Chapter 7 of Chopra

Forecasting of Demand

1

Read: Chap. 7.1-7.4; + pp203-04; p207-210 (all excluding “Trend-corrected …seasonal …”); 7.6; 7.7-upto p217 (excluding “Trend-corrected …”); 7.9-11.

Learning Objectives

• Describe types of forecasts• Describe time series• Use time series forecasting methods• Explain how to monitor & control forecasts

2

What Is Forecasting?• Process of predicting a

future event

• “Forecasting is difficult especially when it has to deal with future” -- Mark Twin

• Underlying basis of all business decisions– Production– Inventory – Facilities, …...

Sales will be $200 Million!

3

Why forecast demand?

• We need to know how much to make ahead of time, i.e. our production schedule– How much raw material– How many workers– How much to ship to the warehouse in HK

• We need to know how much production capacity to build

4

• Components take different lead times beforereaching the destinations

Global Sourcing

wooden casing: sea, Sweden

Cheap peripheral: van, HK LCD: truck,

China

screws: train, China (Sichuan)

microphone: air, Japan

microprocessors: air, Malaysia

destination: USA

Resistors, capacitors,

5

When and In What Quantity to “Buy/Make” of Each Parts/Finished Goods?

Push/Pull Processes (Chapter 1)

• With pull processes, execution is initiated in response to a customer order --reactive

• With push processes, execution is initiated in anticipation of customer orders --speculative

Clock’s assembly factory

Suppliers: Parts, …

Procurement process

Manufacturing/Fulfillment Processes

Orders

Make-to-order, assemble-to-order

Make-to-stock

6

what happens in a supply chain?

Manufacturer(Campbell’s )

Customer(Park’n Shop DC, Stores)

Consumers

Customer places an order

Chain Reaction

Customer order

Issuing orders + producing (1 wk)

Campbell’s Soup

Orders to Metal Processor . . .

Can

Order to farms (1 wk )

Chicken

Chicken raising (30 wks) . . .. . .

Hatching eggs(4 wks)Waiting hens to lay eggs ( 3 mos)

Order to Steel Maker

• Somehow in a SC, some parties must take certain inventory positions (risk!)

• Otherwise, it would take long time for the retail order to be fulfilled

• Therefore, in a typical SC, there is a “break” point: Push to Pull 9

More on Why Forecasting ?

• You’re managing merchandises for Park’n Shop. Fruits take 3 wks to arrive from Australia.

• You need to commit to a number of containers NOW for the month of March in order for a better price

• Coca-Cola Bottling: next quarter’s demand + promotions -> production plan/ orders of concentrates

10

Forecasting is Always Wrong(2nd law of forecasting)

• “I think there is a world mkt for maybe 5 computers” -Thomas Watson, Chairman of IBM, 1955

• “There is no reason anyone would want a computer in their home.” - Ken Olson, CEO and Founder of Digital Equipment Corp. , 1977

• “640K should be enough for anybody.” -- Bill Gates, 1981• “Economists are good at explaining why their forecasts

always went wrong” -- Economist, xx, 1998

• “Fore. represents a constant pain for human being” -- some one

11

Coping with Forecast Errors – to be learned

• Better forecasting methods (e.g., new SCM concepts)

• Buffer mechanism (e.g., safety stock)

• Shorter lead time (i.e., reducing f horizon)

• Flexible ops (mass customisation approach)

12

Forecasting v.s. Planning

• Forecast:– About what will happen in future

• Plan: – About what should happen in future– Forecasts as input

• All plans are based upon some fore. explicitly or implicitly

13

Forecasting v.s. Planning

• When sales dept. shows sales forecasts, be cautious. They may be goals

• Both forecasting and planning are art and science – Quant f methods - educated guessing

• must be tempered by judgement bec’s quant f assumes future is a continuation of the past

14

Types of Forecasts by Time Horizon

• Short-range forecast– Up to 1 year; usually < 3 months– Procurement, worker assignments

• Medium-range forecast– 3 months to 3 years– Sales & production planning, budgeting

• Long-range forecast– 3 + years– Capacity planning, facility location

15

Types of Forecastsby Item Forecast

• Key forecasts in business:

• Future demand for products/services, Sales• Demand (sales = demand - lost sales)• Future price of various commodities• Lead times• Processing times (learning curves) …

16

Forecasting Steps

• Define objectives• Select items to be forecasted• Determine time horizon• Select forecasting model(s)• Gather data• Validate forecasting model• Make forecast• Implement results• Monitor forecast performance 17

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

• Involves mathematical techniques

• e.g., forecasting sales of milk, tissue papers, …

Quantitative Methods

Forecasting Approaches

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

• Involves intuition, experience

• e.g., forecasting sales on Internet

Qualitative Methods

iPhone

18

CausalModels

Quantitative Forecasting Methods

QuantitativeForecasting

Time SeriesModels

RegressionExponentialSmoothing

Trend & Season

MovingAverage

A future is continuation of the past (short run)

Simulation

Qualitative

時間序列因果關係

19

ERP: Enterprise Resource Planning

Black Box

20

What’s 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,

present, & future will continue

21

1st & 2nd Law of Forecasting

1. In forecasting, we assume the future will behave like the past

– If behavior changes, our forecasts can be terrible

2. Even given 1, there is a limit to how accurate forecasts can be (or nothing can be predicted with complete accuracy)

– The achievable accuracy depends on the magnitude of the noise component

22

Monthly Demand for Sport-3506

Monthly Demand

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40

Month

De

man

d

23

Time Series Components

Original T.S.

Time

Sales

24

Time Series Components

Trend

Seasonal

Cyclical

Random

25

Trend Component

• Persistent, overall upward or downward pattern

• Due to population, technology etc.• Several years duration

Mo., Qtr., Yr.

Response

26

HK Regional Headquarters

27

Cyclical Component

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

economy• Usually 2-10 years duration

Mo., Qtr., Yr.

ResponseCycle

28

Seasonal Component

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

Mo., Qtr.

Response

Spring Festives

29

Random Component

• Erratic, unsystematic, ‘residual’ fluctuations

• Due to random variation or unforeseen events– Union strike– Tornado

• Short duration & nonrepeating

30

General Time Series Models

• Any observed value in a time series is the product (or sum) of time series components

• Multiplicative modelYi = Ti · Si · Ci · Ri (if quarterly or mo. data)

• Additive modelYi = Ti + Si + Ci + Ri (if quarterly or mo. data)

• Hybrids

31

Time Series Components

Original T.S.

Time

Sales

32

Time Series Components

Original T.S.

Cycle

Seasonal

Trend

Random33

Sub-summaryCommon Time Series Patterns

Time Time

Time

Dem

and

Time

Dem

and

Dem

and

Dem

and

Purely Random Error -No Recognizable Pattern

Increasing Linear Trend

Seasonal Pattern Seasonal Pattern plus Linear Growth

34

Underlying model and definitions --Static Method

Systematic component = (level + trend) x seasonal factor

L = estimate of level for period 0 (de-seasonalised demand)

T= estimate of trend (increase/decrease in demand per period)

St= Estimate of seasonal factor for period tDt= Actual demand observed for period tFt= Forecast of demand for period t

Ft+k = [ L+ (t+k)T ]St+kNote: pp 207-211 on Static Forecast. – skip 35

HK Regional Headquarters

36You may use 1991-2002 to estimate the “trend line”; after 2003/05, you still use this line to project the future – not update it with 2003/05 new observation!

Static

Time to doThe estimation

Monthly Demand for Sport-3506

Monthly Demand

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40

Month

De

man

d

37

Adaptive forecasting

• The estimates of level, trend and seasonality are updated after each demand observations

ktttkt

t

t

t

t

t

)SkT(LF

t-tFtD

tStT

tL

++ +=

=====

earlier)or 1 periodin made( periodfor demand offorecast periodfor observed demand actual

periodfor factor seasonal of estimate period of endat trendof estimate

ed)seasonalis-(de period of endat level of estimate

38

Moving Average

k allfor

/)(

/)(

)2(111

)1(1

tkt

Nttttt

Ntttt

LF

NDDDDLNDDDL

=

++++=

+++=

+

−−−++

−−−

• Assumes no trend and no seasonality =>• Level estimate is the average demand over most recent N periods• Update: add latest demand observation and drop oldest • Forecast for all future periods is the same• Each period’s demand equally weighted in the forecast• How to choose the value of N?

– N large =>– N small =>

39

You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 1998 using a 3-period moving average.

1994 41995 61996 51997 31998 7

Moving Average Example

40

Time DemandDi

Moving Total(N = 3)

MovingAvg. (N= 3)

1994 4 NA NA1995 6 NA NA1996 5 NA NA1997 3 4 + 6 + 5 = 15 15/3 = 5.01998 7 6 + 5 + 3 = 14 14/3 = 4.71999 NA

Moving Average Solution

1999 NA 5 + 3 + 7 = 15 15/3 = 5.0Forecast for 199941

Forecasts

Moving Average Graph

Year

Sales

02468

94 95 96 97 98 99

Actual

Forecast

42

Milk– weekly data / Pet products – monthly data

0

1000

2000

3000

4000

5000

6000

2002

/Jan

2002

/Feb

2002

/Mar

2002

/Apr

2002

/May

2002

/Jun

2002

/Jul

2002

/Aug

2002

/Sep

2002

/Oct

2002

/Nov

2002

/Dec

2003

/Jan

2003

/Feb

2003

/Mar

2003

/Apr

2003

/May

2003

/Jun

2003

/Jul

2003

/Aug

2003

/Sep

2003

/Oct

2003

/Nov

2003

/Dec

2004

/Jan

2004

/Feb

2004

/Mar

2004

/Apr

2004

/May

2004

/Jun

2004

/Jul

2004

/Aug

2004

/Sep

2004

/Oct

2004

/Nov

2004

/Dec

2005

/Jan

2005

/Feb

2005

/Mar

2005

/Apr

2005

/May

2005

/Jun

2005

/Jul

2005

/Aug

2005

/Sep

2005

/Oct

2005

/Nov

2005

/Dec

2006

/Jan

200

A pet supply product ( 6 varieties)

43This pattern is typical for “staples” – “She bought flour, sugar, salt, and other staples.”

Moving Average Method

• Used if little or no trend

• Used often for smoothing– Provides overall impression of data over

time

• Why “moving” not just overall mean?

44

Cereal Sales in HK

Year

Quantity (kg)

45

Month

Mon

thly

Sal

es Within a year

46

Disadvantages of Moving Averages

• Increasing N makes forecast less sensitive to changes

• Do not forecast trend well• Require much historical

data – N, while exponential only last forecast!

47

Simple Exponential Smoothing (No trend, no seasonality)

1 allfor

)1(

1

11

>=

−+=

++

++

nLF

LDL

tnt

ttt αα

• Rationale: recent past more indicative of future demand• Update: level estimate is weighted average of latest demand

observation and previous estimate� α is called the smoothing constant (0 < α < 1)• Forecast for all future periods is the same• Assume systematic component of demand is the same for all

periods (L)• Lt is the best guess at period t of what the systematic demand

level is48

After observing the demand Dt+1, for period t+1,

Simple Exponential Smoothing – Example 7-2

Data: 120, 127, 114, 122.L0= 120.75 α = 0.1F1 = L0 =120.75

D1= 120 e1 = F1 – D1 = 120.75 – 120 = 0.75

L1 = α D1 + (1 - α ) L0= (0.1)(120) + (0.9)(120.75) = 120.68

F2 = L1= 120.68, F3 = L2 = 121.31, …F5 = L4= 120.72 => the forecast for period 5

49

Simple Exponential Smoothing – Example 7-2

Data: 120, 127, 114, 122.L0= 120.75 α = 0.1F1 = L0 =120.75

D1= 120 e1 = F1 – D1 = 120.75 – 120 = 0.75

L1 = α D1 + (1 - α ) L0= (0.1)(120) + (0.9)(120.75) = 120.68

F2 = L1= 120.68, F3 = L2 = 121.31, …F5 = L4= 120.72 => the forecast for period 5

50

Simple Exponential Smoothing –Example: Table 7-1 & Fig. 7-5

L0= 22083 α = 0.1F1 = L0

D1=8000E1 = F1 – D1 = 22083 – 8000 = 14083

L1 = α D1 + (1 - α ) L0= (0.1)(8000) + (0.9)(22083) = 20675

F2 = L1= 20675, F10 = L1 = 20675

Note: this example appears in the textbook 51

Simple Exponential Smoothing

• Update: new level estimate is previous estimate adjusted by weighted forecast error

• How to choose the value of the smoothing constant α?– Large α ? – Small α ?

• Incorporates more information but keeps less data than moving averages– Average age of data in exponential smoothing is 1/α– Average age of data in moving average is (N+1)/2

If α is 0 then … If α is 1 then ...

1

)( 11

+

++ −−=tE

tttt DLLL α

52

Understanding the exponential smoothing formula

• Demand of k-th previous period carries a weight of hence the name exponential smoothing

• Demand of more recent periods carry more weight

+−++−+−+=

−+−+=

−+−+=−+=

−−+

−+

−+

++

ktk

ttt

ttt

ttt

ttt

DDDD

LDDLDD

LDL

)1()1()1(

)1()1(

))1()(1()1(

12

1

12

1

11

11

ααααααα

αααα

αααααα

53

k)1( αα −

Forecast Effect of Smoothing Constant (α)

The alpha parameter for exponential smoothing ...Period .10 .30 .50 .70

1 .10 .30 .50 .702 .09 .21 .25 .213 .08 .15 .13 .064 .07 .10 .06 .025 .07 .07 .03 .016 .06 .05 .02 .007 .05 .04 .018 .05 .02 .00

Ft = α·Dt - 1 + α·(1-α)·Dt -

+ α·(1- α)2·Dt - 3 +

α·(1- α)3·Dt - 4 + ...

54

You’re organising a international meeting. You want to forecast attendance for 2000 using exponential smoothing (α = .10). The 1994 forecast was 175.

1994 1801995 1681996 1591997 1751998 190

Exponential Smoothing Example

55

Exponential Smoothing Solution

Lt = Lt-1 + α· (Dt - Lt-1)

Time Actual Forecast, Ft

(α = .10)1994 180 175.00 (Given)1995 168 175.00 + .10(180 - 175.00) = 175.501996 159 175.50 + .10(168 - 175.50) = 174.751997 175 174.75 + .10(159 - 174.75) = 173.181998 190 173.18 + .10(175 - 173.18) = 173.361999 NA 173.36 + .10(190 - 173.36) = 175.02

56

Lt+1 = Lt +α(Dt+1 - Lt )Lt+1 = αDt+1 +(1-α) Lt

Trend corrected exponential smoothing (Holt’s model)

ttnt

tttt

tttt

nTLF

TLLTTLDL

+=

−+−=+−+=

+

−−

−−

:Forecast)1()(

))(1(:Update

11

11

ββαα

� β is the smoothing constant for trend updating• If β is large, there is a tendency for the trend

term to “flip-flop” in sign• Typical β is α2

57

Skipped

Holt’s model - ExampleL0= 12015 T0=1549 α = 0.1 β = 0.2F1 = L0 + T0 = 12015 + 1549 = 13564 , D1=8000E1 = F1 – D1 = 13564 – 8000 = 5564L1 = α D1 + (1 - α )(L0 + T0)

= (0.1)(8000) + (0.9)(13564) = 13008T1 = β (L1 − L0) + (1 - β )T0

= (0.2)(13008 − 12015) + (0.8)(1549) = 1438

F2 = L1+T1= 13008+1438 = 14446, F10 = L1 + 9 T1 = 13008 + 9(1438) = 25950

58

Skipped

Trend and seasonality corrected exponential smoothing (Winter’s model)

ntttnt

tt

tpt

tttt

ttt

tt

SnTLF

SLDS

TLLT

TLSDL

++

++

+++

++

+

++

+=

−+

=

−+−=

+−+

=

)(:Forecast

)1(

)1()(

))(1(

:Update

11

11

11

1

11

γγ

ββ

αα

59

Skipped

Special Forecasting Difficulties for Supply Chains

• New products and service introductions– No past history– Use qualitative methods until sufficient data collected– Examine correlation with similar products– Use a large exponential smoothing constant

• Lumpy derived demand– Large but infrequent orders– Random variations “swamps” trend and seasonality– Identify reason for lumpiness and modify forecasts

• Spatial variations in demand– Separate forecast vs. allocation of total forecasts

Not required

60

A Lumpy Demand Example

0

20

40

60

80

100

120

140

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Series1

61

Skipped

Analysing Forecast Errors

• Choose a forecast model• Monitor if current forecasting method/model accurate

– Consistently under-predicting? Over-predicting?– When should we adjust forecasting procedures?

• Understand magnitude of forecast error – In order to make appropriate contingency plans

• Assume we have data for n historical periods

tEAtDFE

tt

ttt

periodfor deviation absolute periodin error forecast

==

=−=

62

Measures of Forecast Error• Mean Square Error

(MSE)– Estimate of variance (σ2)

of random component• Mean Absolute Deviation

(MAD)– If random component

normally distributed, σ=1.25 MAD

• Mean Absolute Percent Error (MAPE)

=

=

=

∑

∑

∑

=

=

=

n

i t

tn

n

itn

n

itn

DE

nMAPE

An

MAD

En

MSE

1

1

1

2

100

1

1

63

Further Error Equations

• What does it mean when MFE ≈ 0 ?• What does it mean when MFE =

MAD? • What does it mean when MSE <

MAD? • Why do we need MAPE?

64

Consumer electronics companies average just 66% SKU-level forecast accuracy, or 34% mean absolute percent error (MAPE), one month ahead of demand. Industrial high-tech sectors are not much better, averaging 76% accuracy. Stephen Hochman, David Aquino, AMR Research, 2007

Guidelines for Selecting Forecasting Model

• No pattern or direction in forecast error– Error = (Fore. -Actual )– Seen in plots of errors over time

• Smallest forecast error– Mean square error (MSE)– Mean absolute deviation (MAD)

65

Read Example 7-X for the whole forecast estimation process!

Pattern of Forecast Error

Trend Not Fully Accounted for Desired Pattern

Time (Years)

Error

0

Time (Years)

Error

0

In software packages, built-in tests. 66

Tracking Errors

• Errors due to:– Random component– Bias (wrong trend, shifting

seasonality, etc.)

• Monitor quality of forecast with a tracking signal

• Alert if signal value exceeds threshold– Indicates underlying environment

changed and model becomes inappropriate

t

tt

n

itn

MADbiasTS

Ebias

=

= ∑=1

You have been using one!

67

Monitoring: Tracking Signal

• Tracking signal -- Checks for consistent bias over many periods

• Measures how well forecast is predicting actual values

• Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)– Good tracking signal has low values

68

TS = RSFE / MADRSFE(t)=RSFE(t-1)+E(t) = BiasMAD = sum of | forecast errors| over time/ n If TS is greater than some maximum value then report a problem.

69

Tracking Signal Equation

( )

( )MAD

ErrorsForecast MAD

MADRSFETS

1

∑=

∑ −=

=

=

n

iii DF

70

Tracking Signal Computation*Mo Forc Act Error RSFE Abs

Error Cum Error

MAD TS

1 100 90 10 10 10 10 10.0 1 2 100 95 5 15 5 15 7.5 2 3 100 115 -15 0 15 30 10.0 0 4 100 90 10 10 10 40 10.0 1 5 100 115 -15 -5 15 55 11.0 -.5 6 100 130 -30 -35 30 85 14.2 -2.5

71

Tracking Signal Plot

-3-2-10123

1 2 3 4 5 6Time

TS

72

Tracking Signal

• Limits used for tracking signal ratio usually between (-3/6, 3/6)

• Used for monitoring

Time

Re-evaluate the model

6

-6

0

73

Tracking Signal

• Cautious! – Is it always good to have TS=0? – TS: the smaller the better? – Can TS be used for comparing models?

74

Summary so far• Importance of forecasting in a supply chain• Forecasting models and methods• Exponential smoothing

– Stationary model– Trend x– Seasonality x

• Measures of forecast errors -- for model selection• Tracking signals – for monitoring the model in use

75

Part 1 of As# 1

Chapter 7 in 4rd edition• Discussion questions

– Q4, Q9, Q10 • Exercises

– Q4 [just MA and Exponential Smoothing]; instead of answering “Which f. method do you prefer?”, answer “What problem(s) do you think for the two methods? Explain why.” ]

The deadline: hand in the class before ?. Part 2 will be released later.

All are posted as downloadable

76