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Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
Manufacturing Planning and Control
MPC 6th EditionChapter 3
3-2
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.
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Agenda
3-4
Forecast Information
The forecast information and technique must match the intended applicationFor 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
3-5
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
3-6
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
3-7
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 softwareProjection techniques are commonAssumption 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
3-8
Regression Analysis
Regression identifies a relationship between two or more correlated variablesLinear regression is a special case where the
relationship is defined by a straight line, used for both time series and causal forecasting
Y = a + bXY 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
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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 + bx22
222
11 )()()( ii YyYyYySquaresofSum
3-10
Least Squares ExampleQuarter (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
Sum 78 33,350 268,200 650 112,502,500
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Least Squares Example
Quarter Sales1 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
6666.441)6153.359(5.617.779,2 xbya
6153.3595.6*12650
17.779,2*5.6*12200,268)( 222
xnxyxnxy
b
xbxaY 6.35967.441
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Least Squares Regression Line
Regression errors are the vertical distance from the point to the line
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Least Squares ExampleQuarter Calculation Forecast13 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
10)1.757,4900,4()5.520,1500,1()9.160,1550,1()3.801600(
2
)( 22221
2
n
YyS
n
iii
yx
3-14
Time Series Decomposition
3-15
Seasonality Seasonality may (or may not) be
relative to the general demand trendAdditive 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)
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Seasonal Factor To account for seasonality within the
forecast, the seasonal factor is calculatedThe amount of correction needed in a time
series to adjust for the season of the year
Season Past Sales
Average Sales for Each Season
Seasonal Factor
Spring 200 1000/4=250 Actual/Average=200/250=0.8Summer 350 1000/4=250 350/250=1.4Fall 300 1000/4=250 300/250=1.2Winter 150 1000/4=250 150/250=0.6Total 1000
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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 ExpectedSales
Average Sales for Each Season
Seasonal Factor
Forecast
Spring 1100/4=275 X 0.8 = 220Summer 1100/4=275 X 1.4 = 385Fall 1100/4=275 X 1.2 = 330Winter 1100/4=275 X 0.6 = 165Total 1,100
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Seasonality–Trend and Season
Quarter AmountI – 2008 300
II – 2008 200
III – 2008 220
IV – 2008 530
I – 2009 520
II – 2009 420
III – 2009 400
IV - 2009 700
Trend = 170 +55t
Estimate of trend, use linear regression software to obtain more precise results
3-19
Seasonality–Trend and Season
Seasonal factors are calculated for each season, then averaged for similar seasonsSeasonal Factor = Actual/Trend
3-20
Seasonality–Trend and Season
Forecasts are calculated by extending the linear regression and then adjusting by the appropriate seasonal factorFITS–Forecast Including Trend and Seasonal
Factors
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Decomposition Using Least Squares Regression
1. Decompose the time series into its componentsa. Find seasonal componentb. Deseasonalize the demandc. Find trend component
2. Forecast future values for each componenta. Project trend component into futureb. Multiply trend component by seasonal
component
3-22
Decomposition Using Least Squares Regression
Period Quarter Actual Demand
Average of Same Quarter of Each Year
Seasonal Factor
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
Calculate average of same period values
3-23
Decomposition Using Least Squares Regression
Period Quarter Actual Demand
Average of Same Quarter of Each Year
Seasonal Factor
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
3-24
Decomposition Using Least Squares Regression
Period Quarter Actual Demand
Average of Same Quarter 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
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
Calculate seasonal factor for each period
3-25
Decomposition Using Least Squares Regression
Period Quarter Actual Demand
Average of Same Quarter 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
3-26
Decomposition Using Least Squares Regression
Period Quarter Actual Demand
Seasonal 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
3-27
Least Squares Regression for Deseasonalized Data
Period Deseasonalized Demand
1 735.7
2 1412.4
3 1544.0
4 1344.8
5 2942.6
6 2824.7
7 2676.2
8 2599.9
9 4659.2
10 4100.4
11 4117.3
12 4392.9
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.929653282R Square 0.864255225Adjusted R Square 0.850680748Standard Error 512.8180268Observations 12
ANOVA df SS MS F Significance F
Regression 1 16743469.64 16743469.64 63.66766059 1.20464E-05Residual 10 2629823.286 262982.3286Total 11 19373292.92
Coefficients Standard Error t Stat P-valueIntercept 555.0045455 315.6176776 1.758471039 0.109173704Period 342.1800699 42.88399775 7.979201751 1.20464E-05
Y= 555.0 + 342.2x
Use linear regression to fit trend line to deseasonalized data
3-28
Create Forecast by Projecting Trend and Reseasonalizing
Period Quarter Y from Regression Seasonal Factor
Forecast
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 Project Seasonality
3-29
Short-Term Forecasting Techniques
Statistical Forecasting ModelsMoving 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
3-30
Moving Average Forecasting
n
ndActualDemaMAFForecastAverageMoving
t
ntii
t
1)(
i – period numbert – current periodn - number of periods in moving average (smaller n makes forecast more responsive to recent values
3-31
Exponential Smoothing Forecasting
1
11
)1()()()(
tt
tttt
ESFndActualDemaESFndActualDemaESFESFForecastSmoothinglExponentia
α – smoothing constant (0≤α≤1) (higher α makes forecast more responsive to recent values)t – current periodESF t-1 – exponential smoothing forecast from previous period
3-32
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
3-33
Forecast Evaluation
dataofperiodsofnumbernnumberperiodi
n
mandForecastDendActualDemaMADDeviationAbsoluteMean
n
mandForecastDendActualDemabiasErrorMean
n
iii
n
iii
1
1
)(
)()(
3-34
Aggregating Forecasts
The SOP process reconciles differences in forecasts from various sourcesCustomer/product knowledgeSum 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
3-35
Pyramid Forecasting
One means of aggregating and disaggregating forecasts is pyramid forecastingEnsures consistency as the forecast sources
are integratedProvides a logical framework for summing
lower level forecasts and distributing higher level forecast changes to individual products
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Pyramid Forecasting
3-37
External Information Activities or conditions that may invalidate the assumption
that history is a good predictor must be accounted for in the forecasting processSpecial 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
3-38
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.
3-39
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 ________.