lecture2 forecasting f06 604

7/28/2019 Lecture2 Forecasting f06 604

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CHAPTER 13FORECASTING

Outline

Forecasting and Choice of a Forecasting Methods Methods for Stationary Series:

Simple and Weighted Moving Average

Exponential smoothing

Trend-Based Methods Regression

Double Exponential Smoothing: Holts Method

A Method for Seasonality and Trend


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Forecasting


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Decisions Based on Forecasts

Production

Aggregate planning,inventory control,scheduling

MarketingNew product

introduction, sales-force allocation,

promotions Finance

Plant/equipmentinvestment, budgetary

planning

Personnel

Workforce planning,hiring, layoff


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Characteristics of Forecasts

Forecasts are always

wrong; so consider

both expected valueand a measure of

forecast error

Long-term forecasts

are less accurate thanshort-term forecasts

Aggregate forecasts

are more accurate than

disaggregate forecasts


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Forecasting

Components of demand

Evaluation of forecasts

Time series: stationary series Time series: trend

Linear regression

Double exponential smoothing Time series: seasonality


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Components of Demand

Average demand Trend

Gradual shift in average demand

Seasonal patternPeriodic oscillation in demand which repeats

Cycle

Similar to seasonal patterns, length andmagnitude of the cycle may vary

Random movements

Auto-correlation


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Qantity

Time

(a) Average: Data cluster about a horizontal line.



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Quantity

| | | | | | | | | | | |J F M A M J J A S O N D

Months

(c) Seasonal influence: Data consistently show

peaks and valleys.

Year 1


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Quantity

| | | | | | | | | | | |J F M A M J J A S O N D

Months

(c) Seasonal influence: Data consistently show

peaks and valleys.

Year 1

Year 2


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Quantity

| | | | | |1 2 3 4 5 6

Years

(c) Cyclical movements: Gradual changes over

extended periods of time.


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Demand

Time

Trend

Random

movement

Dem

and

Time

Trend with

seasonal pattern



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Snow Skiing

Seasonal

Long term growth trend

Demand for skiing products increased

sharply after the Nagano Olympics


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|Et|nEt

2

n

RSFE = EtMAD =

MSE =MAPE =

= MSE[|Et| (100)]/A t

n

Measures of Forecast Error

Et= A t- Ft

Choosing a Method

Forecast Er ror


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AbsoluteError Absolute Percent

Month, Demand, Forecast, Error, Squared, Error, Error,t A

t F

t E

tEt

2 |Et| (|E

t|/A

t)(100)

1 200 2252 240 2203 300 2854 270 2905 230 2506 260 240

7 210 2508 275 240

-

Total

Choosing a Method

Forecast Er ror


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MSE = =

Measures of Error

MAD = =

MAPE = =

RSFE =

Choosing a Method

Forecast Er ror


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Choosing a Method

Forecast Er ror

Running Sum Mean Absoluteof Forecast Errors Deviation

Method (RSFE - bias) (MAD)Simple mov ing averageThree-week (n= 3) 23.1 17.1Six-week (n= 6) 69.8 15.5Weighted mov ing average

0.70, 0.20, 0.10 14.0 18.4Exponent ial smooth ing = 0.1 65.6 14.8 = 0.2 41.0 15.3


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Choosing a Method

Tracking Signals Tracking signal =RSFE

MAD

+2.0

+1.5

+1.0

+0.5

0

- 0.5

- 1.0

- 1.5

| | | | |0 5 10 15 20 25

Observation number

Trackingsignal

Control limit

Control limit


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Choosing a Method

Tracking Signals Tracking signal =RSFE

MAD

+2.0

+1.5

+1.0

+0.5

0

- 0.5

- 1.0

- 1.5

| | | | |0 5 10 15 20 25

Observation number

Trackingsignal

Control limit

Control limit

Out of control


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Choosing a Method

Tracking Signals

Control LimitSpread

(Number ofMAD)

Equivalent

Number of

(=1.25 MAD)

Percentage ofArea within

Control Limits

1.0 0.80 57.62

1.5 1.20 76.98

.0 1.60 89.04

2.5 2.00 95.44

3.0 2.40 98.36

3.5 2.80 99.48

4.0 3.20 99.86


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Problem 13-2: Historical demand for a product is:

Month Jan Feb Mar Apr May Jun

Demand 12 11 15 12 16 15

a. Using a weighted moving average with weights of 0.60,

0.30, and 0.10, find the July forecast.

b. Using a simple three-month moving average, find the July

forecast.

c. Using single exponential smoothing with =0.20 and a June

forecast =13, find the July forecast.

d. Using simple regression analysis, calculate the regression

equation for the preceding demand data

e. Using regression equation in d, calculate the forecast in

July


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Problem 13-15: In this problem, you are to test the validity ofyour forecasting model. Here are the forecasts for a model

you have been using and the actual demands that

occurred:Week 1 2 3 4 5 6

Forecast 800 850 950 950 1,000 975

Actual 900 1,000 1,050 900 900 1,100

Compute MAD and tracking signal. Then decide whether the

forecasting model you have been using is giving

reasonable results.


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Methods for Stationary Series


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Time Series Methods

Simple Moving Averages

Week

450

430

410

390

370P

atientarrivals

| | | | | |0 5 10 15 20 25 30

Actual patientarrivals


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Time Series Methods



450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30

PatientWeek Arrivals

1 400

2 3803 411


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Time Series Methods



450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


1 400

2 3803 411

F4 =


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Time Series Methods



450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


2 380

3 4114 415

F5 =


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Time Series Methods

Simple Moving Averages450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


3-week MAforecast


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Time Series Methods


Week

450

430

410

390

370P

atientarrivals

| | | | | |0 5 10 15 20 25 30


3-week MAforecast

6-week MAforecast


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Taco Bell determined that

the demand for each 15-minute interval

can be estimated from a 6-

week simple moving

average of sales.

The forecast was used to

determine the number of

employees needed.


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Time Series Methods

Weighted Moving Average450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


3-week MAforecast Weighted Moving Average

Assigned weights

t-1 0.70t-2 0.20t-3 0.10

F4 =


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Time Series Methods

Weighted Moving Average450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


3-week MAforecast Weighted Moving Average

Assigned weights

t-1 0.70t-2 0.20t-3 0.10

F5 =


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Time Series Methods

Exponential Smoothing450

430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30

Exponential Smoothing = 0.10

Ft= A t -1+ (1 - )Ft - 1


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Time Series Methods


430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


Ft= A t -1+ (1 - )Ft - 1F3= (400 + 380)/2=390A 3 = 411


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Time Series Methods


430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30

F4 =


Ft= A t -1+ (1 - )Ft - 1F3= (400 + 380)/2=390A 3 = 411


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Time Series Methods

Exponential Smoothing

Week

450

430

410

390

370P

atientarrivals

| | | | | |0 5 10 15 20 25 30

F4 =A 4 = 415


Ft= A t+ (1 - )Ft - 1

F5 =


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Time Series Methods


430

410

390

370P

atientarrivals

Week

| | | | | |0 5 10 15 20 25 30


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Compar ison of Exponential

Smoothing and Simple Moving

Average Both Methods

Are designed for stationary demand

Require a single parameter

Lag behind a trend, if one exists

Have the same distribution of forecast error if

)1/(2 N

C i f E ti l


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Compar ison of Exponential

Smoothing and Simple Moving

Average Moving average uses only the lastNperiods

data, exponential smoothing uses all data

Exponential smoothing uses less memory and

requires fewer steps of computation; store only

the most recent forecast!


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Problem 13-20: Your manager is trying to determine whatforecasting method to use. Based upon the following

historical data, calculate the following forecast and specify

what procedure you would utilize:Month 1 2 3 4 5 6 7 8 9 10 11 12

Actual demand 62 65 67 68 71 73 76 78 78 80 84 85

a. Calculate the three-month SMA forecast for periods 4-12

b. Calculate the weighted three-month MA using weights of

0.50, 0.30, and 0.20 for periods 4-12.

c. Calculate the single exponential smoothing forecast for

periods 2-12 using an initial forecast, F1=61 and =0.30

d. Calculate the exponential smoothing with trend component

forecast for periods 2-12 using T1=1.8,F1=60,=0.30,=0.30

e. Calculate MAD for the forecasts made by each technique in

periods 4-12. Which forecasting method do you prefer?


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Trend-Based Methods


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Turkeys have a long-term trend for increasing demand with a

seasonal pattern. Sales are highest during September to November

and sales are lowest during December and January.


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L inear Regression

Dep

endentvariable

Independent variable

X

Y


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L inear Regression

Dep

endentvariable


X

Y Regressionequation:Y= a+ bX


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L inear Regression

Dep

endentvariable


X

Y

ActualvalueofY

Value ofXusedto estimate Y

Regressionequation:Y= a+ bX


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L inear Regression

Dep

endentvariable


X

Y

ActualvalueofY

Estimate ofY fromregressionequation




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L inear Regression

Dep

endentvariable


X

Y

ActualvalueofY

Estimate ofY fromregressionequation


Deviation,or error

{



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L inear Regression

Sales AdvertisingMonth (000 units) (000 $)

1 264 2.52 116 1.3

3 165 1.44 101 1.05 209 2.0


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L inear Regression

Sales, y Advertising, xMonth (000 units) (000 $)

1 264 2.52 116 1.3

3 165 1.44 101 1.05 209 2.0

a= y- bx b=xy- nxyx2 - n(x)2


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a= y- bx b=xy - nxyx2 - nx2

Sales, y Advertising, xMonth (000 units) (000 $) xy x2

1 264 2.52 116 1.3

3 165 1.44 101 1.05 209 2.0

Totaly= x=

L inear Regression


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300

250

200

150

100

50

b= 109.229

Y=

Sales

(000s)

| | | |1.0 1.5 2.0 2.5


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L inear Regression

Sales, y Advertising, xMonth (000 units) (000 $) xy x2 y2

1 264 2.5 660.0 6.252 116 1.3 150.8 1.69

3 165 1.4 231.0 1.964 101 1.0 101.0 1.005 209 2.0 418.0 4.00

Total 855 8.2 1560.8 14.90y= 171 x= 1.64

nxy- xy[nx2 -(x) 2][ny2 - (y) 2]r=


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L inear Regression

Sales, y Advertising, xMonth (000 units) (000 $) xy x2 y2

1 264 2.5 660.0 6.25 69,6962 116 1.3 150.8 1.69 13,456

3 165 1.4 231.0 1.96 27,2254 101 1.0 101.0 1.00 10,2015 209 2.0 418.0 4.00 43,681

Total 855 8.2 1560.8 14.90 164,259y= 171 x= 1.64

r= 0.98 r2 = 0.96


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L inear Regression

Forecast for Month 6:

Advertising expenditure = $1750

Y=


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Time Series MethodsL inear Regression Analysis

| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80

70

60

50

40

30

Patientarrivals

Week

Yn= a+ bXn

where

Xn= Weekn


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| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80

70

60

50

40

30

Patientarrivals

Week

Yn= a+ bXn

where

Xn= Weekn


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Standard error of estimate is computed as

follows:

2

)(1

2

n

Yy

S

n

i

ii

yx


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An use of the standard error of estimate:

Suppose that a manager forecasts that the demand

for a product is 500 units and Syx is 20. If themanager wants to accept a stockout only 2% time,

how many additional units should be held in the

inventory?


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The method uses two smoothing constants

and

Time Series MethodsDouble Exponential Smoothing

ttt

tttt

ttt

TF

TFFT

AF

FIT

FIT

11

11

)1()(

)1(

A Comparison of Methods


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A Comparison of Methods

6065

70

75

80

8590

0 5 10 15

Months

Dema

nd

Actual

3-Mo MA

3-Mo WMA

Exp Sm

Double Exp S


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Methods for Seasonal Series


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Quarter Year 1 Year 2 Year 3 Year 4

1 45 70 100 1002 335 370 585 725

3 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200Average 250 300 450 550

Time Series MethodsSeasonal I nf luences


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1 45 70 100 1002 335 370 585 725

3 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200Average 250 300 450 550

Seasonal Index =Actual Demand

Average Demand



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1 45 70 100 1002 335 370 585 725

3 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200Average 250 300 450 550

Seasonal Index = =



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1 45/250 = 70 100 1002 335 370 585 725

3 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200Average 250 300 450 550

Seasonal Index = =



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1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32

3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39



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1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39

Quarter Average Seasonal Index

1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20

234



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Quarter Average Seasonal Index Forecast

1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20

234

Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650



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Seasonal I nf luences

Period

Demand

(a) Multiplicative influence

| | | | | | | | | | | | | | | |0 2 4 5 8 10 12 14 16


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Seasonal I nf luences

Period

| | | | | | | | | | | | | | | |0 2 4 5 8 10 12 14 16

Demand

(b) Additive influence


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Time Series MethodsSeasonal I nf luences with Trend

Step 1: Determine seasonal factors

Example: if the demands are quarterly, divide the average demand in

Quarter 1 by the average quarterly demand

Step 2: Deseasonalize the original data Divide the original data by the seasonal factors

Step 3: Develop a regression line on deaseasonalized data

Find parameters a and b in Y=a+bX

Where

yi = deseasonalized data (not the original data)

xi = time; 1, 2, 3, , n

n = Number of periods


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Time Series MethodsSeasonal I nf luences with Trend

Step 4: Make projection using regression line

For each i = n+1, n+2, , computeyi by substituting a, b and xi in

the regression equationyi= a+bxi

Step 5: Reseasonalize projection using seasonal factors Multiply the projected values by the seasonal factors

Problem 13-21: Use regression analysis on deseasonalized


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Problem 13-21: Use regression analysis on deseasonalizeddemand to forecast demand in summer 2006, given the

following historical demand data:

Year Season Actual Demand2004 Spring 205

Summer 140

Fall 375

Winter 575

2005 Spring 475

Summer 275

Fall 685Winter 965


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Reading and Exercises

Chapter 13 pp. 518-539

Problems 1, 7, 13, 14,16

lecture2 forecasting f06 604

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