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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