# Project Network Analysis CPM/PERT - PowerPoint

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```							   Delay in project implementation invariably
results in cost- overrun.

   Delayed project implementation means delay
in getting return on investments made.

2
   Resources cost more

   Any activity two time estimates are made
◦ Normal time
◦ Crash time

3
   In many projects the estimated project duration
may exceed the target duration hence critical
path is reduced so as to complete the project by
target date

Requirement of
◦ More workers
◦ Better equipments
◦ Overtime
These involve direct costs (cost of material , labor,
equipment). Reduces with time
and
indirect costs (overhead costs associated with the project
insurance and maintenance. Increases with time

4
   Project managers may have the option or
requirement to crash the project, or accelerate
the completion of the project.
   This is accomplished by reducing the length of
the critical path's).
   The length of the critical path is reduced by
reducing the duration of the activities on the
critical path.
   Process of shortening a project by using
extra resources
   Project should be shortened up to When
savings in indirect costs = cost of
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   Crashing
◦ reducing project time by expending additional
resources
   Crash time
◦ an amount of time an activity is reduced
   Crash cost
◦ cost of reducing activity time
   Goal
◦ reduce project duration at minimum cost

6
Crash
cost
A Crashing activity

Slope = crash cost per unit time
B
Normal Activity
Normal
cost
Normal
time
Crash                            Activity time
time
7
   If each activity requires the expenditure of an amount of
money to reduce its duration by one unit of time, then the
project manager selects the least cost critical activity,
reduces it by one time unit, and traces that change
through the remainder of the network.

   As a result of a reduction in an activity’s time, a new
critical path may be created.

   When there is more than one critical path, each of the
critical paths must be reduced.

   If the length of the project needs to be reduced further,
the process is repeated.

8
   Direct costs is the cost of materials,
equipment and direct labor (payroll,
overtime, hiring and firing costs) required
in performing an activity
   Indirect costs incurred include costs of
facilities, equipment, machinery, interest on
investment, utilities, labor and personal
costs, late completion penalties

9
   Resource levelling
   Resource allocation

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 Crashing costs increase as project duration decreases
 Indirect costs increase as project duration increases
 Reduce project length as long as crashing costs are less than
indirect costs
Min total cost =      Total project cost
optimal project
Indirect
time
cost

Direct cost

time
11
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Activity      Immediate   Normal       Crash        Normal   Crash Cost
Predecessor Time(days)   Time(Days)   Cost     (Rs.)
P             -                 8      6            6000     9000
Q             -                 12     8            15000    25000
R             -                 4      2            3000     6000
S             P                 10     6            15000    25000
T             R                 4      4            10000    10000
U             P                 14     10           11500    17500
V             S,Q,T             8      4            10000    24000

     Draw an arrow diagram
     Determine the project duration which will
result in minimum total direct cost
     If indirect costs are Rs. 4000 per day then
determine the optimum duration of the
project
 (q4-2008)

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Activity             Normal        Crash Time    Normal         Crash Cost
Time (Days)   (Days)        Cost(Rs)       (Rs)
A       1-2          3             2             8000           10000
B        1-3         3             2             4000           7000
C       2-5          1             1             4000           4000
D       2-6          6             4             40000          60000
E       3-4          2             1             4000           6400
Dummy 4-5 -                        -             -              -
F       4-6          5             3             30000          38000
G       5-6          7             6             24000          30000
H       6-7          4             3             32000          39000

   Draw the network and find the critical path and normal
project duration
   What is minimum length of the project and corresponding
costs when all the critical activities are crashed to the
maximum extent
   If indirect costs is Rs 6000 per day then what is the project –
cost trade off point of the project
   Q4-2007
15
   The following table provides normal and crash
times as well as normal and crash costs for
the activities of a project. (2006)

Activity   Normal    Normal    Crash     Crash
Time      cost      Time      Cost
(weeks)   (Lakhs)   (Weeks)   (Lakhs)
1-2        3         5         1         9
2-3        4         8         3         14
2-4        3         4         2         6
2-5        8         5         7         6
3-6        4         3         2         5
4-6        6         2         4         3
5-7        5         10        4         14
6-7        3         7         1         10

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Normal Time Normal Cost   Crash Time   Crash Cost
Activity     (Days)       (Rs)         (Days)        (Rs)
1-2          6          600            4          1000
1-3          4          600            2          2000
2-4          5          500            3          1500
2-5          3          450            1           650
3-4          6          900            4          2000
4-6          8          800            4          3000
5-6          4          400            2          1000
6-7          3          450            2           800

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   Useful at many stages of project management
   Mathematically simple
   Give critical path and slack time
   Provide project documentation
   Useful in monitoring costs

CPM/PERT can answer the following important
questions:
•How long will the entire project take to be completed? What are the
risks involved?
•Which are the critical activities or tasks in the project which could
delay the entire project if they were not completed on time?
•Is the project on schedule, behind schedule or ahead of schedule?
•If the project has to be finished earlier than planned, what is the best
way to do this at the least cost?
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   Clearly defined, independent and stable activities
   Specified precedence relationships
   Over emphasis on critical paths
   Deterministic CPM model
   Activity time estimates are subjective and depend on
judgment
   PERT assumes a beta distribution for these time
estimates, but the actual distribution may be different
   PERT consistently underestimates the expected project
completion time due to alternate paths becoming critical

To overcome the limitation, Monte Carlo simulations can be
performed on the network to eliminate the optimistic bias

19
 Men , Material, Money are three resources
required for any activity.
 If shortage of resources the activity cannot
be completed in time
 Project mgr has to come across resource
constraints
Hence the job of project mgr is to plan and
allocate resources for different activities so
that resource utilization is optimized.

20
   Resource Leveling – analysis aims at
stabilization of rate of resource utilization
by various activities at different times
without changing the project duration

aims to reduce peak demand for resources
and reallocating among activities of a
project in a manner so that the total
project duration remains shortest

21
Activity   Preceding   Duration (Days)   Total Manpower
Activity                      required
A          -           3                 60
B          -           4                 84
C          A           2                 22
D          A           3                 36
E          B           6                 72
F          D,E         3                 18
G          C           5                 35
H          F           6                 42
I          G,H         7                 56

22
Activity   Immediate     Duration (Days) Total cash flow
Predecessor                   required for the
activity (Rs.
Lakhs)
A          -             5               25
B          -             5               30
C          A             10              40
D          B             7               28
E          A             6               12
F          C,D           8               24
G          C,D           6               15
H          E,F           5               10
I          G             4               12

23

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