Manufacturing
Planning and Control
MPC 6th Edition
Chapter 3
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
The forecasting process involves
much more than just the estimation
of future demand. The forecast also
needs to take into consideration the
intended use of the forecast, the
methodology for aggregating and
disaggregating the forecast, and
assumptions about future
conditions.
3-2
Agenda
Forecast information
Uses for forecast information
Forecasting techniques
Forecast evaluation
Linkage of planning and forecasting
3-3
Forecast Information

The forecast information and technique must
match the intended application
For strategic decisions such as capacity or
market expansion highly aggregated estimates
of general trends are necessary
 Sales and operations planning activities require
more detailed forecasts in terms of product
families and time periods
 Master production scheduling and control
demand highly detailed forecasts, which only
need to cover a short period of time

3-4
Forecasting for Strategic
Business Planning
Forecast is presented in general terms (sales
dollars, tons, hours)
 Aggregation level may be related to broad
indicators (gross national product, income)
 Causal models and regression/correlation
analysis are typical tools
 Managerial insight is critical and top
management involvement is intense
 Forecast is generally prepared annually and
covers a period of years

3-5
Forecasting for Sales and
Operations Planning





Forecast is presented in aggregate measures
(dollars, units)
Aggregation level is related to product families
(common family measurement)
Forecast is typically generated by summing
forecasts for individual products
Managerial involvement is moderate and limited
to adjustment of aggregate values
Forecast is generally prepared several times
each year and covers a period of several months
to a year
3-6
Forecasting for Master
Production Scheduling and
Control


Forecast is presented in terms of individual
products (units)
Forecast is typically generated by mathematical
procedures, often using software




Projection techniques are common
Assumption is that the past is a valid predictor of
the future
Managerial involvement is minimal
Forecast is updated almost constantly and
covers a period of days or weeks
3-7
Regression Analysis

Regression identifies a relationship
between two or more correlated variables


Linear regression is a special case where
the relationship is defined by a straight
line, used for both time series and causal
forecasting
Y = a + bX

Y is value of dependent variable, a is the
y-intercept of the line, b is the slope, and
X is the value of the independent variable
3-8
Least Squares Method

Objective–find the
line that minimizes
the sum of the
squares of the
vertical distance
between each data
point and the line
Y – calculated dependent variable value
yi – actual dependent variable point
a – y intercept
b – slope of the line
x – time period
Y = a + bx
Sum of Squares  ( y1  Y1 ) 2  ( y2  Y2 ) 2    ( yi  Yi ) 2
3-9
Least Squares Example
Sum
Quarter (x)
Sales (y)
xy
x2
y2
Y
1
600
600
1
360,000
801.3
2
1,550
3,100
4
2,402,500
1,160.9
3
1,500
4,500
9
2,250,000
1,520.5
4
1,500
6,000
16
2,250,000
1,880.1
5
2,400
12,000
25
5,760,000
2,239.7
6
3,100
18,600
36
9,610,000
2,599.4
7
2,600
18,200
49
6,760,000
2,959.0
8
2,900
23,200
64
8,410,000
3,318.6
9
3,800
34,200
81
14,440,000
3,678.2
10
4,500
45,000
100
20,250,000
4,037.8
11
4,000
44,000
121
16,000,000
4,397.4
12
4,900
58,800
144
24,010,000
4,757.1
78
33,350
268,200
650
112,502,500
3-10
Least Squares Example
Quarter
Sales
1
600
2
1,550
3
1,500
4
1,500
5
2,400
6
3,100
7
2,600
8
2,900
9
3,800
10
4,500
11
4,000
12
4,900
b
 xy  n x y
 x  n( x )
2
2

268,200  12 * 6.5 * 2,779.17
 359.6153
2
650  12 * 6.5
a  y  b x  2,779.17  6.5(359.6153)  441.6666
Y  a  bx  441.67  359.6x
3-11
Least Squares Regression
Line
Regression
errors are
the vertical
distance
from the
point to the
line
3-12
Least Squares Example
Quarter
Calculation
Forecast
13
Y13=441.6+359.6(13)
5,119.4
14
Y14=441.6+359.6(14)
5,476.0
15
Y15=441.6+359.6(15)
5,835.6
16
Y16=441.6+359.6(16)
6,195.2
Standard Error of Estimate (Syx) – how well the line fits the data
n
S yx 
(y
i 1
i
 Yi ) 2
n2

(600  801.3) 2  (1,550  1,160.9) 2  (1,500  1,520.5) 2    (4,900  4,757.1) 2
10
3-13
Time Series Decomposition
A time series can consist of one
or more components of demand
Trend–the long
term growth (or
decrease) of
demand
Seasonal–
Changes in
demand
associated with
portions of the
year (may be
additive or
multiplicative)
Cyclical–
repetitive
patterns not
associated with
seasonal
demand
Autocorrelation–
Random–
changes in
changes in
demand
demand that
associated with
can’t be linked to
previous
a specific cause
demand levels
3-14
Seasonality

Seasonality may (or may not) be
relative to the general demand
trend
Additive seasonal variation is
constant regardless of changes
in average demand
 Multiplicative seasonal variation
maintains a consistent
relationship to the average
demand (this is the more
common case)

3-15
Seasonal Factor

To account for seasonality within the
forecast, the seasonal factor is calculated

The amount of correction needed in a time
series to adjust for the season of the year
Season
Past
Sales
Average Sales
Seasonal Factor
for Each Season
Spring
200
1000/4=250
Actual/Average=200/250=0.8
Summer
350
1000/4=250
350/250=1.4
Fall
300
1000/4=250
300/250=1.2
Winter
150
1000/4=250
150/250=0.6
Total
1000
3-16
Seasonal Factor

If we expect (forecast) next year’s sales to
be 1,100 units, the seasonal forecast is
calculated using the seasonal factors
Season Expected Average Sales for
Sales
Each Season
Seasonal
Factor
Forecast
Spring
1100/4=275
X 0.8
= 220
Summer
1100/4=275
X 1.4
= 385
Fall
1100/4=275
X 1.2
= 330
Winter
1100/4=275
X 0.6
= 165
Total
1,100
3-17
Seasonality–Trend and
Season
Estimate of trend, use
Quarter
Amount
I – 2008
300
II – 2008
200
III – 2008
220
IV – 2008
530
I – 2009
520
II – 2009
420
III – 2009
400
IV - 2009
700
linear regression software
to obtain more precise
results
Trend = 170 +55t
3-18
Seasonality–Trend and
Season

Seasonal factors are calculated for each
season, then averaged for similar seasons

Seasonal Factor = Actual/Trend
3-19
Seasonality–Trend and
Season

Forecasts are calculated by extending the
linear regression and then adjusting by the
appropriate seasonal factor

FITS–Forecast Including Trend and Seasonal
Factors
3-20
Decomposition Using Least
Squares Regression
1. Decompose the time series into its components
a. Find seasonal component
b. Deseasonalize the demand
c. Find trend component
2. Forecast future values for each component
a. Project trend component into future
b. Multiply trend component by seasonal
component
3-21
Decomposition Using Least
Squares Regression
Period
Quarter
Actual
Demand
Average of Same Quarter
of Each Year
1
I
600
(600+2400+3800)/3=2266.7
2
II
1,550
3
III
1,500
4
IV
1,500
5
I
2,400
6
II
3,100
7
III
2,600
8
IV
2,900
9
I
3,800
10
II
4,500
11
III
4,000
12
IV
4,900
Total
33,350
Seasonal
Factor
Calculate average of
same period values
3-22
Decomposition Using Least
Squares Regression
Period
Quarter
Actual
Demand
Average of Same Quarter
of Each Year
1
I
600
(600+2400+3800)/3=2266.7
2
II
1,550
(1550+3100+4500)/3=3050
3
III
1,500
(1500+2600+4000)/3=2700
4
IV
1,500
(1500+2900+4900)/3=3100
5
I
2,400
6
II
3,100
7
III
2,600
8
IV
2,900
9
I
3,800
10
II
4,500
11
III
4,000
12
IV
4,900
Total
33,350
Seasonal
Factor
3-23
Decomposition Using Least
Squares Regression
Period
Quarter
Actual
Deman
d
Average of Same Quarter
of Each Year
1
I
600
(600+2400+3800)/3=2266.7
2
II
1,550
(1550+3100+4500)/3=3050
3
III
1,500
(1500+2600+4000)/3=2700
4
IV
1,500
(1500+2900+4900)/3=3100
5
I
2,400
6
II
3,100
7
III
2,600
8
IV
2,900
9
I
3,800
10
II
4,500
11
III
4,000
12
IV
4,900
Total
33,350
Seasonal Factor
2266.7/(33350/12)=0.82
Calculate seasonal factor
for each period
3-24
Decomposition Using Least
Squares Regression
Period
Quarter
Actual
Average of Same Quarter
Demand of Each Year
Seasonal Factor
1
I
600
(600+2400+3800)/3=2266.7
2266.7/(33350/12)=0.82
2
II
1,550
(1550+3100+4500)/3=3050
3050/(33350/12)=1.10
3
III
1,500
(1500+2600+4000)/3=2700
2700/(33350/12)=0.97
4
IV
1,500
(1500+2900+4900)/3=3100
3100/(33350/12)=1.12
5
I
2,400
0.82
6
II
3,100
1.10
7
III
2,600
0.97
8
IV
2,900
1.12
9
I
3,800
0.82
10
II
4,500
1.10
11
III
4,000
0.97
12
IV
4,900
1.12
Total
33,350
Seasonal
factors
repeat each
year
3-25
Decomposition Using Least
Squares Regression
Period
Quarter
Actual
Seasonal
Demand Factor
Deseasonalized Demand
(Actual/Seasonal Factor)
1
I
600
0.82
600/0.82=735.7
2
II
1,550
1.10
1550/1.10=1412.4
3
III
1,500
0.97
1500/0.97=1544.0
4
IV
1,500
1.12
1500/1.12=1344.8
5
I
2,400
0.82
2942.6
6
II
3,100
1.10
2824.7
7
III
2,600
0.97
2676.2
8
IV
2,900
1.12
2599.9
9
I
3,800
0.82
4659.2
10
II
4,500
1.10
4100.4
11
III
4,000
0.97
4117.3
12
IV
4,900
1.12
4392.9
Calculate deseasonalized
demand for each period
3-26
Least Squares Regression
for Deseasonalized Data
Period
Deseasonalized
Demand
SUMMARY OUTPUT
1
735.7
2
1412.4
3
1544.0
Regression Statistics
Multiple R
0.929653282
R Square
0.864255225
Adjusted R Square
0.850680748
Standard Error
512.8180268
Observations
12
4
1344.8
ANOVA
df
5
2942.6
6
2824.7
7
2676.2
8
2599.9
9
4659.2
10
4100.4
11
4117.3
12
4392.9
Regression
Residual
Total
Intercept
Period
1
10
11
Use linear regression to
fit trend line to
deseasonalized data
SS
MS
16743469.64 16743469.64
2629823.286 262982.3286
19373292.92
Coefficients Standard Error
t Stat
555.0045455
315.6176776 1.758471039
342.1800699
42.88399775 7.979201751
F
Significance F
63.66766059
1.20464E-05
P-value
0.109173704
1.20464E-05
Y= 555.0 + 342.2x
3-27
Create Forecast by Projecting
Trend and Reseasonalizing
Period Quarter
Y from Regression
13
I
555+342.2*13=5003.5
X 0.82
= 4102.87
14
II
555+342.2*14=5345.7
X 1.10
= 5880.27
15
III
555+342.2*15=5687.9
X 0.97
= 5517.26
16
IV
555+342.2*16=6030.1
X 1.12
= 6753.71
Project Linear Trend
Seasonal
Factor
Forecast
Project Seasonality
3-28
Short-Term Forecasting
Techniques

Statistical Forecasting Models
Moving Average–Unweighted average of a
given number of past periods is used to
forecast the future
 Exponential Smoothing–Weighted average
of all past periods is used to forecast the
future


Both assume that there is an underlying
pattern of demand that is consistent over
some period of time
3-29
Moving Average Forecasting
t
Moving Average Forecast ( MAFt ) 
 ActualDemand
i t  n 1
i
n
i – period number
t – current period
n - number of periods in moving average (smaller n makes forecast
more responsive to recent values
3-30
Exponential Smoothing
Forecasting
Exponential Smoothing Forecast ( ESFt )  ESFt 1   ( ActualDemand t  ESFt 1 )
  ( ActualDemand t )  (1   ) ESFt 1
α – smoothing constant (0≤α≤1) (higher α makes forecast more responsive to recent values)
t – current period
ESF t-1 – exponential smoothing forecast from previous period
3-31
Forecast Evaluation

Is the forecast too high or too low?


Mean Error (bias)
What is the magnitude of the forecast error?
Mean Absolute Deviation (MAD)
 Standard Deviation of forecast error = 1.25*MAD


Measuring both bias and MAD is critical to
understanding the quality of the forecast
3-32
Forecast Evaluation
n
Mean Error (bias ) 
 ( ActualDemand
i 1
 ForecastDemand i )
n
n
Mean Absolute Deviation ( MAD) 
i
 ActualDemand
i 1
i
 ForecastDemand i
n
i  period number
n  number of periods of data
3-33
Aggregating Forecasts

The SOP process reconciles differences in
forecasts from various sources
Customer/product knowledge
 Sum of individual product detailed forecasts
(by product family, for example)

SOP result is an aggregate demand forecast
 Long-term and/or aggregate forecasts are
more accurate than short-term, detailed
forecasts

3-34
Pyramid Forecasting

One means of aggregating and
disaggregating forecasts is pyramid
forecasting
Ensures consistency as the forecast sources
are integrated
 Provides a logical framework for summing
lower level forecasts and distributing higher
level forecast changes to individual products

3-35
Pyramid Forecasting
3-36
External Information

Activities or conditions that may invalidate the
assumption that history is a good predictor must
be accounted for in the forecasting process


Special promotions, product changes,
advertising, competitors’ actions
Changes to forecasting process may be needed
Change exponential smoothing parameter to
place more (or less) emphasis on recent history
 Forecast more frequently to identify conditions
that result in higher forecast errors

3-37
Principles




Forecast models should be as simple as possible.
Simple models often outperform more complicated
approaches.
Inputs (data) and outputs (forecasts) must be
monitored for quality and appropriateness.
Information on the sources of variation (seasonality,
market trends, company policies) should be
incorporated into the forecasting system.
Forecasts from different sources must be reconciled
and made consistent with company plans and
constraints.
3-38
Quiz – Chapter 3






A forecast used for Master Production Scheduling and
Control is likely to cover a period of _____________.
Regression analysis where the relationship between
variables is a straight line is called _______ _______.
In a time series analysis, time is the _________ variable.
An exponential smoothing forecast considers all past data
(T/F).
In an exponential smoothing forecast, a higher level of alpha
(α) will place more emphasis on recent history (T/F).
Mean error of a forecast provides information concerning the
forecast’s ________.
3-39