Materials Planning - Forecasting

8/3/2019 Materials Planning - Forecasting

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Materials Planning


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Dealing with the Problem Complexitythrough Decomposition

AggregatePlanning

Master ProductionScheduling

Materials RequirementPlanning

AggregateUnit Demand

End Item (SKU) Demand

Capacity and Aggregate Production

Plans

SKU-level ProductionPlans

Manufacturing

andProcurement lead times Component Production lots and due

datesPartprocess

plans

(Plan. Hor.: 1 year, Time Unit: 1month)

(Plan. Hor.: a few months, Time Unit: 1week)

(Plan. Hor.: a few months, Time Unit: 1week)

Shop floor-level ProductionControl

(Plan. Hor.: a day or a shift, Time Unit: real-

time)

Forecasting


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Forecasting


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Costs of Forecasting

IBM continues to struggle with shortagesin the Think Pad line. WSJ 5/2/94

Dell stock plunges. Dellwas sharplyoff in its forecast of demand WSJ 8/93

Toyota believes it can save $100M [with] accurate ordering and inventory

management.


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Importance of forecasting


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Methods of Forecasting

Qualitative Approaches Quantitative Approaches


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Qualitative Approaches

intuitive hunches Executive committee consensus Delphi method Survey of sales force Survey of customers Market research

scientifically conducted surveys


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Quantitative Approaches

Time Series Methods use historical dataextrapolated into the future. They are bestsuited for stable environments.

EG - Moving averages, exponentialsmoothing methods. Causal Methods assume demand is

highly correlated with certainenvironmental factors (indicators). EG - Regression models, and econometricmodels.


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Time Series Methods

(Simple) Moving Average Weighted Moving Average Exponential Smoothing


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SIMPLE MOVING AVERAGE

In a moving average, the forecast would be calculatedas the average of the last few observations. If we let Mequal the number of observations to be included in themoving average, then:

Zt+1 =1/M i=t+M -1 Zi For example, if we let M=3, we have a "three period

moving average", and so, for example, at t = 7: Z8= (Z7+Z6+Z5) /3


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T Z M=2 M=3 M=4 M=5 M=6 M=7

1 982 1103 100 1044 94 105 1035 100 97 101 1016 92 97 98 101 1007 96 96 95 97 99 998 102 94 96 96 96 99 999 105 99 97 98 97 97 9910 96 104 101 99 99 98 98


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Weighted Moving Average

This is a variation on the simple movingaverage where the weights used tocompute the average are not equal.

This allows more recent demand datato have a greater effect on the movingaverage, therefore the forecast.

. . . more


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Weighted Moving Average

The weights must add to 1.0 andgenerally decrease in value with the ageof the data.

The distribution of the weights determinethe impulse response of the forecast.


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The weights used to compute theforecast (moving average) areexponentially distributed.

The forecast is the sum of the oldforecast and a portion ( ) of theforecast error (A t-1 - F t-1).

F t = F t-1 + (A t-1 - F t-1)

Exponential Smoothing


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The smoothing constant, , must bebetween 0.0 and 1.0.

A large provides a high impulseresponse forecast.

A small provides a low impulseresponse forecast.


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Example: Central Call Center

Moving Average CCC wishes to forecast the number of incomingcalls it receives in a day from the customers of oneof its clients, BMI. CCC schedules the appropriate

number of telephone operators based on projectedcall volumes. CCC believes that the most recent 12 days of callvolumes (shown on the next slide) are

representative of the near future call volumes.


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Moving Average o Representative Historical Data

Day Calls Day Calls 1 159 7 203 2 217 8 195 3 186 9 188 4 161 10 168 5 173 11 198 6 157 12 159


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Moving Average Use the moving average method with an AP= 3 days to develop a forecast of the callvolume in Day 13. F13 = (168 + 198 + 159)/3 = 175.0 calls


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Weighted Moving Average Use the weighted moving average method with an AP = 3days and weights of .1 (for oldest datum), .3, and .6 todevelop a forecast of the call volume in Day 13.

F13 = .1(168) + .3(198) + .6(159) = 171.6 calls

Note: The WMA forecast is lower than the MA forecastbecause Day 13s relatively low call volume carries almost

twice as much weight in the WMA (.60) as it does in the MA(.33).


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If a smoothing constant value of .25 is used and theexponential smoothing forecast for Day 11 was180.76 calls, what is the exponential smoothing

forecast for Day 13?

F12 = 180.76 + .25(198 180.76) = 185.07 F13 = 185.07 + .25(159 185.07) = 178.55


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Causal Methods


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Simple Linear Regression

Linear regression analysis establishes arelationship between a dependent variableand one or more independent variables.

In simple linear regression analysis thereis only one independent variable.


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Regression Equation This model is of the form: Y = a + bX

Y = dependent variable

X = independent variable a = y-axis intercept b = slope of regression line


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Constants a and b The constants a and b are computed usingthe following equations:


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Once the a and b values are computed, afuture value of X can be entered into theregression equation and a corresponding

value of Y (the forecast) can becalculated.

E l C ll g E ll t


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Example: College Enrollment Simple Linear Regression

At a small regional college enrollments have grown steadilyover the past six years, as evidenced below. Use timeseries regression to forecast the student enrollments for thenext three years. Students Students Year Enrolled (1000s) Year Enrolle(1000s) 1 2.5 4 3.22 2.8 5 3.3 3 2.9 6 3.4


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Example: College Enrollment

Simple Linear Regression x y x2 xy 1 2.5 1 2.5 2 2.8 4 5.6 3 2.9 9 8.7 4 3.2 16 12.8 5 3.3 25 16.5

6 3.4 36 20.4 x=21 y=18.1 x 2=91 xy=66.5


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Y = 2.387 + 0.180X


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Simple Linear Regression Y7 = 2.387 + 0.180(7) = 3.65 or 3,650 students Y8 = 2.387 + 0.180(8) = 3.83 or 3,830 students

Y9 = 2.387 + 0.180(9) = 4.01 or 4,010 students Note: Enrollment is expected to increase by 180students per year.


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Simple linear regression can also be usedwhen the independent variable Xrepresents a variable other than time.

In this case, linear regression isrepresentative of a class of forecastingmodels called causal forecasting models.


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Example: Railroad Products Co.

Simple Linear Regression Causal Model The manager of RPC wants to project the firmssales for the next 3 years. He knows that RPCslong-range sales are tied very closely to nationalfreight car loadings. On the next slide are 7 years ofrelevant historical data. Develop a simple linear regression model betweenRPC sales and national freight car loadings.Forecast RPC sales for the next 3 years, given thatthe rail industry estimates car loadings of 250, 270,and 300 million.

E l R il d P d t C


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Example: Railroad Products Co. Simple Linear Regression Causal Model

RPC Sales Car Loadings Year ($millions) (millions) 1 9.5 120

2 11.0 135 3 12.0 130 4 12.5 150 5 14.0 170

6 16.0 190 7 18.0 220


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Simple Linear Regression Causal Model

x y x2 xy 120 9.5 14,400 1,140 135 11.0 18,225 1,485 130 12.0 16,900 1,560 150 12.5 22,500 1,875 170 14.0 28,900 2,380 190 16.0 36,100 3,040 220 18.0 48,400 3,960

1,115 93.0 185,425 15,440


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Simple Linear Regression Causal Model

Y = 0.528 + 0.0801X


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Simple Linear Regression Causal Model Y8 = 0.528 + 0.0801(250) = $20.55 million Y9 = 0.528 + 0.0801(270) = $22.16 million

Y10 = 0.528 + 0.0801(300) = $24.56 million Note: RPC sales are expected to increase by$80,100 for each additional million national

freight car loadings.

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Materials Planning - Forecasting

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