07/09/2011
A.AMRANI-ZOUGGAR IMS-Lab, University Bordeaux1
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These products Î specific management
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What leads the industrialist to start projects? BENEFITS
Ageing of the range Benchmarking, comparing the market and industrial evolution
A i l off a new llow Arrival cost competitor
Appearance of a new technology Ex: AMOLED screen Î Leads the company to develop new project
Risk of threat for the company Î necessity to design new projects 3 3
Project Activity Non repetitive Irreversibles Decisions
Production Activity Repetitive Periodic Decisions
Strong uncertainty
Weak uncertainty
Strong influence of external variables
Strong Influence of internal variables
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Staff
Turnover
g Management Hardware
g change
unavailability
Requirements Size
change
underestimated
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Projects don’t often reach their objectives :
No respect of lead time
Important over costs
Product technical quality insufficient
Projects are running in a complex environment :
Various actors in enterprises: engineering, production, marketing, having different objectives and different measures
External environment difficult to master: market, policy,
Competition
Î NEED TO SPECIFC METHODS AND TOOLS 6
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PERT method 1. How to draw PERT network? Kind
of constraints
Concepts Steps
to follow calculation
margins
Total margin Free margin
2. Advanced PERT Probabilistic PERT PERT costs
How to draw PERT networks? Kind of constraints Execution of a p project, j , often,, requires q succession of tasks linking g by some constraints. - Constraints of time: Leadtime to respect in performing the task (taking account the time of using resources) - Constraints of anteriority: Some tasks must be executed befor others - Constraints of simultaneity: Some tasks are performed in the same time Î PERT (Program Evaluation and Review Technique) charts represents the project schedule as an activity network.
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How to draw PERT networks? Concepts - Task of project is represented by node - Duration of task is represented by an arc (branch) - Start node and Finish node are also represented For each activity, these values are estimated ES – Earliest start time EF – Earliest finish time LS – Latest start time LF – Latest finish time The ‘length’ of each path has to be calculated The LONGEST path in the project is the CRITICAL PATH
How to draw PERT networks? Steps to follow To draw PERT, 6 Big steps are required 1. Establish a list of tasks
2. Determine anteriority conditions 3. Draw PERT network 4 Calculate the earliest and latest dates 4. 5. Calculation of margins 6.Found the critical path of the project
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How to draw PERT networks? Steps to follow 1. Establish a list of tasks Enounce a list of tasks to perform Assess the durations of tasks (processing times) to determine the required resources Assign a codification to tasks to make easier the construction of the network
How to draw PERT networks? 1. Establish a list of tasks Exemple : The building of storage warehouse Tasks
Duration (t.u)
A
Study, realization and acceptance of plans
4
B
Preparation of the ground
2
C
Order materials (wood, bricks, cement, sheet for the roof)
1
D
Digging of the foundations
1
E
D Doors, Windows Wi d orders d
2
F
Delivery of materials
2
G
Casting of the foundations
2
H
Delivery of doors, windows
10
I
Construction of the walls, the roof
4
J
Installation doors and windows
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How to draw PERT networks? Steps to follow To draw PERT, 5 big steps are required 2. Determine anteriority conditions By answering these questions :
Which task must be ended before another could start ? Which task have to follow some tasks ?
How to draw PERT networks? 2. Determine anteriority conditions Previous tasks
Task
Following tasks
-
A
C,D,E
-
B
D
A
C
F
A,B
D
G
A
E
H
C
F
G
D,F
G
I
E
H
J
G
I
J
H,I
J
-
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How to draw PERT networks? Steps to follow 3. Draw PERT network Network is made of enounced tasks. Tasks are the node and arcs are constraints of precedence
E
4
Start
0
A
4
C
2
1
H F
10
2
G
10
2
4
I
J
1
End
4 0
B
2
D
1
How to draw PERT networks? 4. Calculate the earliest and latest dates
Task i
Earliest start date of task i: The earliest date on which task i could start taking account the required time to process previous tasks
ESi
ESi = max( ES j + p ji ) j∈ P(i)
Latest start date of task j: The latest date on which task i must absolutely start in order to not disturb and delay the overall project.
LSi
Task i
LS i = min ( LS j − pij ) j∈ F(i)
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How to draw PERT networks? 4. Calculation of ES and LS
4/4 E
4
0/0 Start
0
0/0 A
4/7 C
4
2
1
6/6 H 5/8 F
2
4 0
B 0/7
2
D 4/9
10
7/10 2 G
I 9/12
4
17/17 End
1
J 16/16
1
ESi: Forward computation
LSi: Backward computation
How to draw PERT networks? 5. Calculation of margins {
EEi
EEi
Total margin g
Allowed flexibility for task without changing project duration
M i = LS i − ESi ≥ 0 T
Free margin Allowed flexibility of task i without delaying following tasks {
M i = min( ES j − pij − ESi ) ≥ 0 F
Task i ESi
MT
LSi MT
Task i
ESj
EEi
Task j MF
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How to draw PERT networks? 6. Find a critical path 4/4 2 4 E 0/0 Start
0
0/0 A
4/7 C
4
1
6/6 H 5/8 F
2
10
7/10 2 G
4 0
B 0/7
2
D 4/9
I 9/12
1
Find the critical pathÎ each task whose MT=O Project duration (critical path) = 17 t.u Critical tasks are: A, E, H, J
1
4
J 16/16
17/17 End
TASK
MT
MF
A
0
0
B
7
2
C
3
0
D
5
2
E
0
0 0
F
3
G
3
0
H
0
0
I
3
3
J
0
0
P.E.R.T method 1. How to draw PERT network? Kind
of constraints Concepts Steps to follow margins calculation
Total margin Free margin
2. Advanced P.E.R.T Probabilistic PERT PERT costs
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Probabilistic PERT
Inside project appears some difficulties to get the exact durations of tasks
Probabilistic PERT considers the uncertainity about the dates and durations of tasks Uncertainity of durations ?
Necessity to taking account delay variation in margins computations
For each task, it is important to define to: Optimistic time, tr: realistic time (the most probabilistic) tp: pessemistic time
Probabilistic PERT An assessment of random duration of tasks often follows probability distribution of type β β distribution is characterized by these parameters:
Frequency of time existence
The mean m Variance V Standard deviation σ
to + 4tr + tp 6 2 ⎡ ( tp − to ) ⎤ V=
moyenne Mean = tm = ⎢ ⎣
6
⎥ ⎦
to tr
tm
tp Time
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Probabilistic PERT Objectives
Probabilistic PERT allows to determine the probability of fulfilling project in certain duration with variable task’s durations What
is the probability that project would be performed in x units of time?
Total duration of project is distributed according «normale distribution » gaussian curve, with a mean m equal to the sum of average durations of critical tasks
The variance of sum of random variables is equal to the sum of variables. It becomes possible to determine standard deviation of critical path.
σ=
n
∑σ i =1
2 i
Probabilistic PERT Notions: Gauss/normal distribution * Sets of data to collect: Weights, Heights * Number of results (pulling) according to a sample Î Study of the distribution Î Normal distribution if the found values are distributed around a mean μ with standard deviation sigma σ Î Noted N(μ, σ2)
Z P(X
