Supporting Slides

Systems for Planning & Control in Manufacturing

Produced by D K Harrison and D J Petty 21/04/02 Sld - 0000

XSupporting Slides

Professor David K HarrisonGlasgow Caledonian University

Dr David J PettyThe University of Manchester Institute of Science and Technology

Systems for Planning & Control in Manufacturing:Systems and Management for Competitive Manufacture

ISBN 0 7506 49771


Produced by D K Harrison and D J Petty 21/04/02 Sld -

• Qualitative Analysis

• Quantitative AnalysisManagement ScienceOperations Research

Overview 10

1001



The Quantitative Analysis Process

Implement Results

Define Problem Formulate a Clear and Unambiguous Statement of the Problem

Develop Model Models can take several forms

Acquire Data Accurate Input Data is Essential

Develop Solution Algebraic or Numerical Solution

Test Solution Validation

Analyse Results Implications

10

1002



• Basic Rules

1P(e)ni

1ii

1P(e)0 i

• Events

• Mutually Exclusive

• Collectively Exhaustive

ME CE

Draw a Card

Face and Number

King and 7

and , ,

Basic Probability - Definitions 10

and

7 and

Black and

1003



Basic Probability - Law of Addition - 1

• Take a Standard 52 Card Deck (No Jokers)

• Draw a Card and Write Down Result

• Replace Card

• Draw a Second Card and Write Down Result

• What are the Probabilities of Drawing:-a) A Heart or a Diamond?b) A Five or a Diamond? ? ?

10

1004



Adding MutuallyExclusive Events

A B

)P(e)P(e)eor P(e baba

)P()P()or P(

502

1

52

13

52

13.

5) and P()5P()P(5)or P(

0.308 52

16

52

1

52

4

52

13

A B

)e andP(e)P(e)P(e)eor P(e bababa Adding Non MutuallyExclusive Events

)e andP(e ba

Basic Probability - Law of Addition - 2 10

1005



• Marginal or Simple Probability

OutcomesofNumberTotal

EventforOutcomesofNumberP(e)

• Joint Probability Independent Events

)P(e)P(e)eP(e baba

a

b250

2

1

2

1.

502

1.

• Conditional Probability

Then

a

b

)P(e)eP(e aba

)P(e)eP(e bab

Basic Probability - Independence 10

1006



30 Blue10 Spot20 Plain

30 Red6 Spot

24 Plain

5060

30)P(eBlue .

5060

30)P(eRed .

)P(e

)eP(e)eP(e

b

baba Bayes Theorem

0.267 60

16)P(eSpot

0.733 60

44)P(ePlain

If a red ball is drawn, what is the probability that it will have a spot?

)P(e

)eP(e)eP(e

red

RedSpotRedSpot

0.1 60

6 )eP(e RedSpot 0.2

0.5

0.1)eP(e RedSpot

NOT Independent

Statistically Dependent Events 10

1007



H (0.5)

T (0.5)

TH (0.25)

TT (0.25)

HT (0.25)

HH (0.25)

HHT (0.125)

HTH (0.125)

HTT (0.125)

THH (0.125)

THT (0.125)

TTH (0.125)

TTT (0.125)

HHH (0.125)

H

T

H

H

H

H

H

H

H

T

H

T

H

T

H

T

H

T

H

T

H

T

H

T

T

T

T

T

T

T

HHHH (0.0625)

HHHT (0.0625)

HHTH (0.0625)

HHTT (0.0625)

HTHH (0.0625)

HTHT (0.0625)

HTTH (0.0625)

HTTT (0.0625)

THHH (0.0625)

THHT (0.0625)

THTH (0.0625)

THTT (0.0625)

TTHH (0.0625)

TTHT (0.0625)

TTTH (0.0625)

TTTT (0.0625)

0 1 2 3 4

1 4 6 4 1

0 1 2 3 4

Probability Trees 10

1008



Throwing Four Coins

0 1 2 3 4

0.1

0.2

0.3

Pro

bab

ility

P(x

)

Score x

Throwing a Die

0.1

0.05

0.15

0.2

1 2 3 4 5 6

Pro

bab

ility

P(x

)

Score x

Probability Distributions 10

1009



2M)(x

2

1-

e 2

2

1 f(x)

dx

2

1 )x,P(x

2M)(x

2

1-x

x

21 e 2

2

1

Normal Distribution

0

0.02

0.04

0.06

0.08

0.10 8 16 24 32 40 48 56 64 72 80 88 96

x

f(x) x1

x2

M

The Normal Distribution 10

1010



ni

1iix

n

1 (M)Mean

2ni

1ii M)(x

n

1 )(Deviation Standard

M)(xn

1 (MAD)Deviation AbsoluteMean i

ni

1i

Onlytribution Normal Dis MAD2

)F(xn

1 MAD ii

ni

1i

Statistical Formulae 10

1011



• To Provide Information

• To Anticipate Changes• Rationale

Short LongMedium

Forecasting - Overview 11

1101



• Judgement• Conference• Survey• Delphi

ExtrapolationIntuition Prediction

• Graphical• Moving Average• Exponential

Smoothing

• Regression• Multiple

Regression

Forecasting

Forecasting Approaches 11

1102



Intuitive Forecasting Approaches 11

• Judgment

• Conference

• Survey

• Delphi

The Opinion of One Person

The Collective Opinion of a group of People

Collecting the Independent Opinion of Several People

Combining the Conference and Survey Approaches

1103



Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

2001 105 100 106 105 100 108 107 106 113 109 113 112

114 118 116 115 114 117 116 122 120 122 121 125

DecNovOctSepAugJulJunMayAprMarFebJan

2002

Forecasting Exercise (1) 11

1104



90

95

100

105

110

115

120

125

130

Months (2001 - 2002)

Sales

Sales Best Fit

December 2002 Sales -

Forecasting Exercise (2) 11

125

1105



• MovingAverage

• Exponential Smoothing

ni

k)(nii)-(n1)(i x

n

1 F

Forecast for next period is the average of previous n data points

Advantage• Simple

Analytical Extrapolation 11

n = Number of data pointsk = Number of points used to averagexi = Data elementF(i+1) = Forecast for next period. = Smoothing factor

)F(xF F

FFx F

)F(1x F

iii1)(i

iii1)(i

ii1)(i

Forecast is a weighted average (most recent is most important) of all data points

Advantage• Logical• Only two data elements needed

1)(iF

ix

)F(x ii

iF

)F(x ii Move up by1106



Exponential Smoothing - 1

80859095

100105110115120125130

Months

Sales

Actual Forecast

20.

11

1107



80859095

100105110115120125130

Months

Sales

Actual Forecast

Trend

20.

Exponential Smoothing - 2 11

1108




80859095

100105110115120125130

Months

Sales

Actual Forecast

Seasonal

20.

11

1109



959799

101103105107109111113115

Months

Sales

Actual Forecast


Combined

20.

11

1110



1)(iF

ix

)F(x ii

iF

CEqTF F

B EqF)(FTT

A Eq)F(xF F

1)(i1)(i1)(i

1)(ii1)(i

iii1)(i

)F(xF F iii1)(i

• Second Order Smoothing Correction “Anticipates” Changes in the Data.

• Also Called Trend Correction

)1(iF

iF

)F(F i1)(i

1)(iF

ix

1)-(ix

)1(iF

Trend Correction 11

1st Order Smoothing

2nd Order Smoothing

1111



Second Order Smoothing - 1 11

80859095

100105110115120125130

Months

Sales

Actual Forecast Corrected

Random

Random

20

20

.

.

1112



80859095

100105110115120125130

Months

Sales


Trend

20

20

.

.

Second Order Smoothing - 2

Trend

11

1113



80859095

100105110115120125130

Months

Sales



20

20

.

.

Seasonal

11

1114



959799

101103105107109111113115

Months

Sales


Combined


Combined

20

20

.

.

11

1115



0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10

Car Sales X 1,000,000

DB

P S

ales

x 1

,000

,000

in F

ive

Yea

rs

????0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

Attendance

Mo

du

le M

ark

Regression Analysis - 1 11

Aftermarket Disc Brake Pads Sales + 5 Yrs vs Car Sales Now

Student Attendance vsStudent Marks

• Is There a Correlation Between Students Marks and Attendance?

• Is There a Correlation Between Car Sales Now and Demand for DBPs in 5 Years?

1116



x

y

(x1, y1)

(x2, y2)

(x3, y3)

(x4, y4)

(d1)

(d2)

(d3)(d4)

y=a+bx

• What Line Will Minimise Total Distance?

BEqxbya

2AEqxxn

yxxynb

1AEq

xxn

yxyxn

b

22

2ni

1ii

ni

1i

2i

ni

1i

ni

1iii

ni

1iii

ni

1ii

ni

1ii

yn

1y

xn

1x

Regression Analysis - 2 11

a

1117



454.0b

(22.18)4)4.18(28

15.79)(22.18-12.91)(28b

2AEqxxn

yxxynb

2

22

0.204a

28

22181.07

28

1579a

xbya

Person x y xy x*xA 0.35 0.38 0.13 0.12B 0.44 0.31 0.14 0.19C 0.53 0.55 0.29 0.28D 0.54 0.36 0.20 0.30E 0.61 0.74 0.45 0.37F 0.66 0.38 0.25 0.44G 0.67 0.43 0.29 0.45H 0.70 0.65 0.46 0.49I 0.71 0.32 0.23 0.51J 0.73 0.60 0.44 0.53K 0.75 0.56 0.42 0.57L 0.79 0.57 0.45 0.63M 0.79 0.57 0.45 0.63N 0.82 0.61 0.50 0.67O 0.83 0.56 0.46 0.69P 0.83 0.62 0.52 0.69Q 0.83 0.60 0.50 0.69R 0.88 0.62 0.55 0.78S 0.89 0.51 0.46 0.80T 0.91 0.53 0.48 0.83U 0.95 0.65 0.62 0.90V 0.97 0.48 0.47 0.95W 0.97 0.66 0.65 0.95X 1.00 0.75 0.75 1.00Y 1.00 0.75 0.75 1.00Z 1.00 0.64 0.64 1.00A1 1.00 0.62 0.62 1.00B1 1.00 0.73 0.73 1.00

28 22.18 15.79 12.91 18.44

Marks Vs Attendance

0.000.100.200.300.400.500.600.700.80

0.00 0.20 0.40 0.60 0.80 1.00

Attendance

Mo

du

le M

ark

Regression Analysis – 3 11

1118



Use of Regression Analysis

• Inside the company

• Inside the Industry

• Outside the Industry

11

1119



2222 yynxxn

yxxynr

Perfect Positiver =+1

Positive Correlation0 < r < 1

Perfect Negativer =-1

Negative Correlation0 > r > -1

No Correlation

Correlation Coefficients 11

1120



Multiple Regression Analysis 11

New

Mar

k

Attendance

Old Mark

Multiple Regressiony=a+b1x1+b2x2

1121



• Reduce Lead Time

• Aggregate Forecast

CEqx

σ

x

σ

BEqσσ

AEqxx

ni

1i i

i

a

a

ni

1i

2i

2a

ni

1iia

Improving Forecast Accuracy - 1 11

1122



Improving Forecast Accuracy - 2 11

0

10

20

30

40

50

M S M S

Months

Sales

Product 1 Product 2 Product 3

Product 4 Total Norm. Total

1123



• Essential for all Businesses

• Three Approaches

• Uncertainty is Inherent

• Uncertainty Must be Anticipated

• Forecast Accuracy can be Improved

If We Make this Man Accountable for the Weather, Will it make the Sun Shine?

Forecasting Summary 11

1124



The most favourable conditions; the best compromise between opposing tendencies;

the best or most favourable.

• Objective Functions

• Basic Optimisation

• Linear Programming

• Sensitivity Analysis

Optimisation 12

1201



• Different Objectives e.g.: Profit Cashflow Sales

• Strategic and Judgmental

• Basis for Optimisation

Objective Functions 12

1202



1.05- 6.38, RootsQuadratic

32

20341616RootsQuadratic

AEq2

4

02016x3x(x)f

520x8xxf(x)

2

2

2

2

23

a

acbbRootsQuadratic

cbxaxyFor

0.00

50.00

100.00

150.00

200.00

250.00

0 2 4 6 8 10 12

x

f(x

)

6.38

Simple Optimisation (1) 12

1203



0.000

2.000

4.000

6.000

8.000

10.000

12.000

0 2 4 6 8 10 12

x

f(x

)

1x-5

10f(x) 2

8.008.208.408.608.809.009.209.409.609.80

10.00

4.50 4.70 4.90 5.10 5.30 5.50

x

f(x

)

9.97

9.98

9.98

9.99

9.99

10.00

10.00

4.95 4.97 4.99 5.01 5.03 5.05

x

f(x

)

Simple Optimisation (2) 12

Low Resolution

Medium Resolution

High Resolution

1204



0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.0

00.00

2.50

5.00

7.50

10.00

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

f(x,y)

x

y

(7.1, 6.7)

20y20y2y20x20x2xy)f(x, 2323

Optimisation - 2 Variables 12

1205



Linear Programming (1)

• Linear Objective Function

• A Set of Linear Constraints

• Non-Negativity

12

1206



75 )60(1.25150X

600.667

160200Y

1602000.667Y

0.667Y200160

Y1.667Y200160

Y1.25Y-1501.34160

1.25Y-150X

1.25YX150

Y1.34X 160

Optimum

Point

10 20 30 40 50 60 70 80 90 100 110 120130 140 150

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

X

1. Power Limitation:160 = 1.34X + Y

Power

160

160

Linear Programming (2) 12

112 = 1.6X + 1. 4Y

Objective Function - Sales

3. Objective Function:Sales = 1.6X + 1.4Y

Machining Capacity

2. Machining Capacity:150 = X + 1.25Y

1207



10 20 30 40 50 60 70 80 90 100 110 120130 140 150

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150



X

Y

Machining Capacity

Power

160

160


Lab Capacity

3. Labour Capacity:130 = X + Y

1208



10 20 30 40 50 60 70 80 90 100 110 120130 140 150

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

X

Y160

160



3. Labour Capacity:130 = X + Y


224 = 1.6X + 1. 4Y

196 = 1.6X + 1. 4YObjective Function:Sales = 1.6X + 1.4Y

Optimum Point

Optimum: X= 50, Y = 80

1209


Produced by D K Harrison and D J Petty 21/04/02 Sld - X

YZ

Y Material

X Material

Z Material

Total Capacity

Objective Function

Multiple Variables 12

1210



• Problems So Far Assume Perfect Information

• Sensitivity Analysis Determines Criticality of Base Data

5.95

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

0 2 4 6 8 10 12

x

f(x

)

6.38

520.1x8.1xx11g(x)

520x8xxf(x)

23

23

.f(x)g(x)

Sensitivity Analysis - 1 12

1211



SalesCost

Profit

Different Variables May Have Different Effects

Sensitivity Analysis - 2 12

Costs = £1000K

100%Sales

ProfitSalesROS

Sensitivity - Effect of Sales Volume

-40%

-30%

-20%

-10%

0%

10%

20%

30%

750 800 850 900 950 1000 1050 1100 1150 1200 1250

Sales (£K)

Ret

urm

of

Sal

es (

%)

1212



EOQ Model

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Lot Size

To

tal

Co

st

is

s

psspr CL2

1

L

TLTCDCost

Sensitivity Analysis – 3

i

spr

C

TC2DEOQ

12

1213



Sensitivity Analysis – 4

• Test the Sensitivity of the Model Itself

• Test the Sensitivity of the Model to Input Variables

• Can be Used for a Variety of Problems

12

1214



• Optimisation Requires an Objective Function

• Analytical or Numerical Methods Can be Used

• Sensitivity Analysis Checks the Robustness of any ModelConstantsParameters

• Optimisation Supports, not Replaces Management

Summary 12

1215



Course Book

Systems for Planning & Control in Manufacturing:

Systems and Management for Competitive Manufacture

Professor David K HarrisonDr David J Petty

ISBN 0 7506 49771

X

0000

Supporting Slides

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