Slides by: Ms. Shree Jaswal
Introduction
developing the project schedule
Scheduling Charts
logic diagrams and network (AOA,AON)
critical path
calendar scheduling and time based network
management schedule reserve
PDM network,
PERT
CPM
Resource loading, resource leveling
allocating scarce resources to projects and several projects
Goldratt’s critical chain.
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Activity definition
Activity sequencing
Activity duration estimation
Schedule development
Schedule control
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Project Management Tools
Gantt Charts
Project Network Diagrams
Activity on the Node (AON), Activity on arrow (AOA)
Critical Path Analysis
Pert
Precedence Diagramming Method (PDM)
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Simplest and most commonly used scheduling
technique
The chart consists of horizontal scale divided into
time units-days, weeks or months and vertical
scale showing project work elements.
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Advantages:
Gives a clear pictorial model of the project.
Simplicity for the planner and the user.
Easy to construct & understand.
Is a means for assessing the status of individual work elements and the project as a whole.
It can be used as Expense Charts
1.for labor planning
2.resource allocation
3.budgeting
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Drawbacks:
It does not explicitly show interrelationships
among work elements.
Gantt charts are often maintained manually. This
is easy task in small projects, but is burdensome
and a disadvantage in large projects; it causes
apathy and results in charts becoming outdated.
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Activity Start time Duration
A 0 5
B 6 3
C 7 4
D 8 5
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0 6 12 18 24 30
Gantt charts
Time
Activitie
s
14 Chapter 4 Slides by: Ms. Shree Jaswal
Suppose C & D must start only after activity B is
completed.
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0 6 12 18 24 30
Gantt charts
Time
Activitie
s
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Gantt charts don’t explicitly show task
relationships
don’t show impact of delays or shifting
resources well
network models clearly show
interdependencies
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network of relationships
elements & relationships (sequence)
this is ACTIVITY-ON-NODE
can have ACTIVITY-ON-ARC
research
what’s
been done
research
what needs
doing pick
final
topic internet
research
write print
18 Chapter 4 Slides by: Ms. Shree Jaswal
Activity on node diagrams
A,6 B,9
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Activity on arc or arrow
2 1 3
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Activity Duration Immediate Predecessor
A 6 _
B 9 A
C 8 A
D 4 B,C
E 6 B,C
Duration is given in weeks
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AON diagram corresponding to data in prev table
Critical path A-B-E:21 weeks
Start A,6
B,9 D,4
C,8 E,6
Finish
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Activity on arc or arrow
Same example on AON network
1 2
A,12
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Activity Immediate Predecessors Duration
A _ 6
B A 9
C A 8
D B,C 4
E B 6
F D,E 6
Duration is in days
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1 2
25 Chapter 4 Slides by: Ms. Shree Jaswal
Activity Immediate Predecessors Duration
A _ 6
B A 9
C A 8
D B,C 4
E B 6
F D,E 6
Duration is in days
26 Chapter 4 Slides by: Ms. Shree Jaswal
1 2
4
3
27 Chapter 4 Slides by: Ms. Shree Jaswal
Activity Immediate Predecessors Duration
A _ 6
B A 9
C A 8
D B,C 4
E B 6
F D,E 6
Duration is in days
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1 2
4
3
5 5 6
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Activity Immediate Predecessors Duration
A _ 6
B A 9
C A 8
D B,C 4
E B 6
F D,E 6
Duration is in days
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1 2
4
3
5 6
7
31 Chapter 4 Slides by: Ms. Shree Jaswal
Activity Immediate Predecessors Duration
A _ 6
B A 9
C A 8
D B,C 4
E B 6
F D,E 6
Duration is in days
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3-5, 4-5, 7-8,6-8 are dummy activities
1 2
4
3
5 6
7
8 9
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Dummy activities are used in AOA diagrams in case a node has more than one immediate predecessor.
In previous example: Activity Immediate Predecessors Duration
D B,C 4
F D,E 6
To represent activities D & F we use dummy activities
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ACTIVITY PREDECESSOR IMMEDIATE PRED: REDUNDANT PRED:
A --
B A A
C A A
D A,B,C B,C A
E A,B,C,D D A,B,C
F A,B,C B,C A
REDUNDANT ACTIVITY
35 Chapter 4 Slides by: Ms. Shree Jaswal
It is only essential to know the immediate
predecessor of a node while constructing a
network.
All the predecessors except the immediate
predecessors of a node are redundant
predecessors( activities).
36 Chapter 4 Slides by: Ms. Shree Jaswal
AON n/ws
There are no dummy activities
They are simpler
They are easier to construct.
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AOA n/w’s
AOA method used just as often, probably because it was developed first and is better suited for PERT procedures
The PERT model places emphasis on events and in the AOA method events are specifically designated by nodes.
AOA diagrams use line segments to represent flow of work and time, it is easy to construct schedules that are similar in appearance to Gantt charts but incorporate advantage of networks
38 Chapter 4 Slides by: Ms. Shree Jaswal
Most software packages create AOA n/w’s
that look similar to Gantt charts.
In particular it is best to select one form of
technique., AON or AOA, and stick to it.
39 Chapter 4 Slides by: Ms. Shree Jaswal
The longest path from the origin node to the terminal
node
Gives the expected project duration (Te)
One project can have more than one CP
Shortening activities on CP (critical activities) will
help reduce the project duration
Shortening activities NOT on CP has no effect on
project duration
Delay in any activities on CP will result in delay of
project completion
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Start A,6
B,9 D,4
C,8 E,6
Finish
Critical path A-B-E:21 weeks
Activity,
duratio
n
predece
ssor
A,6 -
B,9 A
C,8 A
D,4 B,C
E,6 B,C
41 Chapter 4 Slides by: Ms. Shree Jaswal
Specifies when at the earliest the activities can be
performed.
ES & EF are computed by taking a FORWARD pass
through the network
When an activity has several predecessors, its ES is
the MAXIMUM of all EF of predecessors
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Latest allowable times that the activity can be started
and finished without delaying the completion of the
project.
LS & LF are computed by taking a REVERSE pass
through the network. LS for the last activity (Ts) is
taken same as the EF for that activity (Te); larger value
can be selected if project does not have to be
completed by EF.
When an activity with multiple paths leading back,
backward path with MINIMUM of all LS is selected.
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Eg:
activity duration__predecessor
A requirements analysis 3 weeks -
B programming 7 weeks A
C get hardware 1 week A
D train users 3 weeks B, C
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Critical path is: A-B-D 13 weeks
1 2
3
4
5 6
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Total slack= LS-ES or LF-EF
Total slack of all activities along critical path
is zero.
Hence delaying any of these activities will
delay the project.
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Free Slack= ES( earliest successor)- EF
In the eg, activity C has a free slack of 6
weeks( 10-4=6)
Free slack indicated the amount by which
activity can be delayed without affecting the
start of its successor activity.
47 Chapter 4 Slides by: Ms. Shree Jaswal
can have more than one critical path
activity duration predecessor
A requirements analysis 3 weeks -
B programming 7 weeks A
C get hardware 7 weeks A
D train users 3 weeks B, C
critical paths A-B-D
A-C-D
both with duration of 13 weeks
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Need for PDM: “Predecessor - Sucessor” type of networks
assume a “strict” sequential relationship between activities
They do not provide for tasks that can be started when their predecessors are only “partially” complete
PDM allows multiple relationships between activities Finish-to-Start (FS)
Start-to-Start (SS)
Start-to-Finish (SF)
Finish-to-Finish (FF)
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Finish-to-Start (FS)
The start of the Activity B can occur n days, at the earliest after the finish of Activity A
Start-to-Start (SS)
The start of Activity B can occur n days, at the earliest after the start of Activity A
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Start-to-Finish (SF)
The finish of Activity B must occur n days,
at the latest after the start of Activity A
Finish-to-Finish (FF)
The finish of Activity B will occur in n
days, at the latest after Activity A finishes
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PDM: Relationships A 15
Plaster Wall
B 10 Tear-down scaffolding
FS=5
A
FS=5
B
A 15 Furniture move in
B 10 People
move in SS=5
A
SS=5
B
A 15 Test
new system
B 10 Phase out old system
SF=20
A
SF=20
B
A 15 Lay
asphalt
B 10 Paint
parking lines FF=5
A
FF=5
B
52 Chapter 4 Slides by: Ms.
Shree Jaswal
The two most commonly used methods for project planning and scheduling are:
Program Evaluation and Review Technique (PERT)
Critical Path method (CPM)
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Program Evaluation & Review Technique (PERT)
The Framework for PERT and CPM
There are six steps which are common to both
1. Define the Project and all of it’s significant activities or tasks.
2. Develop the relationships among the activities. Decide which activities must precede and which must follow others.
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3. Draw the "Network" connecting all the activities. Each Activity should have unique event numbers. Dummy arrows are used where required to avoid giving the same numbering to two activities
4.Assign time and/or cost estimates to each activity
5. Compute the longest time path through the network. This is called the critical path.
6.Use the Network to help plan, schedule, monitor and control the project.
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PERT was developed for application in projects where there is uncertainty associated with the duration and nature of activities.
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reflects PROBABILISTIC nature of durations
assumes BETA distribution
same as CPM except THREE duration estimates
optimistic
most likely
pessimistic
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Three time estimates :
The Optimistic (a) The minimum time in which the activity can be
completed
The Most Likely (m) Completion time having the highest probability
(normal time to complete the job)
The Pessimistic (b)
The longest time an activity could take to complete
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a = optimistic duration estimate m = most likely duration estimate b = pessimistic duration estimate Mean or expected time for completion of an
activity , te is given by te = (a + 4m + b)/6 Variance, V is given by V = sqr((b-a)/6)
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The expected time Te , represents the point on distribution where there is a 50-50 chance that the activity will be completed earlier or later than it.
a=3,b=5,c=13
Te= (3+4(5)+13)/6= 6 days
Variance is the measure of variability in the activity completion time:
V=sqr((13-3)/6)=sqr(1.67)= 2.78
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The larger V, the less reliable Te, and the higher the likelihood that the activity will be completed much earlier or much later than Te.
More dispersed the distribution and greater the chance that the actual time will be significantly different from the expected time Te
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Probability of finishing by a target completion
date
The expected duration of a project - Te, is the
sum of expected activity times along the
critical path.
Te = ∑ te
The variation in the project duration
distribution is computed as the sum of the
variances of the activity durations along the
critical path
Vp = ∑ V
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Putting too much emphasis on the critical
path can lead managers to ignore other paths
that are near-critical or have large variances,
and which themselves could easily become
critical
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Need to have considerable amount of
historical data to make time estimates
PERT gives overly optimistic results.
Beta distribution gives large errors in
estimating Te.
Most of the errors in Te come from faulty
time estimates not Beta distribution.
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Although PERT and CPM employ networks and use the concept of critical path, the methods have two points of divergence.
CPM is a deterministic approach. CPM includes a mathematical procedure
for estimating the trade-off between project duration and cost.
CPM features analysis of reallocation of resources from one job to another to achieve the greatest reduction in project duration for the least cost.
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Tn- how long the activity will take under normal work conditions.
Also associated with normal pace is the normal cost, Cn, the price of doing the activity in normal time.
Usually normal pace is assumed to be the most efficient and thus least costly pace.
When maximum effort is applied, the duration so that activity can be completed in the shortest possible time, the activity is said to be crashed.
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In our example, cost slope for the activity
is $3K per week.
Thus, for each week the activity duration
is reduced( sped up) from the normal
time of 8 weeks, the additional cost will
be $3K.
Completing the project 1 week earlier i.e.
7 weeks, would increase the project cost
by ($9K +$3K=$12K)
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Basic rules:
Reducing the duration of an activity,
increases the cost by the cost-slope.
Increasing the cost of activity, reduces the
duration of the activity
Reduce the duration of activity with min
value of cost slope.
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Activity Normal Crash Cost Slope
Tn Cn Tc Cc_____________
A 9 10 6 16 2
B 8 9 5 18 3
C 5 7 4 8 1
D 8 9 6 19 5
E 7 7 3 15 2
F 5 5 5 5 _
G 5 8 2 23 5
$55K $104K
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1
2
6
3
5
4
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Activity Normal Crush Cost Slope
Tn Cn Tc Cc_____________
A 9 10 6 16 2
B 8 9 5 18 3
C 5 7 4 8 1
D 8 9 6 19 5
E 7 7 3 15 2
F 5 5 5 5 _
G 5 8 2 23 5
$55K $104K
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1
2
6
3
5
4
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1
2
6
3
5
4
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CCPM was introduced in 1997 by Eliyahu
Goldratt.
CCPM is based on the idea that people often
inflate or add cushioning to their time
estimate in order to give themselves a form
of “safety” to compensate for uncertainty.
There are 3 basic reasons for inflating:
If your work is dependent upon the work of
someone else
Because of pessimism arising from a previous
experience where things did not go as planned
To guard against the cut which the project
sponsor or customer may put
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Added safety does not ensure timely
completion of projects due to following
reasons:
1. Student’s syndrome
2. Parkinson’s law
3. Resource contention
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CCPM follows a completely different
assumption: instead of adding safety to each
task, put that safety in the form of buffers
where needed the most.
This would be in the form of feeding buffers,
resource buffers & a buffer at the end of the
project
CCPM begins by asking each person or team
assigned to a task to provide an estimate that
would have a 50 % chance of being completed
Critical chain is different from the critical path
in that it also takes into account resource
contention. Chapter 4 Slides by: Ms. Shree Jaswal 81
Chapter 4 Slides by: Ms. Shree Jaswal 82
A,10 B,10 C,10 E,10
D,10
A,5 B,5 C,5 E,5
D,5
10
2.5
Buffer
Feeder buffer
Project schedule with safety in each task
Critical chain project schedule
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Jaswal 83
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85 Chapter 4 Slides by: Ms. Shree Jaswal
In earlier slides, it was assumed that the
resources are available (may be at a cost) in
abundance
In reality, some resources may be scarce or
shared
Resource loading refers to the amount of
resource required to conduct a project
Note: resource loading keeps changing
throughout a project because the amount of
resources needed for individual activities differs
86 Chapter 4 Slides by: Ms. Shree Jaswal
Resource leveling refers to scheduling activities in a
manner such that the resource loading is somewhat
“balanced” (or “smoothed”)
SMOOTHING: “flatten” as much as possible
Smoothed: Manpower
87 Chapter 4 Slides by: Ms. Shree Jaswal
Equipment Requirement(!Erratic!)
88 Chapter 4 Slides by: Ms. Shree Jaswal
LEVELING: flatten with reference to available resource
Leveled: Manpower
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Activities must be scheduled so that the allocation of a particular resource to project activities does not exceed a specified maximum
Attention is given to maximum availability of resource
Most project management scheduling software use heuristics (procedure based upon a simple rule) for making the decisions
The heuristic rule for determining the scheduling priority are:
90 Chapter 4 Slides by: Ms. Shree Jaswal
A
E
B
C
D
F
5
5
5
5
10
10
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The critical path length is 9 weeks and the
constrained-resource level is of 10 workers
Chapter 4 Slides by: Ms. Shree Jaswal 92
a. As soon as possible: activities that can be started sooner are
given priority over those that must be started later
10
5
As Soon As Possible
A
B
C D
F
E
b. As late as possible: activities that can be finished
later are given lower priority than those that must
be finished earlier
10
5
As Late As Possible
A
B
C D
F
E
93 Chapter 4 Slides by: Ms. Shree Jaswal
c. Most resources : activities requiring more resources
are given priority over those requiring fewer
resources
10
5
Most Resources
A
B
C D
F
E
94 Chapter 4 Slides by: Ms. Shree Jaswal
d. Shortest Task Time: activities of shorter duration
are given priority over those of longer duration
10
5
Shortest Task First
A
B
C D
F
E
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e. Least Slack: activities with less slack time are given
priority over those with more slack time (critical
path activities are given highest priority)
10
5
Least Slack time
A
B
C D
F
E
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• All these rules are subordinate to precedence
requirements, which means whatever the rule, the
resulting schedule will not violate the necessary
predecessor-successor relationship.
• Other ways to account for resource constraints in project
scheduling include:
• Reduce the level of resources per activity
• Split activities
• Alter the network: use PDM, convert FS to SS
relationships
97 Chapter 4 Slides by: Ms. Shree Jaswal