The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
Discover the best professional documents and content resources in AnyFlip Document Base.
Search
Published by soedito, 2019-11-18 11:29:14

CH_15_FORECASTING

CH_15_FORECASTING

Forecasting

Chapter 15 15-1

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Chapter Topics

■ Forecasting Components
■ Time Series Methods
■ Forecast Accuracy
■ Time Series Forecasting Using Excel
■ Time Series Forecasting Using QM for Windows
■ Regression Methods

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-2

Forecasting Components

■ A variety of forecasting methods are available for use depending on

the time frame of the forecast and the existence of patterns.

■ Time Frames:
Short-range (one to two months)
Medium-range (two months to one or two years)
Long-range (more than one or two years)

■ Patterns:
Trend
Random variations
Cycles
Seasonal pattern

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-3

Forecasting Components
Patterns (1 of 2)

Trend - A long-term movement of the item being forecast.
Random variations - movements that are not predictable and follow
no pattern.
Cycle - A movement, up or down, that repeats itself over a lengthy
time span.
Seasonal pattern - Oscillating movement in demand that occurs
periodically in the short run and is repetitive.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-4

Forecasting Components
Patterns (2 of 2)

Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend w/Season

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-5

Forecasting Components
Forecasting Methods

Times Series - Statistical techniques that use historical data
to predict future behavior.

Regression Methods - Regression (or causal ) methods
that attempt to develop a mathematical relationship
between the item being forecast and factors that cause it
to behave the way it does.

Qualitative Methods - Methods using judgment, expertise
and opinion to make forecasts.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-6

Forecasting Components
Qualitative Methods

“Jury of executive opinion,” a qualitative technique, is the most

common type of forecast for long-term strategic planning.

Performed by individuals or groups within an organization,
sometimes assisted by consultants and other experts, whose

judgments and opinions are considered valid for the

forecasting issue.

Usually includes specialty functions such as marketing,
engineering, purchasing, etc. in which individuals have

experience and knowledge of the forecasted item.

Supporting techniques include the Delphi Method, market
research, surveys, etc.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-7

Time Series Methods
Overview

Statistical techniques that make use of historical data collected

over a long period of time.

Methods assume that what has occurred in the past will
continue to occur in the future.

Forecasts based on only one factor - time.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-8

Time Series Methods
Moving Average (1 of 5)

Moving average uses values from the recent past to develop
forecasts.

This dampens or smoothes random increases and decreases.

Useful for forecasting relatively stable items that do not display

any trend or seasonal pattern.

Formula for:

MAn = i∑=n1Di
n

where:

n = number of periods in the moving average

Di = data in period i

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-9

Time Series Methods
Moving Average (2 of 5)

Example: Instant Paper Clip Supply Company forecast of orders
for the month of November.

Three-month moving average:

MA = i∑=31Di = 90+110+130 =110 orders
3 3 3

Five-month moving average:

MA = i∑=51Di = 90+110+130+75+50 = 91 orders
5 5 5

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-10

Time Series Methods
Moving Average (3 of 5)

Table 15.2 Three- and Five-Month Moving Averages 15-11

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Moving Average (4 of 5)

Figure 15.2 Three- and Five-Month Moving Averages 15-12

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Moving Average (5 of 5)

Longer-period moving averages react more slowly to changes in

demand than do shorter-period moving averages.

The appropriate number of periods to use often requires trial-and-
error experimentation.

Moving average does not react well to changes (trends, seasonal

effects, etc.) but is easy to use and inexpensive.

Good for short-term forecasting.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-13

Time Series Methods
Weighted Moving Average

In a weighted moving average, weights are assigned to the most
recent data.

WMAn =i∑=n1WiDi

where Wi = the weight for period i, between 0% and 100%

∑Wi = 1.00

Example: Paper clip company weights 50% for October, 33%
for September, 17% for August:

WMA = i∑=31Wi Di = (.50)(90)+(.33)(110)+(.17)(130) = 103.4 orders
3

Determining precise weights and number of periods requires trial-
and-error experimentation.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-14

Time Series Methods
Exponential Smoothing (1 of 11)

Exponential smoothing weights recent past data more strongly

than more distant data.

Two forms: simple exponential smoothing and adjusted

exponential smoothing.

Simple exponential smoothing:

Ft + 1 = αDt + (1 - α)Ft
where: Ft + 1 = the forecast for the next period

Dt = actual demand in the present period
Ft = the previously determined forecast for the
present period
α = a weighting factor (smoothing constant).

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-15

Time Series Methods
Exponential Smoothing (2 of 11)

The most commonly used values of α are between 0.10 and
0.50.

Determination of α is usually judgmental and subjective

and often based on trial-and -error experimentation.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-16

Time Series Methods
Exponential Smoothing (3 of 11)

Example: PM Computer Services (see Table 15.4).
Exponential smoothing forecasts using smoothing constant of .30.

Forecast for period 2 (February):
F2 = α D1 + (1- α)F1 = (.30)(.37) + (.70)(.37) = 37 units

Forecast for period 3 (March):
F3 = α D2 + (1- α)F2 = (.30)(.40) + (.70)(37) = 37.9 units

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-17

Time Series Methods
Exponential Smoothing (4 of 11)

Table 15.4 Exponential Smoothing Forecasts, α = .30 and α = .50 15-18

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Exponential Smoothing (5 of 11)

The forecast that uses the higher smoothing constant (.50) reacts
more strongly to changes in demand than does the forecast with the
lower constant (.30).

Both forecasts lag behind actual demand.

Both forecasts tend to be consistently lower than actual demand.

Low smoothing constants are appropriate for stable data

without trend; higher constants appropriate for data with trends.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-19

Time Series Methods
Exponential Smoothing (6 of 11)

Figure 15.3 Exponential Smoothing Forecasts 15-20

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Exponential Smoothing (7 of 11)

■ Adjusted exponential smoothing: exponential smoothing with a

trend adjustment factor added.

Formula:

AFt + 1 = Ft + 1 + Tt+1

where: T = an exponentially smoothed trend factor
Tt + 1 + β(Ft + 1 - Ft) + (1 - β)Tt
Tt = the last period trend factor
β = smoothing constant for trend ( a value

between zero and one).

■ Reflects the weight given to the most recent trend data.

■ Determined subjectively.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-21

Time Series Methods
Exponential Smoothing (8 of 11)

Example: PM Computer Services exponential smoothed
forecasts with α = .50 and β = .30 (see Table 15.5).

Adjusted forecast for period 3:
T3 = β(F3 - F2) + (1 - β)T2
= (.30)(38.5 - 37.0) + (.70)(0) = 0.45
AF3 = F3 + T3 = 38.5 + 0.45 = 38.95

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-22

Time Series Methods
Exponential Smoothing (9 of 11)

Table 15.5 Adjusted Exponentially Smoothed Forecast 15-23
ValuesCopyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Exponential Smoothing (10 of 11)

■ Adjusted forecast is consistently higher than the simple
exponentially smoothed forecast.

■ It is more reflective of the generally increasing trend of the data.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-24

Time Series Methods
Exponential Smoothing (11 of 11)

Figure 15.4 Adjusted Exponentially Smoothed Forecast 15-25

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Linear Trend Line (1 of 5)

■ When demand displays an obvious trend over time, a least squares
regression line , or linear trend line, can be used to forecast.

■ Formula:

y = a+bx b = ∑ xy − nx y
∑x2 −nx
where:
a = intercept (at period 0) a= y−bx
b = slope of the line
x = the time period where:
y = forecast for demand
for period x n = number of periods
∑x
x = n

y = ∑y
n

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-26

Time Series Methods
Linear Trend Line (2 of 5)

Example: PM Computer Services (see Table 15.6)

x = 78 = 6.5 y = 557 = 46.42
12 12

b = ∑ xy − nx y = 3,867 − (12)(6.5)(46.42) =1.72
∑x2 −nx2 650 −12(6.5)2

a = y −bx = 46.42−(1.72)(6.5) =35.2

y =35.2+1.72x linear trend line

for period 13, x = 13, y =35.2+1.72(13) =57.56

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-27

Time Series Methods 15-28
Linear Trend Line (3 of 5)

Table 15.6
Least Squares Calculations

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Linear Trend Line (4 of 5)

■ A trend line does not adjust to a change in the trend as does the

exponential smoothing method.

■ This limits its use to shorter time frames in which trend will not

change.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-29

Time Series Methods
Linear Trend (5 of 5)

Figure 15.5 Linear Trend Line 15-30

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Seasonal Adjustments (1 of 4)

■ A seasonal pattern is a repetitive up-and-down movement in

demand.
■ Seasonal patterns can occur on a quarterly, monthly, weekly, or daily

basis.

■ A seasonally adjusted forecast can be developed by multiplying

the normal forecast by a seasonal factor.

■ A seasonal factor can be determined by dividing the actual demand

for each seasonal period by total annual demand:
Si =Di/∑D

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-31

Time Series Methods
Seasonal Adjustments (2 of 4)

■ Seasonal factors lie between zero and one and represent the portion
of total annual demand assigned to each season.

■ Seasonal factors are multiplied by annual demand to provide
adjusted forecasts for each period.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-32

Time Series Methods
Seasonal Adjustments (3 of 4)

Example: Wishbone Farms

Table 15.7 Demand for Turkeys at Wishbone Farms 15-33

S1 = D1/ ∑D = 42.0/148.7 = 0.28
S2 = D2/ ∑D = 29.5/148.7 = 0.20
S3 = D3/ ∑D = 21.9/148.7 = 0.15
S4 = D4/ ∑D = 55.3/148.7 = 0.37

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Methods
Seasonal Adjustments (4 of 4)

Multiply forecasted demand for entire year by seasonal factors to
determine quarterly demand.
Forecast for entire year (trend line for data in Table 15.7):

y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17
Seasonally adjusted forecasts:

SF1 = (S1)(F5) = (.28)(58.17) = 16.28
SF2 = (S2)(F5) = (.20)(58.17) = 11.63
SF3 = (S3)(F5) = (.15)(58.17) = 8.73
SF4 = (S4)(F5) = (.37)(58.17) = 21.53

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-34

Forecast Accuracy
Overview

Forecasts will always deviate from actual values.

Difference between forecasts and actual values referred to as

forecast error.

Would like forecast error to be as small as possible.

If error is large, either technique being used is the wrong one, or
parameters need adjusting.

Measures of forecast errors:

Mean Absolute deviation (MAD)
Mean absolute percentage deviation (MAPD)
Cumulative error (E bar)
Average error, or bias (E)

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-35

Forecast Accuracy
Mean Absolute Deviation (1 of 7)

MAD is the average absolute difference between the forecast

and actual demand.

Most popular and simplest-to-use measures of forecast error.

Formula: ∑ Dt −Ft
n
MAD =

where:

t = the period number

Dt = demand in period t
Ft = the forecast for period t
n = the total number of periods

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-36

Forecast Accuracy
Mean Absolute Deviation (2 of 7)

Example: PM Computer Services (see Table 15.8).

Compare accuracies of different forecasts using MAD:

MAD = ∑ Dt − Ft = 531.141= 4.85
n

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-37

Forecast Accuracy
Mean Absolute Deviation (3 of 7)

Table 15.8 Computational Values for MAD and error 15-38

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Forecast Accuracy
Mean Absolute Deviation (4 of 7)

The lower the value of MAD relative to the magnitude of the
data, the more accurate the forecast.

When viewed alone, MAD is difficult to assess.

Must be considered in light of magnitude of the data.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-39

Forecast Accuracy
Mean Absolute Deviation (5 of 7)

Can be used to compare accuracy of different forecasting
techniques working on the same set of demand data (PM Computer
Services):

Exponential smoothing (α = .50): MAD = 4.04
Adjusted exponential smoothing (α = .50, β = .30): MAD = 3.81
Linear trend line: MAD = 2.29

Linear trend line has lowest MAD; increasing α from .30 to .50
improved smoothed forecast.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-40

Forecast Accuracy
Mean Absolute Deviation (6 of 7)

A variation on MAD is the mean absolute percent deviation

(MAPD).

Measures absolute error as a percentage of demand rather than

per period.

Eliminates problem of interpreting the measure of accuracy relative
to the magnitude of the demand and forecast values.

Formula:

MAPD = ∑ Dt −Ft = 5532.401=.103 or 10.3%
∑ Dt

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-41

Forecast Accuracy
Mean Absolute Deviation (7 of 7)

MAPD for other three forecasts:
Exponential smoothing (α = .50): MAPD = 8.5%
Adjusted exponential smoothing (α = .50, β = .30):
MAPD = 8.1%
Linear trend: MAPD = 4.9%

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-42

Forecast Accuracy
Cumulative Error (1 of 2)

Cumulative error is the sum of the forecast errors (E =∑et).
A relatively large positive value indicates forecast is biased low,

a large negative value indicates forecast is biased high.

If preponderance of errors are positive, forecast is consistently low;
and vice versa.

Cumulative error for trend line is always almost zero, and is

therefore not a good measure for this method.

Cumulative error for PM Computer Services can be read directly
from Table 15.8.
E = ∑ et = 49.31 indicating forecasts are frequently below actual
demand.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-43

Forecast Accuracy
Cumulative Error (2 of 2)

Cumulative error for other forecasts:

Exponential smoothing (α = .50): E = 33.21

Adjusted exponential smoothing (α = .50, β =.30):
E = 21.14

Average error (bias) is the per period average of cumulative error.

Average error for exponential smoothing forecast:

E = ∑ et = 49.31 = 4.48
n 11
A large positive value of average error indicates a forecast is biased

low; a large negative error indicates it is biased high.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-44

Forecast Accuracy
Example Forecasts by Different Measures

Table 15.9 Comparison of Forecasts for PM Computer Services

Results consistent for all forecasts:

Larger value of alpha is preferable.

Adjusted forecast is more accurate than exponential smoothing.

Linear trend is more accurate than all the others. 15-45

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Time Series Forecasting Using Excel (1 of 4)

Exhibit 15.1

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-46

Time Series Forecasting Using Excel (2 of 4)

Exhibit 15.2

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-47

Time Series Forecasting Using Excel (3 of 4)

Exhibit 15.3

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-48

Time Series Forecasting Using Excel (4 of 4)

Exhibit 15.4

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-49

Exponential Smoothing Forecast with Excel QM

Exhibit 15.5

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 15-50


Click to View FlipBook Version