View
216
Download
1
Category
Preview:
Citation preview
1
©The McGraw-Hill Companies, Inc., 2006 McGraw-Hill/Irwin
Chapter 15
Demand Management
and Forecasting
2
Simple & Weighted Moving Average Forecasts
Exponential Smoothing
Simple Linear Regression
Multiple Regression
OBJECTIVES
3
Types of Forecasts
Qualitative (Judgmental)
Quantitative
Time Series Analysis
Causal Relationships
Simulation
4
Components of Demand
Average demand for a period of time
Trend
Seasonal element
Cyclical elements
Random variation
Autocorrelation
5
Finding Components of Demand
1 2 3 4
x
x x x
x x
x x x
x x x x x
x x x x x x x x
x x
x x x x
x x
x x
x
x x
x x
x x
x x
x x
x x
x
x
Year
Sale
s
Seasonal variation
Linear
Trend
6
Time Series Analysis
Time series forecasting models try to predict the
future based on past data
You can pick models based on:
1. Time horizon to forecast
2. Data availability
3. Accuracy required
4. Size of forecasting budget
5. Availability of qualified personnel
7
Simple Moving Average Formula
The simple moving average model assumes an average is a
good estimator of future behavior
The formula for the simple moving average is:
Ft = Forecast for the coming period
N = Number of periods to be averaged
A t-1 = Actual occurrence in the past period for up to “n” periods
n
A+...+A +A +A =F n-t3-t2-t1-t
t
8
Simple Moving Average Problem (1)
Week Demand 3 week 6 week
1 650
2 678
3 720
4 785
5 859
6 920
7 850
8 758
9 892
10 920
11 789
12 844
Question: What are the 3-week and 6-week moving average forecasts for demand?
Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
n
A+...+A +A +A =F n-t3-t2-t1-t
t
9
500
550
600
650
700
750
800
850
900
950
1 2 3 4 5 6 7 8 9 10 11 12Week
Dem
an
d
Demand
3-Week
6-Week
Plotting the moving averages and comparing them shows how the
lines smooth out to reveal the overall upward trend in this example
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
10
Simple Moving Average Problem (2) Data
Week Demand
1 820
2 775
3 680
4 655
5 620
6 600
7 575
Question: What is the 3 week moving
average forecast for this data?
Assume you only have 3 weeks and 5
weeks of actual demand data for the
respective forecasts
11
Simple Moving Average Problem (2) Solution
Week Demand 3-Week 5-Week
1 820
2 775
3 680
4 655
5 620
6 600
7 575
12
Weighted Moving Average Formula
While the moving average formula implies an equal weight being placed on
each value that is being averaged, the weighted moving average permits an
unequal weighting on prior time periods
wt = weight given to time period “t”
occurrence (weights must add to one)
The formula for the moving average is:
n-tn3-t32-t21-t1t Aw+...+Aw+A w+A w=F
1=wn
1=i
i
13
Weighted Moving Average Problem (1) Data
Weights:
t-3 .2
t-2 .3
t-1 .5
Week Demand
1 650
2 678
3 720
4
Question: Given the weekly demand and weights, what is the forecast for the
4th period or Week 4?
Note that the weights place more emphasis on the most recent data, that is time
period “t-1”
In Excel use the =SUMPRODUCT(…, …) function.
15
Weighted Moving Average Problem (2) Data
Weights:
t-3 .1
t-2 .2
t-1 .7
Week Demand
1 820
2 775
3 680
4 655
Question: Given the weekly demand information and weights, what is the three
week weighted moving average forecast of the 5th period or week?
16
Excel Example of Weighted Moving Average
A B C D E
1 Week Demand Forecast Weights
2 1 820 0.1
3 2 775 0.2
4 3 680 0.7
5 4 655
6 5
17
Exponential Smoothing Model
Premise: The most recent observations might have the highest predictive value
Therefore, we should give more weight to the more recent time periods when forecasting
Ft = Ft-1 + a(At-1 - Ft-1)
constant smoothing Alpha
period epast t tim in the occurance ActualA
period past time 1in alueForecast vF
period t timecoming for the lueForcast vaF
:Where
1-t
1-t
t
a
18
Exponential Smoothing Model – Alternate form
11 )1( ttt FAF aa
Microsoft Excel uses the
dampening factor in the Data
Analysis Exponential Smoothing
routine
factor Dampening -1
constant smoothing Alpha
a
a
19
Exponential Smoothing Problem (1) Data
Week Demand
1 820
2 775
3 680
4 655
5 750
6 802
7 798
8 689
9 775
10
Question: Given the weekly demand
data, what are the exponential
smoothing forecasts for periods
2-10 using a=0.10 and a=0.60?
Assume F1=D1
20
Week Demand 0.1 0.6
1 820 820.00 820.00
2 775 820.00 820.00
3 680 815.50 793.00
4 655 801.95 725.20
5 750 787.26 683.08
6 802 783.53 723.23
7 798 785.38 770.49
8 689 786.64 787.00
9 775 776.88 728.20
10 776.69 756.28
Answer: The respective alphas columns denote the forecast values. Note
that you can only forecast one time period into the future.
21
Exponential Smoothing Problem (1) Plotting
500
550
600
650
700
750
800
850
1 2 3 4 5 6 7 8 9 10
Dem
and
Week
Demand
Note how that the smaller alpha results in a smoother line in this example
22
The MAD Statistic to Determine
Forecasting Error
The ideal MAD is zero which would mean there is no forecasting error
The larger the MAD, the less the accurate the resulting model
MAD 1.25 deviation standard 1
deviation standard 0.8 MAD 1
n
F-A
=MAD
n
1=t
tt
23
MAD Problem Data
Question: What is the MAD value given the forecast values in the table below?
Month Sales Forecast 1 220 n/a
2 250 255
3 210 205
4 300 320
5 325 315
24
MAD Problem Solution
Month Sales Forecast Abs Error
1 220 n/a
2 250 255 5
3 210 205 5
4 300 320 20
5 325 315 10
40
Note that by itself, the MAD only lets us know the mean error in a
set of forecasts
10=4
40=
n
F-A
=MAD
n
1=t
tt
25
Tracking Signal Formula
The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand.
Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts.
The TS formula is:
deviation absoluteMean
errorsforecast of sum Running=
MAD
RSFE=TS
26
Tracking Signal
Month Forecast Actual Deviation RSFE Abs. Dev. Sum of AD MAD TS
1 1000 950 -50 -50 50 50 50 -1
2 1000 1070 70 20 70 120 60 0.33
3 1000 1100 100 120 100 220 73.33 1.64
4 1000 960 -40 80 40 260 65 1.23
5 1000 1090 90 170 90 350 70 2.43
6 1000 1050 50 220 50 400 66.67 3.30
27 Simple Linear Regression Model
Yt = a + bx
0 1 2 3 4 5 x
Y The simple linear regression model
seeks to fit a line through various
data over time
Is the linear regression model
a
Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.
28
Multiple Regression:
Using time series data Forecasting based on many pieces of information that are
historically related.
Independent data (data used to forecast another set of data) is
generally lagged in time.
Examination of the “errors” reveals model structure
weaknesses.
Errors should be random and unpredictable.
29
Algebra 1 Review
Draw a line between two points
(x1,y1)
(x2,y2)
12 xxx
General line equation
bmxy where,
m is the slope
12
12
xx
yy
x
ym
12 yy
y
b is the intercept
(you need the slope and one point)
),( yx
xmyb
Intercept b
30
Simple Linear Regression
Draw a line among many points General line equation
ii xbby 10ˆ where,
b1 is the estimated slope
21)var(
),cov(
x
xy
s
s
x
yxb
b0 is the intercept
(you need the slope and one point)
xbyb 10
Intercept b
31
Simple Regression - example
The owner of Best of Beans Café believes that the
store sells more coffee in the morning hours when
the temperature is cold and fewer cups of coffee
when the temperature is warm.
Develop a regression to help forecast the sales any
day based on the morning temperature.
32
Cu
ps
of
Co
ffe
e o
ld
Temperature (F)
Example: Best of Beans Café
Date Temperature
7:00AM
Cups of Coffee Sold
(7-9AM)
1/1/2009 20 187
1/15/2009 -3 305
1/29/2009 14 276
2/12/2009 -2 296
2/26/2009 15 238
3/12/2009 34 159
3/26/2009 28 190
4/9/2009 40 150
4/23/2009 42 133
5/7/2009 50 127
33
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.95105994
R Square 0.90451501
Adjusted R Square 0.89257939
Standard Error 21.9427493
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 36488.23 36488.23 75.7828 2.36537E-05
Residual 8 3851.874 481.4842
Total 9 40340.1
Coefficients Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 300.670433 11.8265 25.42344 6.14E-09 273.3984671 327.9424
Temperature 7:00AM -3.5029594 0.402392 -8.70533 2.37E-05 -4.43087791 -2.57504
34
Simple Regression - example
How many cups of coffee would the owner of Best of Beans
Café estimate will be sold if the morning temperature is 32
degrees?
How many cups of coffee would the owner of Best of Beans
Café estimate will be sold if the morning temperature is -15
degrees?
35
Multiple Regression - example
You are working for General Motors in the light truck
division. Your responsibilities include forecasting the
number of units to produce in the next six months.
36 Interest Rates & Light Vechicles
0
2
4
6
8
10
12
141
98
4
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
Mill
ion
s o
f u
nit
s
0
2
4
6
8
10
12
14R
ea
ga
n
H.W
.Bu
s
Ira
q W
ar
Be
rlin
Clin
ton
G.W
.Bu
9/1
1/0
1T
alib
an
Ira
q W
ar
Pri
me
Ra
te
Autos and light truck assemblies(millions)
Average majority prime rate chargedby banks on short-term loans tobusiness, quoted on an investmentbasis (lagged 6 months)
37
Gasoline Price & Units Produced
0
2
4
6
8
10
12
14
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
Mill
ion
s o
f u
nit
s
0
50
100
150
200
250
Re
ag
an
H.W
.Bu
s
Ira
q W
ar
Be
rlin
Clin
ton
G.W
.Bu
9/1
1/0
1T
alib
an
Ira
q W
ar
ce
nts
pe
r g
allo
n o
f g
as
olin
e
Autos and light truck assemblies(millions)
Gasoline price (cents per gallon 2000 prices)
38
34. War is good for business. ("Destiny")
35. Peace is good for business. ("Destiny")
Ferengi Rules of Acquisition
Download the “Forecasting Spreadsheet.xls”
Recommended