Manufacturing Planning and Control - McGraw Hill...

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Manufacturing Planning and Control

MPC 6th EditionChapter 3

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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

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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

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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

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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

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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

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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

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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

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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

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Seasonal factors are calculated for each season, then averaged for similar seasonsSeasonal Factor = Actual/Trend

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Forecast Evaluation

dataofperiodsofnumbernnumberperiodi

n

mandForecastDendActualDemaMADDeviationAbsoluteMean

n

mandForecastDendActualDemabiasErrorMean

n

iii

n

iii

1

1

)(

)()(

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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

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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

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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

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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.

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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 ________.

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