Supporting Slides

1
Supporting Slides
X
Systems for Planning Control in
Manufacturing Systems and Management for
Competitive Manufacture
Professor David K Harrison Glasgow Caledonian
University Dr David J Petty The University of
Manchester Institute of Science and Technology
ISBN 0 7506 49771
0000
2
Overview
10

• Qualitative Analysis
• Quantitative Analysis
• Management Science
• Operations Research

1001
3
The Quantitative Analysis Process
10
1002
4
Basic Probability - Definitions
10

• Basic Rules

Draw a Card
ME
CE

• Mutually Exclusive

Face and Number

• Events

King and 7

• Collectively Exhaustive

and , ,
1003
5
Basic Probability - Law of Addition - 1
10

• 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?

?
?
1004
6
Basic Probability - Law of Addition - 2
10
Adding Mutually Exclusive Events
A
B
Adding Non Mutually Exclusive Events
A
B
1005
7
Basic Probability - Independence
10

• Marginal or Simple Probability

• Joint Probability Independent Events

a
b
a

• Conditional Probability

Then
b
1006
8
Statistically Dependent Events
10
If a red ball is drawn, what is the probability
that it will have a spot?
30 Blue 10 Spot 20 Plain
30 Red 6 Spot 24 Plain
Bayes Theorem
NOT Independent
1007
9
Probability Trees
10
0
1
2
3
4
HHH (0.125)
H
HHHH (0.0625)
HH (0.25)
H
HHHT (0.0625)
T
H
HHT (0.125)
H
HHTH (0.0625)
H (0.5)
T
HHTT (0.0625)
T
H
HTH (0.125)
H
HTHH (0.0625)
H
HTHT (0.0625)
T
T
HTT (0.125)
H
HTTH (0.0625)
HT (0.25)
T
T
HTTT (0.0625)
THH (0.125)
H
THHH (0.0625)
TH (0.25)
H
T
THHT (0.0625)
H
THT (0.125)
H
THTH (0.0625)
0
1
2
3
4
T
T
THTT (0.0625)
T
TTH (0.125)
H
TTHH (0.0625)
T (0.5)
H
T
TTHT (0.0625)
T
TTT (0.125)
H
TTTH (0.0625)
TT (0.25)
T
T
TTTT (0.0625)
1
4
6
4
1
1008
10
Probability Distributions
10
Throwing Four Coins
Throwing a Die
0.2
0.15
0.3
Probability P(x)
0.1
Probability P(x)
0.2
0.1
0.05
0
1
2
3
4
1
2
3
4
5
6
Score x
Score x
1009
11
The Normal Distribution
10
M
x1
x2
1010
12
Statistical Formulae
10
1011
13
Forecasting - Overview
11

• To Provide Information
• To Anticipate Changes

• Rationale

Short
Long
Medium
1101
14
Forecasting Approaches
11
Forecasting
Extrapolation
Intuition
Prediction

• Judgement
• Conference
• Survey
• Delphi

• Graphical
• Moving Average
• Exponential Smoothing

• Regression
• Multiple Regression

1102
15
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
16
Forecasting Exercise (1)
11
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
105
100
106
105
100
108
107
106
113
109
113
112
2001
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
Jan
114
118
116
115
114
117
116
122
120
122
121
125
2002
1104
17
Forecasting Exercise (2)
11
1105
18
Analytical Extrapolation
11

• Moving
• Average
• Exponential Smoothing

Forecast for next period is the average of
previous n data points
n Number of data points k Number of points
used to average xi Data element F(i1)
Forecast for next period. ? Smoothing factor

• Advantage
• Simple

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

• Advantage
• Logical
• Only two data elements needed

Move up by
1106
19
Exponential Smoothing - 1
11
1107
20
Exponential Smoothing - 2
11
Trend
1108
21
Exponential Smoothing - 3
11
Seasonal
1109
22
Exponential Smoothing - 4
11
Combined
1110
23
Trend Correction
11
1st Order Smoothing 2nd Order Smoothing

• Second Order Smoothing Correction Anticipates
  Changes in the Data.
• Also Called Trend Correction

1111
24
Second Order Smoothing - 1
11
Random
Random
1112
25
Second Order Smoothing - 2
11
Trend
Trend
1113
26
Second Order Smoothing - 3
11
Seasonal
1114
27
Second Order Smoothing - 4
11
Combined
Combined
1115
28
Regression Analysis - 1
11
Aftermarket Disc Brake Pads Sales 5 Yrs vs Car
Sales Now
Student Attendance vs Student 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
29
Regression Analysis - 2
11
y

• What Line Will Minimise Total Distance?

(x3, y3)
(d4)
(d3)
(x4, y4)
yabx
(d2)
(x1, y1)
(x2, y2)
(d1)
a
x
1117
30
Regression Analysis 3
11
1118
31
Use of Regression Analysis
11

• Inside the company
• Inside the Industry
• Outside the Industry

1119
32
Correlation Coefficients
11
Positive Correlation 0 lt r lt 1
Perfect Positive r 1
Perfect Negative r -1
Negative Correlation 0 gt r gt -1
1120
33
Multiple Regression Analysis
11
Multiple Regression yab1x1b2x2
New Mark
Attendance
Old Mark
1121
34
Improving Forecast Accuracy - 1
11

• Reduce Lead Time
• Aggregate Forecast

1122
35
Improving Forecast Accuracy - 2
11
1123
36
Forecasting Summary
11

• 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?
1124
37
Optimisation
12
The most favourable conditions the best
compromise between opposing tendencies the best
or most favourable.

• Objective Functions
• Basic Optimisation
• Linear Programming
• Sensitivity Analysis

1201
38
Objective Functions
12

• Different Objectives e.g. Profit
• Cashflow
• Sales
• Strategic and Judgmental
• Basis for Optimisation

1202
39
Simple Optimisation (1)
12
6.38
1203
40
Simple Optimisation (2)
12
Medium Resolution
Low Resolution
High Resolution
1204
41
Optimisation - 2 Variables
12
1205
42
Linear Programming (1)
12

• Linear Objective Function
• A Set of Linear Constraints
• Non-Negativity

1206
43
Linear Programming (2)
12
160
Optimum Point
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
X
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
1207
44
Linear Programming (3)
12
Y
160
150
140
Power
130
120
110
1. Power Limitation 160 1.34X Y 2.
Machining Capacity 150 X 1.25Y
100
90
80
70
60
50
40
30
Machining Capacity
20
10
X
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
1208
45
Linear Programming (4)
12
Y
160
150
140
130
1. Power Limitation 160 1.34X Y 2.
Machining Capacity 150 X 1.25Y 3. Labour
Capacity 130 X Y
120
110
100
90
80
70
60
50
40
30
20
10
X
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
1209
46
Multiple Variables
12
Y Material
Total Capacity
Y
Z
Objective Function
Z Material
X Material
X
1210
47
Sensitivity Analysis - 1
12

• Problems So Far Assume Perfect Information
• Sensitivity Analysis Determines Criticality of
  Base Data

6.38
5.95
f(x) g(x)
1211
48
Sensitivity Analysis - 2
12
Profit
Different Variables May Have Different Effects
Sales
Cost
Costs 1000K
1212
49
Sensitivity Analysis 3
12
1213
50
Sensitivity Analysis 4
12

• Test the Sensitivity of the Model Itself
• Test the Sensitivity of the Model to Input
  Variables
• Can be Used for a Variety of Problems

1214
51
Summary
12

• Optimisation Requires an Objective Function
• Analytical or Numerical Methods Can be Used
• Sensitivity Analysis Checks the Robustness of any
  Model
• Constants
• Parameters
• Optimisation Supports, not Replaces Management

1215
52
Course Book
X
Systems for Planning Control in
Manufacturing Systems and Management for
Competitive Manufacture Professor David K
Harrison Dr David J Petty ISBN 0 7506 49771
0000