Forecasting
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
 Forecast – a statement about the future value of a
variable of interest
 We make forecasts about such things as weather,
demand, and resource availability
 Forecasts are an important element in making informed
decisions
Instructor Slides
3-2
 Expected level of demand
 The level of demand may be a function of some
structural variation such as trend or seasonal variation
 Accuracy
 Related to the potential size of forecast error
Instructor Slides
3-3
The forecast

should be timely

should be accurate

should be reliable

should be expressed in meaningful units

should be in writing

technique should be simple to understand and use

should be cost effective
1.
2.
3.
4.
5.
6.
Determine the purpose of the forecast
Establish a time horizon
Select a forecasting technique
Obtain, clean, and analyze appropriate data
Make the forecast
Monitor the forecast
1.
2.
3.
4.
Techniques assume some underlying causal system that
existed in the past will persist into the future
Forecasts are not perfect
Forecasts for groups of items are more accurate than
those for individual items
Forecast accuracy decreases as the forecasting horizon
increases
Instructor Slides
3-6
 Forecast errors should be
monitored
 Error = Actual – Forecast
 If errors fall beyond acceptable bounds,
corrective action may be necessary
Actual

MAD 
Actual

MSE 
t
 Forecast t
MAD weights all errors
evenly
n
t
 Forecast t 
2
n 1
Actual

MAPE 
t
 Forecast t
n  Actual t
100
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error
Period
Actual
(A)
Forecast
(F)
(A-F)
Error
|Error|
Error2
1
107
110
-3
3
9
2
125
121
4
4
16
3
115
112
3
3
9
4
118
120
-2
2
4
5
108
109
-1
1
1
Sum
13
39
n=5
n-1 = 4
MAD
MSE
AVG(A)
114.6
= 2.6
MAPE=MAD / AVG(A)
= 9.75 =2.6/114.6= 2.27%
 Qualitative Forecasting
 Qualitative techniques permit the inclusion of soft information such as:
 Human factors
 Personal opinions
 Hunches
 These factors are difficult, or impossible, to quantify
 Quantitative Forecasting
 Quantitative techniques involve either the projection of historical data or
the development of associative methods that attempt to use causal
variables to make a forecast
 These techniques rely on hard data
 Forecasts that use subjective inputs such as
opinions from consumer surveys, sales staff,
managers, executives, and experts
 Executive opinions
 Sales force opinions
 Consumer surveys
 Delphi method
 Forecasts that project patterns identified in
recent time-series observations
 Time-series - a time-ordered sequence of observations
taken at regular time intervals
 Assume that future values of the time-series can
be estimated from past values of the time-series
 Trend
 Seasonality
 Cycles
 Irregular variations
 Random variation
Exhibit 9.4
Exhibit 9.5a
Exhibit 9.5b
 Trend
 A long-term upward or downward movement in data
 Population shifts
 Changing income
 Seasonality
 Short-term, fairly regular variations related to the calendar or time
of day
 Restaurants, service call centers, and theaters all experience
seasonal demand
 Cycle
 Wavelike variations lasting more than one year
 These are often related to a variety of economic, political, or even
agricultural conditions
 Random Variation
 Residual variation that remains after all other behaviors have been
accounted for
 Irregular variation
 Due to unusual circumstances that do not reflect typical behavior
 Labor strike
 Weather event
 Naïve Forecast
 Uses a single previous value of a time series as the basis
for a forecast
 The forecast for a time period is equal to the previous
time period’s value
 Can be used when
 The time series is stable
 There is a trend
 There is seasonality
 These Techniques work best when a series tends
to vary about an average
 Averaging techniques smooth variations in the data
 They can handle step changes or gradual changes in the
level of a series
 Techniques
 Moving average
 Weighted moving average
 Exponential smoothing
 Technique that averages a number of the most
recent actual values in generating a forecast
n
Ft  MA t 
A
t i
i 1
n
where
Ft  Forecast for time period t
MA t  n period moving average
At 1  Actual value in period t  1
n  Number of periods in the moving average
Week
Demand
Forecast
Forecast
(3-week)
(5-week)
1
800
2
1400
3
1000
4
1500
(1000+1400+800)/3 =1067
5
1500
(1500+1000+1400)/3 = 1300
6
1300
(1500+1500+1000)/3 = 1333
(1500+1500+1000+1400+ 800)/5 =1240
7
1800
(1300+1500+1500)/3 = 1433
(1300+1500+1500+1000+1400)/5 =1340
8
1700
(1800+1300+1500)/3 = 1533
(1800+1300+1500+1500+1000)/5 =1420
9
1300
1600
(1700+1800+1300+1500+1500)/5 =1560
10
1700
1600
(1300+1700+1800+1300+1500)/5 =1520
11
1700
1567
(1700+1300+1700+1800+1300)/5 =1560
 As new data become available, the forecast is
updated by adding the newest value and dropping
the oldest and then recomputing the the average
 The number of data points included in the
average determines the model’s sensitivity
 Fewer data points used-- more responsive
 More data points used-- less responsive
Exhibit 9.6
Exhibit 9.7
 The most recent values in a time series are given
more weight in computing a forecast
 The choice of weights, w, is somewhat arbitrary and
involves some trial and error
Ft  w n Atn  w n1 At(n1)  ... w1 At1
where
w t  weight for period t, w t1  weight for period t 1, etc.
At  the actual value for period t, At1  the actual value for period t 1, etc.
 A weighted averaging method that is based on the
previous forecast plus a percentage of the forecast
error
Ft  Ft 1   ( At 1  Ft 1 )
where
Ft  Forecast for period t
Ft 1  Forecast for the previous period
 =Smoothing constant
At 1  Actual demand or sales from the previous period
Saturday Hotel Occupancy (  =0.5)
Period
t
1
2
3
4
5
6
Occupancy
Forecast
At
Ft
79
--84
79.00
83
79+.5(84-79)=81.50 or 82
81
81.5+.5(83-81.5)=82.25 or 82
98
82.25+.5(81-82.25)=81.63 or 82
100
81.63+.5(98-81.63)= 89.81 or 90
Forecast
Error
|At - Ft|
5
1
1
16
10
MAD =33/5= 6.6
Forecast Error (Mean Absolute Deviation) = ΣlAt – Ftl / n
The first actual value as the forecast for period 2
17-29
 A simple data plot can reveal the existence and
nature of a trend
 Linear trend equation
Ft  a  bt
where
Ft  Forecast for period t
a  Value of Ft at t  0
b  Slope of the line
t  Specified number of time periods from
t 0
 Wine quality = 12.145
+ 0.00117 winter rainfall
+ 0.0614 average growing season temperature
- 0.00386 harvest rainfall

~ Ian Ayres, Yale University
 Slope and intercept can be estimated from
historical data
b
n ty   t  y
n t 2    t 
y  b t

a
n
2
or y  bt
where
n  Number of periods
y  Value of the time series
3-33
Week (t)
Sales (y)
t2
ty
1
150
1
150
2
157
4
314
3
162
9
486
4
166
16
664
5
177
25
885
t= 15
y= 812
t2=55
(ty)=2499
b
n ty   t  y
n t    t 
2
2
5(2499)  15(812)

5(55)  225
12495  12180

 6.3
275  225
y  b t 812-6.3(15)

a
=
 143.5
n
5
y  143.5  6.3t
Substituting values of t into this equation,
the forecast for next 2 periods are:
F6= 143.5+6.3 (6) = 181.3
F7= 143.5+6.3 (7) = 187.6
 Seasonality – regularly repeating movements in series
values that can be tied to recurring events
 Expressed in terms of the amount that actual values deviate
from the average value of a series
 Models of seasonality
 Additive
 Seasonality is expressed as a quantity that gets added to or
subtracted from the time-series average in order to incorporate
seasonality
 Multiplicative
 Seasonality is expressed as a percentage of the average (or trend)
amount which is then used to multiply the value of a series in order
to incorporate seasonality
Instructor Slides
3-37
Instructor Slides
3-38
 Manager of a Call center recorded the volume of calls received
between 9 and 10 a.m. for 21 days and wants to obtain a seasonal
index for each day for that hour.
Volume
Season
Overall
Day
Week 1
Week 2
Week 3
Average
÷
Average
=
SA Index
Tues
67
60
64
63.667
71.571
=
0.8896
Wed
75
73
76
74.667
71.571
=
1.0432
Thurs
82
85
87
84.667
71.571
=
1.1830
Fri
98
99
96
97.667
71.571
=
1.3646
Sat
90
86
88
88.000
71.571
=
1.2295
Sun
36
40
44
40.000
71.571
=
0.5589
Mon
55
52
50
52.333
÷
÷
÷
÷
÷
÷
÷
71.571
=
0.7312
Overall Avg
71.571
7.0000
 Seasonal relatives
 The seasonal percentage used in the multiplicative seasonally
adjusted forecasting model
 Using seasonal relatives
 To deseasonalize data
 Done in order to get a clearer picture of the nonseasonal
components of the data series
 Divide each data point by its seasonal relative
 To incorporate seasonality in a forecast
 Obtain trend estimates for desired periods using a trend
equation
 Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative
 A coffee shop owner wants to predict quarterly
demand for hot chocolate for periods 9 and 10, which
happen to be the 1st and 2nd quarters of a particular
year. The sales data consist of both trend and
seasonality. The trend portion of demand is projected
using the equation Ft = 124 + 7.5 t. Quarter relatives
are
Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95,
 Use this information to deseasonalize sales for Q1 through
Q8.
Period
Quarter
Sales
÷
Quarter
Relative
=
Deseasonalized
sales
1
1
158.4
÷
1.20
=
132.0
2
2
153.0
1.10
=
139.1
3
3
110.0
0.75
=
146.7
4
4
146.3
0.95
=
154.0
5
1
192.0
1.20
=
160.0
6
2
187.0
1.10
=
170.0
7
3
132.0
0.75
=
176.0
8
4
173.8
÷
÷
÷
÷
÷
÷
÷
0.95
=
182.9
 Use this information to predict for periods 9 and 10.
 F9 = 124 +7.5( 9) = 191.5
F10= 124 +7.5(10) = 199.0
Multiplying the trend value by the appropriate quarter
relative yields a forecast that includes both trend and
seasonality.
Given that t =9 is a 1st quarter and t = 10 is a 2nd quarter.
The forecast demand for period 9 = 191.5(1.20) = 229.8
The forecast demand for period 10 = 199.0(1.10) = 218.9