Mechanical Engineering 101 - University of California,...

© 2003‐2012, McMains, DornfeldME 101 lecture 4 1

Mechanical Engineering 101

University of California, Berkeley

Lecture #4

© 2003‐2012, McMains, Dornfeld ME 101 lecture 4 2

Today’s lecture

• Shortage Costs• Forecasting


Holding costs vs. shortage costs

• tradeoff!• Higher holding costs for more safety stock

Sho

rtage

cost

s

Safety stock, SS


Your demand forecast for time period 116?

Period 0 30 50 70 90 115

120

160

80

Dem

and

1. D <802. 80 <= D <1203. 120 <= D <1504. 150 <= D <1705. 170 <= D <1806. 180 <= D <1907. 190 <= D <2008. 200 <= D <2109. 210 <= D


Forecasting

• looking at existing products, sales…– examine past data– find historical trends– extrapolate forward

• assumptions– past trends will continue– demand values a function of time


Demand Data

• typically look at:– shipments– past customer orders

• is this the same as demand?


Today’s lecture


– unweighted models• constant & linear demand models• measuring error• least squares

– weighted model– non-trendbased forecasting


Short term forecasting

• constant demand model• demand in period t, (Dt) =

– mean expected demand – + “random error” term t (0, 2)


demand in period t estimated as constant mean + “random error” term:Dt = + t

Time (t)

1

1 2 3 10

Constant mean demand


slope, m

y

x

b

Linear Demand Model

y = mx + b + y = mx + b


Today’s lecture



– weighted model– non-trendbased


slope, m

y

xb

•prediction - actual = error (residual)•if residuals all zero

•model is “perfect”•you faked the data•or your model has too many DOFs

• If model captures all significant information•residuals appear as “random noise” •(i.e. no predictable form)

. . . . . . . . .+

-

resi

dual

s

Goodness of Fity = mx + b +


•Determine “average forecast error” measured over some historical set of data points, T:

e et

t1

T

T

We’d like this to be zero!

Model errors


Demand (order size)

Frequency

+-

Averageorder size

Predicted average demand

bias

• Bias indicates model has some “dc level” offseterror in estimation

• usually easy to correct (-dc!)

Bias


• zero “on average” not sufficient

• need low magnitude of forecast errore.g. low mean squared error (MSE)

MSE et e 2

t1

T

T 1

Model errors


Today’s lecture



– weighted model– non-trendbased forecasting


Least squares fits

• Excel will do least squares fits:– linear– log– exponential– power– polynomial

• choose “order” e.g. quadratic, cubic, etc.


Excel least squares fits

• To compare least squares fits– compare R^2 values Excel calculates– higher (closer to 1) is a better fit

Better fit may not be better model!

• To calculate errors– Choose option “display equation on chart”– program equation in spreadsheet for

predictions of data points– calculate difference from actual value


Which least squares fit is best model?

Least Squares Fits

7,600

7,800

8,000

8,200

8,400

8,600

8,800

9,000

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and Demand

Poly. (Demand)Expon. (Demand)Linear (Demand)

1. Polynomial2. Exponential3. Linear


Announcements

• OH mods• HW due today 5pm,

– 3rd floor south side, homework box as indicated• No SID on HW• Include nick-name if any (in quotes)• Collaboration policy



Period 0 30 50 70 90 115

120

160

80

Dem

and

1. D <802. 80 <= D <1203. 120 <= D <1504. 150 <= D <1705. 170 <= D <1806. 180 <= D <1907. 190 <= D <2008. 200 <= D <2109. 210 <= D


Today’s lecture


– unweighted models– weighted model

• exponential smoothing– non-trendbased forecasting


Simple exponential smoothing

• use weighted average of all past data• weight so importance of older data decays

is weighting factor• proportion of weight for most recent data

• estimate St (for future periods given data through period t):St = Dt + (1 - )St-1 (text eqn 3.3)



• St = Dt + (1 - )St-1

• St = Dt + (1 - )[Dt-1 + (1- ) St-2]• St = Dt + (1 - )Dt-1 + (1- )2 [Dt-2 + (1 - )St-3]• St = Dt + (1 - )Dt-1 + (1- )2Dt-2 + (1 - )3[ Dt-3+ (1 -

) St-4]



• St = Dt + (1 - )St-1


) St-4]

…• St = Dt + (1 - )Dt-1 + (1- )2Dt-2 + … + (1 - )t-1D1+ (1 - )tS0



• St = Dt + (1 - )St-1


) St-4]

…St (1)k

k 0

Dtk


Exponential smoothing

• for 0< < 1, sum of all weight terms is 1• 0.001 < ≤ 0.3 typically • higher the faith in recent data, higher

St (1)k

k 0

Dtk


Exponential smoothing

• how to get initial mean demand S0 from before we had data?– average all your data (assume constant mean process)

• first “prediction” = – S1 = D1 + (1 - )S0

• recurse to find St

• use as prediction for future periods– update as more data arrives

i

t

iD

tS

1

01


Exponential Smoothing Example.


Today’s lecture


– unweighted models– weighted model– non-trendbased forecasting


Market surveys

• random survey of potential customers– how likely to buy?

• survey existing customers– when will buy again?


Delphi method

• ask the experts!– collect written forecasts from multiple “experts”

• including justifications

– compile all (anonymous) and redistribute• repeat

– anonymity reduces undue influences– caveats

• groupthink still possible• or may not converge at all• watch wording of questions


Uses of Demand Forecasts

• Production planning– assembly line

• need for setting cycle time

– batch production• need for setting batch size

– EOQ formula

• when to add/close/upgrade production facilities• when to develop new products

– product life cycle


Homework 2, due next Tues. 5pm

• read Askin, pp.19‐35, 50‐56• HW (Askin unless otherwise specified).

Always show your work, including formulas used.• E.g. print Excel spread‐sheets 2x, once with values and once with formulas used in

your calculations, or turn in Matlab code• graph everything for forecasting, including plotting residuals to evaluate model

– 2.12

– 2.22 (“sketch” means on a graph, with quantities and labels on axes.)Plus: Assume that batch size was set using EOQ. If the annual holding cost for the

product is $8/unit, what must the setup cost have been?

– 3.5• do it twice, the 2nd time reversing the order of the data

– 3.8

Mechanical Engineering 101 - University of California,...

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