

2000 1 74 1 74

2001 2 79 4 158

2002 3 80 9 240

2003 4 90 16 360

2004 5 105 25 525

2005 6 142 36 852

2006 7 122 49 854

x=28 y=692 x2=140 xy=3,063

The Trend Line Equation

megawatts 151.56 10.54(9) 56.70 2008in Demand

megawatts 141.02 10.54(8) 56.70 2007in Demand

56.70 10.54(4) - 98.86 xb - y a

10.5428

295

(7)(4)140

86)(7)(4)(98.3,063

xnΣx

yxn -Σxy b

98.867

692

n

Σyy 4

7

28

n

Σxx

222

Actual and Trend ForecastElectric Power Demand

60

70

80

90

100

110

120

130

140

150

160

1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

Answers: ‘how strong is the linear relationship between the variables?’

Coefficient of correlation Sample correlation coefficient denoted rValues range from -1 to +1Measures degree of association

Used mainly for understanding

Correlation ( 상관관계 )

Sample Coefficient of Correlation (想关系数 )

n

i

n

iii

n

i

n

iii

n

i

n

i

n

iiiii

yynxxn

yxyxnr

r = 1 r = -1

r = .89 r = 0

Y

XYi = a + b X i^

Y

X

Y

X

Y

XYi = a + b X i^ Yi = a + b X i

^

Yi = a + b X i^

Coefficient of Correlation and Regression Model

r2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation

You want to achieve: No pattern or direction in forecast error

Error (or Bias) = (Yi - Yi) = (Actual - Forecast)

Seen in plots of errors over time Smallest forecast error

Mean square error (MSE) Mean absolute deviation (MAD)

Guidelines for Selecting Forecasting Model

^

Time (Years)

ErrorError

00

Desired Pattern

Time (Years)

Error

0

Trend Not Fully Accounted for

Pattern of Forecast Error

You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use?

Actual Linear Model Exponential Smoothing

Year Sales Forecast Forecast (.9)

2003 1 0.6 1.02004 1 1.3 1.02005 2 2.0 1.92006 2 2.7 2.02007 4 3.4 3.8

Selecting Forecasting Model Example

MSE = Σ Error2 / n = 1.10 / 5 = 0.220MAD = Σ |Error| / n = 2.0 / 5 = 0.400MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240

Linear Model Evaluation

Y i

11224

Y i^

0.61.32.02.73.4

Year

20032004200520062007Total

0.4-0.3 0.0-0.7 0.60.0

Error

0.160.090.000.490.361.10

Error2

0.40.30.00.70.62.0

|Error||Error|Actual

0.400.300.000.350.151.20

MSE = Σ Error2 / n = 0.05 / 5 = 0.01MAD = Σ |Error| / n = 0.3 / 5 = 0.06MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02

Exponential Smoothing Model Evaluation

Year

20032004200520062007Total

Y i11224

Y i1.0 0.01.0 0.01.9 0.12.0 0.03.8 0.2

0.3

^ Error

0.000.000.010.000.040.05 0.3

Error2

0.00.00.10.00.2

|Error||Error|Actual

0.000.000.050.000.05

0.10

Exponential Smoothing Model Evaluation ( 어떤 모델이 더 좋은가 ?)

Linear Model:MSE = Σ Error2 / n = 1.10 / 5 = .220MAD = Σ |Error| / n = 2.0 / 5 = .400MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240

Exponential Smoothing Model:MSE = Σ Error2 / n = 0.05 / 5 = 0.01

MAD = Σ |Error| / n = 0.3 / 5 = 0.06

MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02

Measures how well the forecast is predicting actual values

Ratio of running sum of forecast errorsrunning sum of forecast errors (RSFE) to mean absolute deviationmean absolute deviation (MAD) = RSFE/MAD Good tracking signal has low values

Should be within upper and lower control limits

Tracking Signal (跟踪信号 )

Tracking Signal Equation

ˆ

1

MAD

yy

MAD

RSFETS

n

iii

MoMo FcstFcst ActAct ErrorError RSFERSFE AbsAbsErrorError

CumCum MADMAD TSTS

11 100100 9090

22 100100 9595

33 100100 115115

44 100100 100100

55 100100 125125

66 100100 140140

|Error||Error|

Tracking Signal Computation

MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError

CumCum MADMAD TSTS

11 100100 9090

22 100100 9595

33 100100 115115

44 100100 100100

55 100100 125125

66 100100 140140

-10-10 -10-10 1010 1010 10.010.0 -1-1

-5-5 -15-15 55 1515 7.57.5 -2-2

|Error||Error|

TS = RSFE/MAD = -15/7.5 = -2

TS = RSFE/MAD = -15/7.5 = -2

Tracking Signal Computation

Plot of a Tracking Signal

Time

Lower control limit

Upper control limit

Signal exceeded limit

Tracking signal

Acceptable rangeMAD

+

0

-

The % of Points included within the Control Limits for a range of 1 to 4 MAD

1 03 2 1 2 3 44

±1 MAD

±2 MAD

±3 MAD

±4 MAD

Number of MAD Related STDEV %

±1 0.798 57.048%

±2 1.596 88.946%

±3 2.394 98.334%

±4 3.192 99.895%

Formula Review

Summary What is Forecasting? Types of Forecasting

Qualitative Methods Quantitative Methods

Quantitative Methods Naïve MA Exponential Smoothing Regression

Evaluation Measures MSE, MAD, MAPE

What to do

HW Example 1, 2, 3, 8, 9, 10 Solved Problems 1, 6, 7