Demand Forecasting
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
1
Objectives
• Understand the role of forecasting
• Understand the issues
• Understand basic tools and techniques
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
2
Forecasting
• Developing predictions or estimates of
future values
– Demand volume
– Price levels
– Lead times
– Resource availability
– ...
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
3
The Role of Forecasting
• Necessary Input to all Planning Decisions
– Operations: Inventory, Production Planning &
Scheduling
– Finance: Plant Investment & Budgeting
– Marketing: Sales-Force Allocation, Pricing
Promotions
– Human Resources: Workforce Planning
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
4
Demand Forecasting
For manufactured items and conventional
goods, forecasts are used to determine
• Replenishment levels and safety stocks
• Set production plans
• Determine procurement schedules
• Capacity planning, financial planning, &
workforce planning
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
5
Demand Forecasting
For services, demand forecasts are used for
• Capacity planning, workforce scheduling,
procurement & budgeting.
• Because services cannot be stored,
demand forecasting for services is often
concerned with forecasting the peak
demand, rather than the average demand
and its range.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
6
Characteristics of Forecasts
• Forecast are always wrong. A good
forecast is more than a single value.
• Forecast accuracy decreases with the
forecast horizon.
• Aggregate forecasts are more accurate
than disaggregated forecasts.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
7
Independent vs. Dependent Demand
• Independent
– Exogenously controlled
– Subject to random or unpredictable changes
– What we forecast
• Dependent or Derived
– Calculated or derived from other sources
– Do not forecast
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
8
Forecasting Methods
Qualitative or Judgmental
– Ask people who ought to know
• Historical Projection or Extrapolation
– Time Series Models
• Moving Averages
• Exponential Smoothing
– Regression based methods
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
9
Basic Approach to Demand
Forecasting
• Identify the Objective of the Forecast
• Integrate Forecasting with Planning
• Identify the Factors that Influence the
Demand Forecast
• Identify the Appropriate Forecasting Model
• Monitor the Forecast (Measure Errors)
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
10
Time Series Methods
• Appropriate when future demand is
expected to follow past demand patterns.
• Future demand is assumed to be
influenced by the current demand, as well
as historical growth and seasonal patterns.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
11
Time Series Models
With time series models observed demand
can be broken down into two components:
systematic and random.
Observed Demand = Systematic
Component + Random Component
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
12
Time Series Methods
The systematic component is the expected
demand value. It is comprised of the
underlying average demand, the trend in
demand, and the seasonal fluctuations
(seasonality) in demand.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
13
Idea Behind Time Series Models
Distinguish between random
fluctuations and true changes in
underlying demand patterns.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
14
Time Series Components of
Demand
Demand
Random component
Time
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
15
Monthly chart of the DJIA's changes from month to month
along with a 3 period simple moving average.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
16
Time Series Methods
• The random component cannot be
predicted. However, its size and variability
can be estimated to provide a measure of
forecast error. The objective of
forecasting is to filter the random
component and model (estimate) the
systematic component.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
17
Moving Averages
• Simple, widely used
• Reduce random noise
• One Extreme
– Prediction next period = Demand this period
• Another Extreme
– Prediction next period = Long run average
• Intermediate View
– Prediction next period = Average of last n
periods
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
18
Moving Average Models
Period
1
2
3
4
5
6
7
8
Fall, 2012
Demand
12
15
11
9
10
8
14
12

n
Ft 1 
 Dt 1i
i 1
n
3-period moving average
forecast for Period 8:
=
=
EMBA 512 Demand Forecasting
Boise State University
(14 + 8 + 10) / 3
10.67
19
Weighted Moving Averages
n
 Wt 1i Dt 1i
Ft 1  i 1
n
 Wt 1i
i 1
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.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
20
Table of Forecasts and Demand
Values . . .
Two-Period
Moving
Average
Forecast
Three-Period Weighted Moving
Average Forecast Weights =
0.5, 0.3, 0.2
Period
Actual
Demand
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
13
11.8
9
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
21
. . . and Resulting Graph
20
Volume
15
Demand
10
2-Period Avg
3-Period Wt. Avg.
5
0
1
2
3
4
5
6
7
8
9
Period
Note how the forecasts smooth out variations
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
22
Simple Exponential Smoothing
• Sophisticated weighted averaging model
• Needs only three numbers:
Ft = Forecast for the current period t
Dt = Actual demand for the current period t
a = Weight between 0 and 1
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
23
Exponential Smoothing
• Moving Averages
– Equal weight to older observations
• Exponential Smoothing
– More weight to more recent observations
• Forecast for next period is a weighted
average of
– Observation for this period
– Forecast for this period
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
24
Simple Exponential Smoothing
Formula
Ft+1
= Ft + a (Dt – Ft)
= a × Dt + (1 – a) × Ft
• Where did the current forecast come from?
• What happens as a gets closer to 0 or 1?
• Where does the very first forecast come from?
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
25
Exponential Smoothing Forecast
with a = 0.3
Period
Actual
Demand
Exponential
Smoothing
Forecast
1
12
11.00 (given)
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
Fall, 2012
F2 = 0.3×12 + 0.7×11
= 3.6 + 7.7
= 11.3
F3 = 0.3×15 + 0.7×11.3
= 12.41
11.41
EMBA 512 Demand Forecasting
Boise State University
26
Resulting Graph
16
14
Demand
12
10
Demand
8
Forecast
6
4
2
0
1
2
3
4
5
6
7
8
9
Period
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
27
Time Series with
Demand
random and trend components
Time
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
28
Linear Trend
Dow Jones Monthly Average
3500
3300
3100
2900
2700
2500
2300
2100
1900
1700
1500
Jan-88
Fall, 2012
Jul-88
Feb-89
Aug-89
Mar-90
Oct-90
EMBA 512 Demand Forecasting
Boise State University
Apr-91
Nov-91
29
Exponential Trend
Intel Quarterly Sales in Millions of Dollars
$5,000
$4,500
$4,000
$3,500
$3,000
$2,500
$2,000
$1,500
$1,000
$500
$0
12/19/85
Fall, 2012
5/3/87
9/14/88
1/27/90
6/11/91
10/23/92
3/7/94
EMBA 512 Demand Forecasting
Boise State University
7/20/95
30
Trends
What do you think will happen to a moving
average or exponential smoothing model
when there is a trend in the data?
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
31
Simple Exponential Smoothing Always Lags A Trend
Period
Actual
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
Fall, 2012
Because the model
is based on
historical demand,
it always lags
the obvious
upward trend
15.86
EMBA 512 Demand Forecasting
Boise State University
32
Simple Linear Regression
• Time Series
– Find best fit of proposed model to past data
– Project that fit forward
y
• Assumes a linear relationship:
y = a + b(x)
x
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
33
Definitions
Y = a + b(X)
Y = predicted variable (i.e., demand)
X = predictor variable
“X” is the time period for linear trend models.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
34
Example:
Regression Used to Estimate
A Linear Trend Line
Period (X)
Fall, 2012
Demand
(Y)
1
110
2
190
3
320
4
410
5
490
EMBA 512 Demand Forecasting
Boise State University
35
Resulting Regression Model:
Forecast = 10 + 98×Period
600
Demand
500
400
Demand
300
Regression
200
100
0
1
2
3
4
5
Period
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
36
Time series with
Demand
random, trend and seasonal components
June
Fall, 2012
June
June
EMBA 512 Demand Forecasting
Boise State University
June
37
Trend & Seasonality
Coca Cola Quarterly Sales in Millions of Dollars
$5,500
$5,000
$4,500
$4,000
$3,500
$3,000
$2,500
$2,000
$1,500
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
196
Q
395
Q
195
Q
394
Q
194
Q
393
Q
193
Q
392
Q
192
Q
391
Q
191
Q
390
Q
190
Q
389
Q
189
Q
388
Q
188
Q
387
Q
187
Q
386
Q
Q
186
$1,000
38
Seasonality
Toys "R" Us Quarterly Revenues in Millions of Dollars
$4,500
$4,000
$3,500
$3,000
$2,500
$2,000
$1,500
$1,000
$500
Q1-92
Fall, 2012
Q2-92
Q3-92
Q4-92
Q1-93
Q2-93
Q3-93
Q4-93
Q1-94
Q2-94
Q3-94
Q4-94
EMBA 512 Demand Forecasting
Boise State University
Q1-95
Q2-95
Q3-95
Q4-95
39
Modeling Trend & Seasonal Components
Fall, 2012
Quarter
Period
Winter 07
Spring
Summer
Fall
Winter 08
Spring
Summer
Fall
1
2
3
4
5
6
7
8
EMBA 512 Demand Forecasting
Boise State University
Demand
80
240
300
440
400
720
700
880
40
What Do You Notice?
Forecasted Demand = –18.57 + 108.57 x Period
Period
Actual
Demand
Regression
Forecast
Forecast
Error
Winter 07
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 08
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
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
41
Regression picks up trend, but
not the seasonality effect
1000
800
600
Demand
400
Forecast
200
0
1
Fall, 2012
2
3
4
5
6
7
8
EMBA 512 Demand Forecasting
Boise State University
42
Calculating Seasonal Index:
Winter Quarter
(Actual / Forecast) for Winter Quarters:
Winter ‘07:
Winter ‘08:
(80 / 90) = 0.89
(400 / 524.3) = 0.76
Average of these two = 0.83
Interpret!
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
43
Seasonally Adjusted Forecast
Model
For Winter Quarter
[ –18.57 + 108.57×Period ] × 0.83
Or more generally:
[ –18.57 + 108.57 × Period ] × Seasonal Index
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
44
Seasonally Adjusted Forecasts
Forecasted Demand = –18.57 + 108.57 x Period
Period
Actual
Demand
Regression
Forecast
Demand/
Forecast
Seasonal
Index
Seasonally
Adjusted
Forecast
Winter 07
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 08
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
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
Forecast
Error
45
Would You Expect the Forecast Model to
Perform This Well With Future Data?
1000
800
600
Demand
400
forecast
200
0
1
Fall, 2012
2
3
4
5
6
7
8
EMBA 512 Demand Forecasting
Boise State University
46
The Perfect (Imaginary) Forecast
Actual vs. Forecast
Forecast Demand
1400
1200
1000
800
600
400
200
0
0
200
400
600
800
1000
1200
1400
Actual Demand
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
47
A More Realistic Forecast
Actual vs. Forecast
Forecast Demand
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
0
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Actual Demand
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
48
Forecast Error
• Building a Forecast
– Fit to historical data
– Project future data
• Forecast Error
– How well does model fit historical data
– Do we need to tune or refine the model
– Can we offer confidence intervals about our
predictions
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
49
Forecast Error
• The forecast error measures the difference
between the actual demand and the
forecast of demand. The forecast is based
on the systematic component and the
random component is estimated based on
the forecast error.
• Forecast Error = Actual – Forecast
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
50
Measures of Forecast Accuracy
•
•
•
•
•
•
Forecast Errort (Et)= Demandt-Forecastt
Mean Squared Error (MSE)
Mean Absolute Deviation (MAD)
Bias
Tracking Signal
Relative Forecast Errors
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
51
Mean Squared Error (MSE)
1 n
2
MSEn   E t
n t 1
The MSE estimates the variance of
the forecast error.
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
52
Mean Absolute Deviation (MAD)
n
1
MADn   Et
n t 1
The MAD can be used to
estimate the standard deviation
of the random component,
assuming the random
component is normally
distributed:
σ = 1.25MAD
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
53
Bias
• To determine whether
a forecasting method
consistently over-orunderestimates
demand, calculate the
sum of the forecast
errors:
Fall, 2012
n
Bias n   Et
EMBA 512 Demand Forecasting
Boise State University
t 1
54
Tracking Signal
The tracking signal (TS) is
the ratio of the bias to the
MAD. Tracking signals
outside the range + 6
indicates that the forecast
is biased and either under
predicting (negative) or
over predicting (positive)
demand.
Fall, 2012
Bias t
TSt 
MADt
EMBA 512 Demand Forecasting
Boise State University
55
Forecast Accuracy & Demand Variability
(Normally Distributed Demand)
Fall, 2012
Coefficient
of Variation
Probability
Demand is Within
25% of the
Forecast
0.10
98.76%
0.25
68.27%
0.50
38.29%
0.75
26.11%
1.00
19.74%
1.50
13.24%
2.00
9.95%
3.00
6.64%
EMBA 512 Demand Forecasting
Boise State University
56
Issues
• Forecasting is a necessary evil, try to
reduce the need for it.
• Complexity costs money, does it provide
better forecasts?
• Aggregation provides accuracy, but
precludes local information
• Forecast the right thing
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
57
Forecasting Success Story
Taco Bell
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
58
Taco Bell
Feed the dog
• Labor is 30% of revenue
• Make to order environment
• Significant “seasonality”
– 52% of days sales during lunch
– 25% of days sales during busiest hour
• Balance staff with demand
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
59
Value Meals
• Drove demand
• Forecasting system in each store
– forecasts arrivals within 15 minute intervals
• Simulation system
– “predicts” congestion and lost sales
• Optimization system
– Finds the minimum cost allocation of workers
Fall, 2012
EMBA 512 Demand Forecasting
Boise State University
60
Forecasting System
• Customer arrivals by 15-minute interval of
day (e.g., 11:15-11:30 am Friday)
• Fed by in-store computer system
• 6-week moving average
• Estimated savings: Over $40 Million in 3
years.
Fall, 2011
EMBA 512 Demand Forecasting
Boise State University
61