forecasting. chapter objectives be able to: discuss the importance of forecasting and identify the...
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Forecasting
Chapter Objectives
Be able to: Discuss the importance of forecasting and
identify the most appropriate type of forecasting approach, given different forecasting situations.
Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models.
Develop causal forecasting models using linear regression and multiple regression.
Calculate measures of forecasting accuracy and interpret the results.
Why Forecast?
• Assess long-term capacity needs
• Develop budgets, hiring plans, etc.
• Plan production or order materials
• Get agreement within firm and across supply chain partners (CPFR, discussed later)
Types of Forecasts
• Demand– Firm-level– Market-level
• Supply– Materials– Labor supply
• Price– Cost of supplies and services– Cost of money — interest rates, currency rates– Market price for firm’s product or service
Forecast Laws
Almost always wrong by some amount
More accurate for shorter time periods
More accurate for groups or families
No substitute for calculated values.
Qualitative Forecasting
• Executive opinions
• Sales force composite
• Consumer surveys
• Outside opinions
• Delphi method
• Life cycle analogy*
*See accompanying notes
Quantitative Methods • Used when situation is
‘stable’ and historical data exists– Existing products– Current technology
• Heavy use of mathematical techniques
*******************************• E.g., forecasting sales of
a mature product
Qualitative Methods• Used when situation is
vague and little data exists– New products– New technology
• Involves intuition, experience
*****************************• E.g., forecasting sales
to a new market
Forecasting Approaches
“Q2” Forecasting
Quantitative, then qualitative factors to “filter” the answer
Demand Forecasting
• Uses historical data
• Basic time series models
• Linear regression
– For time series or causal modeling
• Measuring forecast accuracy
Time Series Models
Period Demand1 122 153 114 95 106 87 148 12
What assumptionsmust we make touse this data toforecast?
Time Series Components of Demand . . .
Time
Demand
. . . randomness
Time Series with . . .
Time
Demand
. . . randomness and trend
Time series with . . .
Demand
. . . randomness, trend, and seasonality
May May May May
Idea Behind Time Series Models
Distinguish between random fluctuations and true changes in
underlying demand patterns.
Moving Average Models
Period Demand1 122 153 114 95 106 87 148 12
3-period moving averageforecast for Period 8:
= (14 + 8 + 10) / 3= 10.67
n
DF
n
iit
t
11
1
Weighted Moving Averages
Forecast for Period 8= [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.2)= 11.4
What are the advantages?What do the weights add up to?Could we use different weights?Compare with a simple 3-period moving average.
n
iit
n
iitit
tW
DWF
11
111
1
Table of Forecasts and Demand Values . . .
PeriodActual Demand
Two-Period Moving Average Forecast
Three-Period Weighted Moving Average
Forecast Weights = 0.5, 0.3, 0.2
1 12
2 15
3 11 13.5
4 9 13 12.4
5 10 10 10.8
6 8 9.5 9.9
7 14 9 8.8
8 12 11 11.4
9 13 11.8
. . . and Resulting Graph
Note how the forecasts smooth out demand variations
0
5
10
15
20
1 2 3 4 5 6 7 8 9
Period
Volu
me Demand
2-Period Avg
3-Period Wt. Avg.
Exponential Smoothing I
• Sophisticated weight averaging model
• Needs only three numbers:
Ft = Forecast for the current period t
Dt = Actual demand for the current period t
= Weight between 0 and 1
Exponential Smoothing II
Formula
Ft+1 = Ft + (Dt – Ft)
= ×Dt + (1 – × Ft
• Where did the current forecast come from?• What happens as gets closer to 0 or 1?• Where does the very first forecast come from?
Exponential Smoothing Forecast with = 0.3
F2 = 0.3×12 + 0.7×11 = 3.6 + 7.7 = 11.3
F3 = 0.3×15 + 0.7×11.3 = 12.41
PeriodActual
Demand
Exponential Smoothing Forecast
1 12 11.00
2 15 11.30
3 11 12.41
4 9 11.99
5 10 11.09
6 8 10.76
7 14 9.93
8 12 11.15
9 11.41
Resulting Graph
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9
Period
Dem
and
Demand
Forecast
Trends
What do you think will happen to a moving average or exponential smoothing model
when there is a trend in the data?
Same Exponential Smoothing Model as Before:
Since the modelis based onhistorical demand,it always lagsthe obviousupward trend
PeriodActual
Demand
Exponential Smoothing Forecast
1 11 11.00
2 12 11.00
3 13 11.30
4 14 11.81
5 15 12.47
6 16 13.23
7 17 14.06
8 18 14.94
9 15.86
Adjusting Exponential Smoothing for Trend
• Add trend factor and adjust using exponential smoothing
• Needs only two more numbers:Tt = Trend factor for the current period t
= Weight between 0 and 1
• Then: Tt+1 = × (Ft+1 – Ft) + (1 – ) × Tt
• And the Ft+1 adjusted for trend is = Ft+1 + Tt+1
Simple Linear Regression
• Time series OR causal model
• Assumes a linear relationship: y = a + b(x)y
x
Definitions
Y = a + b(X)
Y = predicted variable (i.e., demand)
X = predictor variable
“X” can be the time period or some other type of variable (examples?)
The Trick is Determining a and b:
xbya
n
xx
n
yxyx
bn
i
n
ii
i
n
i
n
i
n
iii
ii
1
1
2
2
1
1 1
)(
))((
Example:Regression Used for Time Series
Period (X)
Demand (Y) X2 XY
1 110 1 110
2 190 4 380
3 320 9 960
4 410 16 1640
5 490 25 2450
15 1520 55 5540
105
1598
51520
98
515
55
5152015
5540
2
a
b
Column Sums
Resulting Regression Model:Forecast = 10 + 98×Period
0
100
200
300
400
500
600
1 2 3 4 5
X
Y
Demand
Regression
Example:Simplified Regression I
• If we redefine the X values so that their sum adds up to zero, regression becomes much simpler– a now equals the average of the y values– b simplifies to the sum of the xy products
divided by the sum of the x2 values
Example:Simplified Regression II
30450
985
1520
98
50
10
515200
980
2
a
b
Period (X)
Period (X)'
Demand (Y) X2 XY
1 -2 110 4-
220
2 -1 190 1-
190
3 0 320 0 0
4 1 410 1 410
5 2 490 4 980
0 1520 10 980
Dealing with Seasonality
Quarter Period Demand
Winter 02 1 80Spring 2 240Summer 3 300Fall 4 440Winter 03 5 400Spring 6 720Summer 7 700Fall 8 880
What Do You Notice?
Forecasted Demand = –18.57 + 108.57 x Period
PeriodActual
DemandRegression
Forecast Forecast Error
Winter 02 1 80 90 -10
Spring 2 240 198.6 41.4
Summer 3 300 307.1 -7.1
Fall 4 440 415.7 24.3
Winter 03 5 400 524.3 -124.3
Spring 6 720 632.9 87.2
Summer 7 700 741.4 -41.4
Fall 8 880 850 30
Regression picks up trend, butnot seasonality effect
0
200
400
600
800
1000
1 2 3 4 5 6 7 8
Demand
Forecast
Calculating Seasonal Index: Winter Quarter
(Actual / Forecast) for Winter Quarters:
Winter ‘02: (80 / 90) = 0.89Winter ‘03: (400 / 524.3) = 0.76
Average of these two = 0.83
Interpret!
Seasonally adjusted forecast model
For Winter Quarter
[ –18.57 + 108.57×Period ] × 0.83
Or more generally:
[ –18.57 + 108.57 × Period ] × Seasonal Index
Seasonally adjusted forecasts
Forecasted Demand = –18.57 + 108.57 x Period
PeriodActual
DemandRegression
ForecastDemand/Forecast
Seasonal Index
Seasonally Adjusted Forecast
Forecast Error
Winter 02 1 80 90 0.89 0.83 74.33 5.67
Spring 2 240 198.6 1.21 1.17 232.97 7.03
Summer 3 300 307.1 0.98 0.96 294.98 5.02
Fall 4 440 415.7 1.06 1.05 435.19 4.81
Winter 03 5 400 524.3 0.76 0.83 433.02 -33.02
Spring 6 720 632.9 1.14 1.17 742.42 -22.42
Summer 7 700 741.4 0.94 0.96 712.13 -12.13
Fall 8 880 850 1.04 1.05 889.84 -9.84
Would You Expect the Forecast Model to Perform This Well With Future Data?
0
200
400
600
800
1000
1 2 3 4 5 6 7 8
Demand
forecast
More Regression Models I
Non-linear models
– Example: y = a + b × ln(x)
More Regression Models II
Multiple regression– More than one independent variable
y
x
z
y = a + b1 × x + b2 × z
Causal Models
Time series models assume that demand is a function of time. This is not always true.1. Pounds of BBQ eaten at party.
2. Dollars spent on drought relief.
3. Lumber sales.
Linear regression can be used in these situations as well.
Measuring Forecast Accuracy
How do we know:If a forecast model is “best”?If a forecast model is still working?What types of errors a particular
forecasting model is prone to make?
Need measures of forecast accuracy
Measures of Forecast Accuracy
Error = Actual demand – Forecast
or
Et = Dt – Ft
Mean Forecast Error (MFE)
For n time periods where we have actual demand and forecast values:
n
En
ii
MFE 1
Mean Absolute Deviation (MAD)
For n time periods where we have actual demand and forecast values:
What does this tell us that MFE doesn’t?
n
En
ii
MAD 1
Example
Period Demand Forecast Error AbsoluteError
3 11 13.5 -2.5 2.54 9 13 -4.0 4.05 10 10 0 0.06 8 9.5 -1.5 1.57 14 9 5.0 5.08 12 11 1.0 1.0
What is the MFE? The MAD? Interpret!
MFE and MAD:A Dartboard Analogy
Low MFE and MAD:
The forecast errorsare small and unbiased
An Analogy (continued)
Low MFE, but highMAD:
On average, thedarts hit thebulls eye (so muchfor averages!)
An Analogy (concluded)
High MFE and MAD:
The forecastsare inaccurate andbiased
Collaborative Planning, Forecasting, and Replenishment
(CPFR)
Supply chain partners, supported by information technology,
working together
CPFR Elements
• Mutual business objectives & measures
• Joint sales and operations plans
• Collaboration on sales forecasts & replenishment plans
• Electronic interchange of information
Case Study in Forecasting
Top-Slice Drivers