Transcript Slide 1

Forecasting
(part 2)
Chapter 15
4-1
Exponential Smoothing with
Trend Adjustment (Holt)
Forecast including trend (FITt)
= exponentially smoothed forecast (Ft)
+ exponentially smoothed trend (Tt)
4-2
Exponential Smoothing with
Trend Adjustment (Holt)
Ft = Forecast with Trend last period + (Last period’s actual –
last period’s Forecast with Trend
or
Ft = FITt-1 +  (At-1 – FITt-1)
Tt = Trend estimate last period + (Forecast this period Forecast with Trend last period)
or
Tt = Tt-1 + (Ft - FITt-1)
4-3
Exponential Smoothing with
Trend Adjustment (Holt)
Ft = exponentially smoothed forecast of the data
series in period t
Tt = exponentially smoothed trend in period t
At = actual demand in period t
 = smoothing constant for the average
 = smoothing constant for the trend
4-4
Comparing Actual and Forecasts
40
35
Actual
Demand
30
Demand
25
20
15
Smoothed
Forecast
Forecast including
trend
10
Smoothed Trend
5
0
1
2
3
4
5
6
Month
4-5
7
8
9
10
Exponential Smoothing with
Trend - Example
With the following data, calculate
the Holt forecast for each period.
Assume that the initial forecast for
month 1 was 11 units and the
trend for that period was 2 units.
4-6
Month
1
2
3
4
5
6
7
8
9
10
Demand
12
17
20
19
24
21
31
28
36
?
Seasonality
Repeating up and down movements in data

Related to recurring events
 Christmas sales of toys
 Lawnmower sales
When seasonality exists in data must incorporate into
forecasting model
4-7
Model with Seasonality
1.
2.
3.
4.
5.
Find average historical demand for each “season” by
summing the demand for that season in each year, and
dividing by the number of years for which you have data.
Compute the average demand over all seasons by dividing the
total average annual demand by the number of seasons.
Compute a seasonal index by dividing that season’s historical
demand (from step 1) by the average demand over all
seasons.
Estimate next year’s total demand
Divide this estimate of total demand by the number of
seasons, then multiply it by the seasonal index for that
season. This provides the seasonal forecast.
4-8
Monthly Sales of Laptop Computers
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
2000
80
70
80
90
113
110
100
88
85
77
75
82
Sales Demand
2001
85
85
93
95
125
115
102
102
90
78
72
78
Average Demand
2000-2002 Monthly
2002
105
85
82
115
131
120
113
110
95
85
83
80
4-9
Seasonal Index
Monthly Sales of Laptop Computers
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
2000
80
70
80
90
113
110
100
88
85
77
75
82
Sales Demand
2001
2002
85
105
85
85
93
82
95
115
125
131
115
120
102
113
102
110
90
95
78
85
72
83
78
80
Average Demand
2000-2002 Monthly
90
94
80
94
85
94
100
94
123
94
115
94
105
94
100
94
90
94
80
94
80
94
80
94
4-10
Seasonal Index
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
Example 2 - Seasonality
Over the past year Meredith and Smunt
Manufacturing had annual sales of 10,000 portable
water pumps. The average quarterly sales for the
past 5 years have averaged: spring 4,000, summer
3,000, fall 2,000 and winter 1,000. Compute the
quarterly index.
If annual sales for next year are 11,000, forecast
quarterly sales.
4-11
Forecast Error Equations
 Mean Absolute Deviation (MAD)
 | y  yˆ |  | forecast
n
MAD 
i
i 1
n
i

errors |
n
 Mean Absolute Percent Error (MAPE)
n
MAPE  100

i 1
actual i  forecast i
actual i
n
4-12