Forecasting

1
Operations Management William V.
Gehrlein University of Delaware
Forecasting
Part 1 Introduction through Obtaining Forecasts
for Items that only have an Average Component to
Expected Demand
2
University of Delaware
F-1 Forecasting
Techniques
Qualitative (Judgement Based)

• Sales Force Opinions

• Consumer Surveys

• Executive Opinion

• Delphi

Quantitative (Time Series Techniques)
Use patterns of past demand to develop a
forecast by projecting that pattern into the
future.
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University of Delaware
F-2 Components of Time Series Forecasting Models
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Average, Trend and Seasonality Effect
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Demand
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Average and Trend Effect
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Average Effect
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Year 1
Year 2
Year 3
Year 4
Time
4
University of Delaware
F-3 Time Series Forecasting Models

• Moving Averages

Average Effect Only

• Exponential Smoothing

• Trend Adjusted Smoothing

Average and Trend Effect

• Linear Regression

• Seasonality

5
University of Delaware
F-4 Moving Average Forecast
Set a number of periods, k, and the forecast for
any period is the average value of demand over
the last k periods
For example, with k 3
Demand
Forecast
Month
A(t)
F(t)
January
120
---
February
130
---
March
140
---
April
130.0
150
May
140.0
160
June
150.0
180
July
140
163.3
August
130
160.0
September
120
150.0
October
130.0
6
University of Delaware
F-5 Moving Average Forecast
Fewer Periods

• Less Lag

• More Reaction to Randomness

More Periods

• More Lag

• Less Reaction to Randomness

7
University of Delaware
F-4 Moving Average Forecast - Continued
Set a number of periods, k, and the forecast for
any period is the average value of demand over
the last k periods
For example, with k 3
Demand
Forecast
Deviation
Absolute
Month
A(t)
F(t)
A(t)-F(t)
Deviation
January
120
---
---
---
February
130
---
---
---
March
140
---
---
---
April
130.0
150
20.0
20.0
May
140.0
160
20.0
20.0
June
150.0
180
30.0
30.0
July
140
163.3
-23.3
23.3
August
130
160.0
-30.0
30.0
September
120
150.0
-30.0
30.0
October
130.0
Sum 153.3
MAD 153.3/6 25.6
8
University of Delaware
F-6 Simple Exponential Smoothing Forecast
Set a parameter
to reflect the confidence that there is a trend.
Arbitrarily set
Demand
Forecast
Month
A(t)
F(t)
January
120
---
February
130
---
March
140
130.0
April
150
134.5
141.5
May
160
June
180
149.8
163.4
July
140
August
130
152.9
September
120
142.6
October
132.4
9
University of Delaware
F-7 Simple Exponential Smoothing Forecast
Arbitrarily set
Small

• More Lag

• Less Reaction to Randomness

Large

• Less Lag

• More Reaction to Randomness

10
University of Delaware
F-6 Simple Exponential Smoothing Forecast
- Continued
Set a parameter
to reflect the confidence that there is a trend.
Arbitrarily set
Demand
Forecast
Deviation
Absolute
Month
A(t)
F(t)
A(t)-F(t)
Deviation
January
---
---
---
120
February
130
---
---
---
March
140
130.0
---
---
April
15.5
150
134.5
15.5
141.5
May
160
18.5
18.5
June
180
149.8
30.2
30.2
163.4
July
140
-23.4
23.4
August
130
152.9
-22.9
22.9
September
120
142.6
-22.6
22.6
October
132.4
Sum 133.1
MAD 133.1/6 22.2
11
Operations Management William V.
Gehrlein University of Delaware
Forecasting
Part 2 Forecasting when a Trend Exists and
Dealing with Seasonality
12
University of Delaware
F-3 Time Series Forecasting Models

• Moving Averages

Average Effect Only

• Exponential Smoothing

• Trend Adjusted Smoothing

Average and Trend Effect

• Linear Regression

• Seasonality

13
University of Delaware
F-8 Trend Adjusted Exponential Smoothing
Forecast
Similar to simple exponential smoothing, but
there are two smoothing factors
Demand
Month
A(t)
S(t)
T(t)
TAF(t)
January
120
February
130
March
140
140.0
140.0
10.0
150.0
150.0
April
150
10.0
10.0
160.0
160.0
160
May
170.0
June
180
176.0
10.0
186.0
July
140
158.4
12.4
170.8
August
130
146.3
1.4
147.7
September
120
131.1
-8.4
122.7
October
14
University of Delaware
F-9 Trend Adjusted Exponential Smoothing
Forecast
15
University of Delaware
F-10 Trend Lines and
Seasonality
Any of the forecasting techniques that have been
discussed can deal with the issue of seasonality,
with an appropriate use of seasonal indexes.
Consider their use in forecasting with
linear regression Quarter Year 1
Year 2 Spring 165 210
Summer 140 190 Fall
490 685 Winter 855
1025
16
University of Delaware
F-11 Trend Lines and
Seasonality
17
University of Delaware
F-10 Trend Lines and
Seasonality
Any of the forecasting techniques that have been
discussed can deal with the issue of seasonality,
with an appropriate use of seasonal indexes.
Consider their use in forecasting with linear
regression Quarter Year 1 Year
2 Spring 165 210
Summer 140 190 Fall
490 685 Winter 855
1025
Quarter Average
Index
187.5/470.0 0.40
187.5
165.0/470.0 0.35
165.0
587.5/470.0 1.25
587.5
940.0/470.0 2.00
940.0
4.00
Annual Sum
1650
2110
Overall Quarterly Average (1650 2110)/8
470.0
18
University of Delaware
F-12 Trend Lines and
Seasonality
Deseasonalized Demand
Quarter
Demand
Index
12345678
SP-1 SU-1 FA-1 WI-1 SP-2 SU-2 FA-2 WI-2
165 140 490 855 210 190 685 1025
0.40 0.35 1.25 2.00 0.40 0.35 1.25 2.00
413.6
398.8
392.0 427.5 526.4 541.2 548.0 512.5
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University of Delaware
F-11 Trend Lines and
Seasonality
20
University of Delaware
F-12 Trend Lines and
Seasonality
(Y)
Deseasonalized Demand
(X)
Quarter
Demand
Index
12345678
SP-1 SU-1 FA-1 WI-1 SP-2 SU-2 FA-2 WI-2
165 140 490 855 210 190 685 1025
0.40 0.35 1.25 2.00 0.40 0.35 1.25 2.00
413.6
398.8
392.0 427.5 526.4 541.2 548.0 512.5
Use Linear Regression to get
Y a bX
21
University of Delaware
Flashback to Statistics
Y a bX
22
University of Delaware
F-12 Trend Lines and
Seasonality
(Y)
(X)
Deseasonalized Demand
Quarter
Demand
Index
XY
12345678
SP-1 SU-1 FA-1 WI-1 SP-2 SU-2 FA-2 WI-2
413.6 797.6 1176.0 1710.0 2632.0 3247.3 3836.0
4100.0
1 4 9 16 25 36 49 64
165 140 490 855 210 190 685 1025
0.40 0.35 1.25 2.00 0.40 0.35 1.25 2.00
413.6
398.8
392.0 427.5 526.4 541.2 548.0 512.5
36
204
Sum
3760.0
17912.4
n 8
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University of Delaware
F-13 Trend Lines and
Seasonality
Forecast for Winter of Year 3
X
Y 363.8 23.6X
1 2 3 4 5 6 7 8 9 10 11 12
SP-1 SU-1 FA-1 WI-1 SP-2 SU-2 FA-2 WI-2 SP-3 SU-3
FA-3 WI-3
X ?
12
Y 363.8 23.612 647.0
Seasonalize the forecast
Winter Index 2.00
Forecast 647.02.00 1294
24
University of Delaware
F-14 Dealing with Seasonality
Step 1 Calculate seasonal indexes.
Step 2 Deseasonalize actual demand values.
Step 3 Forecast with deseasonalized demand to
get deseasonalized forecasts.
Step 4 Bring seasonality back into the forecasts.
25
Operations Management William V.
Gehrlein University of Delaware
Forecasting
Part 3 Evaluating and Controlling Forecasting
Systems
26
University of Delaware
F-15 Selecting a Forecasting
Procedure
27
University of Delaware
F-16 Selecting a Forecasting
Procedure
28
University of Delaware
F-15 Selecting a Forecasting
Procedure
Alpha .2

MAD 2095
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University of Delaware
F-17 Controlling a Forecasting
Policy
D(t) Deviation of forecast in period t
CD(t) Cumulative deviation of forecasts up to
period t
MAD(t) Mean Absolute Deviation of forecasts up
to period t
30
University of Delaware
F-18 Controlling a Forecasting
Policy
Alpha .2

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University of Delaware
F-17 Controlling a Forecasting
Policy
D(t) Deviation of forecast in period t
CD(t) Cumulative deviation of forecasts up to
period t
MAD(t) Mean Absolute Deviation of forecasts up
to period t