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
Evaluating Alternatives
13

• Decision Trees and Risk
• Expected Monetary Value
• Value of Perfect Information
• Uncertainty
• Time Value of Money

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Example
13
1. Define the Problem. A student is considering
moving out of rented accommodation and taking on
a mortgage. 2. List the Possible Alternatives.
The alternatives are- Buy a house. Buy a
flat. Remain in rented accommodation. 3.
Identify the Possible Outcomes. Conditions could
be favourable or otherwise. 4. List the Benefits
in Numerical Terms Favourable Unfavourable Hou
se 10,000 -2,000 Flat 6,000 -1,000 Rent
0 0 5/6. Select a Mathematical Decision
Making Model and Apply.

• Do not ignore any alternatives, including doing
  nothing.

• Do not ignore possible outcomes (positive or
  negative). Outcomes over which you have no
  control are called states of nature.

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Decision Making Situations
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• Decision Making Under Certainty
• Decision Making Under Uncertainty
• Decision Making Under Risk

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Decision Trees and Risk
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10,000
7,500
State of Nature Node
Favourable (0.75)
Decision Node
Unfavourable (0.25)
-2,000
-500
Buy a House
6,000
4,500
Favourable (0.75)
Buy a Flat
Unfavourable (0.25)
-1,000
-250
Do Nothing
0
-0
EMV Expected Monetary Value

• Multi-Stage Decisions Can be Analysed

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Value of Perfect Information
13
Should the Student Take Professional Advice?
This is the Value Where Bad Decisions Have Been
Avoided.
This is the Value that Would be Obtained Under
Conditions of Risk.
This is the Most that the Advice would be Worth -
An Offer of Advice at 1000 should be declined.
EVOPI Expected Value of Perfect Information,
EVWPI Expected Value with Perfect Information.
How Would You Make the Decision?
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Uncertainty
13
House
Flat
Do Nothing

• Maximax (Optimistic) - House

• Maximin (Pessimistic) - Nothing

• Equally Likely (Balanced) - House

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Decision Making Example Question
13
Two sisters plan to go to a party. A lift is
available to get to the party, but there is no
guarantee this will be available for the return
journey. It may be necessary to use a taxi
therefore, and this will cost 7.50. Taking the
car will cost 2.00.

• Produce a decision table for this case
• What is the best decision based on the Maximax,
  Maximin and Equally Likely criteria?
• The probability of obtaining a lift is 0.4. Draw
  a decision tree for this case
• Should the sisters take the car based on the
  probability information given?

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Decision Making Example Answer
13
States of Nature
No Lift
Row Max
Row Min
Row Average
Alternatives
Lift
-2.00
-2.00
-2.00
-2.00
-2.00
Take Car
Leave Car
0.00
-7.50
0.00
-7.50
-3.75
Maximax Leave Car Maximin Take Car Equally
Likely Take Car
-0.00
Lift (0.4)
-7.50
Leave Car
No Lift (0.6)
Take Car
But are There Any Other Factors?
-2.00
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Summary
13

• Evaluating Alternatives is a Common Management
  Task
• There are Three Conditions for Evaluating
  Alternatives
• Decision Making Under Certainty
• Decision Making Under Uncertainty
• Decision Making Under Risk
• Analytical Approaches Can Support Decision Making
• Ultimately, Decisions Must be Taken by Managers

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Overview
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• Definition The Imitation of a Real World System
• Examples Flow of People Through an Airport
• Nuclear War
• Traffic Flow in a Large City
• Behaviour of a Suspension System
• World Economy
• Temperature/Stress in a Piston
• Forces in a Metal Cutting Process
• Queues within a Manufacturing System

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Reasons for Simulation
14

• Practicality
• Safety
• What-if Analysis
• Understanding

Large Systems Extreme of Systems Cost Time Repea
tability Visualisation (VR) Verification of
Analytical Solutions
Simulation is Becoming an Increasingly Common
Engineering Technique
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Terminology
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Simulation Methodology
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Step 1. Build Conceptual Model
Step 2. Covert the Conceptual Model
Inputs (Procedures)
Outputs (Responses)
Step 3. Verify the Model
Step 4. Model Experimentation
Experimentation
Step 5. Draw Conclusions
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Hierarchy of Simulation Techniques
14
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Continuous Simulation
14
x
Linear Second Order Differential Equation
k (N/m)
c (Ns/m)
Analytical Solution
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Kinematic Simulation
14
1407
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Static Simulation
14
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Simple Example
14
1409
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Simple Example - 10 Coins
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1410
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Probability Distribution Function
14
PDF
CDF
Discrete Distribution
ContinuousDistribution
Mapping Random Number to PDF
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PDF/CDF Example (1)
13
1412
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Random Numbers
13
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PDF/CDF Example (2)
13
0.785
0.744
0.119
5.78
2.65
5.55
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PDF/CDF Example (3)
13
An Accurate Picture Takes Many Iterations This
is Called Warm-Up
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Dynamic Discrete Event Simulation
13

• Behaviour of a System Over Time
• Concerned with Discrete Variables
• Applied in a Variety of Fields
• Useful for Examining Material Flow
• Two forms Deterministic and Stochastic
• Originally Used Standard Languages (Fortran,
  Pascal)
• Specialised Systems Now Exist (HOCUS, ProModel)

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Dynamic Simulation - Example 1
13
Time Period
Q
Event(s)
Initial Queue 15
10 Every 5 Hours Starting 5th Hr
Queue (Q)
Process
Output
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Dynamic Simulation - Example - 2
14
Initial Queue 15
10 Every 5 Hours Starting 5th Hr
Queue (Q)
7 Every 3 Hours (Max) Starting 2nd Hr
Process
Output
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Simulation Method - Time Slicing
14
ti
t0
Time is incremented by t
Statistics
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Simulation Method Advanced
14
t0
Next ti
Future Event List
Statistics
Update ti
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Stochastic Simulation
14

• Stochastic Processes are Uncertain
• Many Processes are Stochastic
• Stochastic Variation can be Modelled
• General Conclusions
• CDFs Model Stochastic Variation

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Example - Waiting Line Model
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1422
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Simulation Limitations
14

• Simulations Themselves Can be Costly
• Base Data can be Difficult to Collect
• Simulations are Not Reality
• A False Sense of Security

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Simulation - Summary
14

• It Uses Models of Real-World Situations
• It Can be Applied to Many Different Problems
• It is a Powerful Tool
• Standard Packages are Now Available

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Project Management
15

• Common Activity for Engineers
• Essential for Any Complex Task
• Allows Tasks to be Divided
• Allows Progress Monitoring
• Provides a Critical Path
• Formal Methods Available
• Techniques and Good Practice

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Activities and Events
04
Event
Event
Activity
Building Site
Completed Frame
Construct Frame
Activity
Activity on Node (AON)
AON
Event
Event
Event
Event
Activity on Arrow (AOA)
AOA
Activity
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Modelling Projects Example (1)
04

1. Boil Water
2. Locate Coffee
3. Locate Sugar
4. Locate Milk
5. Add Coffee and Sugar
6. Add Boiling Water
7. Add Milk
8. Serve Coffee
9. Drink Coffee

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Modelling Projects Example (2)
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Locate Milk
4
Add Milk
Drink Coffee

• Activity Precedence is Critical

Boil Water
6
7
8
9
1
Add Boiling Water
Serve Coffee
AON
Locate Coffee
2
5
Add Coffee And Sugar
Locate Sugar
3
Add Milk
Serve Coffee
Drink Coffee
Locate Milk
6
5
7
8
1
Boil Water
Add Boiling Water
4
Locate Coffee
2
Dummy Activity
Add Coffee And Sugar
Locate Sugar
AOA
3
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Modelling Projects Example (3)
15
Locate Milk
4
7
Add Milk
Drink Coffee

• Activity Precedence is Critical

Boil Water
6
1
8
9
Add Boiling Water
Serve Coffee
AON
Locate Coffee
2
5
Add Coffee And Sugar
Locate Sugar
Note Change in Diagrams
3
Add Milk
Serve Coffee
Drink Coffee
Locate Milk
6
8
5
7
1
Boil Water
Add Boiling Water
4
Locate Coffee
2
Dummy Activity
Add Coffee And Sugar
Locate Sugar
AOA
3
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Modelling Projects Example (4)
15

• CPM AON
• PERT AOA
• AOA Easy to Visualise
• AOA Needs Dummy Activities
• Infinite Resources Assumed

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AON Diagram (MS Project Format)
15
Locate Milk
60 secs
4
60
0
Boil Water
Add Boiling Water
Add Milk
Serve Coffee
Drink Coffee
540 Secs
1
300 secs
6
15 Secs
7
15 Secs
8
120 Secs
9
990
0
300
301
315
316
330
331
450
451
Add Coff. Sug.
Locate Coffee
2
60 Secs
5
15 Secs
60
61
0
75
Locate Sugar
Activity Name
3
60 Secs
0
60
Activity Number
Duration
Earliest Finish Time
Earliest Start Time
Note MS Project Does Not Handle Seconds
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Use of a Gantt Chart
15
Time (in Seconds)
200
400
600
800
100
300
500
700
900
Locate Milk
Locate Coffee
Locate Sugar
Boil Water
Add Coffee Sugar
Add Boiling Wat.
Add Milk
Serve Coffee
Drink Coffee
Critical Path
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Activity Scheduling - Definitions
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• Critical Path Longest Path Through a Network
• Critical Activity Activity on the Critical Path
• Slack Length of Time Available Before an
  Activity Needs to Start
• ESD Earliest Date that an Activity Could Start
• EFD - Earliest Date that an Activity Could Finish
• LSD Latest Date that an Activity Could Start
  Without Extending Project
• LFD Latest Date that an Activity Could Finish
  Without Extending Project

ESD LSD, EFD LFD, Slack 0 for Critical
Activities
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Activity Scheduling Principles
15
Forward Pass
Backward Pass

• ESD LSD, EFD LFD, Slack 0 for Critical
  Activities
• ESD for an Activity is the Largest EFD of
  Immediate Predecessors
• LFD for an Activity is the Smallest LSD of
  Immediate Successors

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Activity Scheduling Standard Form
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• Boil Water
• Locate Coffee
• Locate Sugar
• Locate Milk
• Add Coffee and Sugar
• Add Boiling Water
• Add Milk
• Serve Coffee
• Drink Coffee

D
Activity
60
Duration
A
300
S
I
H
G
F
E
B
F
540
120
15
15
15
60
C
Imm. Pred.
60
Activity
ESD
LSD
EFD
LFD
Crit.
Slack
Dur.
A
300
B
60
C
60

• Note the Slight Difference to MS Project
• Slack Cannot be Used Twice in All Cases

D
60
E
B, C
15
A, E
F
15
G
D, F
15
H
G
120
H
I
540
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Activity Scheduling Logic Summary
15
Greater of Two EFDs
0
20
30
40
A
E
20
0
20
10
40
50
20
30
C
F
10
20
30
0
10
30
50
B
E
10
10
20
20
30
50
Greater of Two EFDs
Smaller of Two LSDs
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Stochastic Activity Times
15

• Activity Times Generally Stochastic
• This Implies Project Times are Stochastic
• What are the Chances of Success?
• Need to Use Probability Distributions
• Traditional to Use a Beta Distribution
• Only Provides an Estimate

Where- a Pessimistic Estimate b Optimistic
Estimate m Most Probable Time t Expected
Time Sigma Standard Dev.
P(x)
m,t
m
m
t
t
P(x)
P(x)
a
a
b
b
b
a
x
x
x
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Project Uncertainty Example - 1
15
What are the Chances of this Project Being
Completed in Less than 17 Minutes (1020 Seconds)?
D
0
60
60
255
315
Slack 255
A
0
300
300
0
300
S
I
H
G
F
E
B
450
990
330
450
315
330
300
315
60
75
0
60
F
540
120
15
15
15
60
450
990
330
450
315
330
300
315
285
300
225
285
Slack 225
Slack 225
C
0
60
60
225
285
Slack 225
Project Deadline 1020 Project Time
990 Project Slack 30 Slack as
30 42 0.715
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Normal Distributions
15
x1
x2
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Project Uncertainty Example - 2
15
By Linear Interpolation
y
(x2, y2)
More Accurate Tables for Standard Deviation Yield
a Probability of 0.7625
(xv, yv)
(x1, y1)
x
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Project Uncertainty Review
15
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
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Limitations of the Method
15

• Distributions May Not be Appropriate
• Non-Critical Paths May be Significant
• Tasks May not be Independent
• Summation of Variances May not be Appropriate
• Assumptions in Calculations Must be Taken into
  Account
• Still a Useful Technique

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Use of Project Planning Packages
15

• Now Very Common (e.g., MS Project)
• Minimises Manual Effort
• Improves Reporting Quality
• Can Provide Multi-User Access
• Can Encourage Over-Planning
• Large Benefits for Complex Projects

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Good Project Planning Practice
15

• Good Planning is Usually Rewarded
• Lack of Planning is Usually Punished
• Uncertain Situations Still Need Plans
• Avoid Over Simplification
• Avoid Over Complication
• Do Not Allow Plans to Inhibit Action

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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