Project Management
PROJECT MANAGEMENT
NETWORK ANALYSIS
(PERT and CPM)
INTRODUCTION
PERT and CPM are two well-known network techniques or models especially useful
for planning, scheduling and executing large time-bound projects which
involve careful co-ordination of a variety of complex and
interrelated activities and resources. PERT is the
abbreviated form for Program Evaluation and Review Techniques and CPM for Critical
Path Method. Both the techniques were developed in U.S.A. during the
late 1950s. PERT was developed by US Navy Engineers to plan and control
the huge Polaris Submarine Program. CPM was developed by E.I. DuPont
Nemours & Co., U.S.A. and the Univac Division of Remington Rand
Corporation in 1956 in connection with the periodic overhauling and
maintenance of chemical plants.
It resulted in reducing the shut-down period from 130 hours to 90 hours
and saving hours and saving the company $1 million.
Both the techniques have been
applied successfully to improve efficiency of execution of large projects
within pre-determined time and cost limits. Any new venture may be
regarded as a project, such as constructing a new plant, bridge, dam, shopping
centre or residential complex, design of a new aircraft, manufacture of
ships, R& D projects, introduction of a new product, installing
pipeline, floating a new issue of shares, major repairs and overhaul of
plant and machinery units, organizing a large conference/convention,
handling an earthquake relief work and so on.
PERT and CPM converge on several aspects,
and are almost treated as twins; there are, however, some points of
difference between them which will be discussed later. The techniques recognize
the systems or inter-related nature of activities on large work projects
and translate the job proposed into a model by drawing a network of the
activities involved. They are used in planning
and controlling (monitoring) the projects. Planning in this context
implies developing the overall layout of the project with estimates of
time, the resources required and the detailed time scheduling and sequence
of various jobs to be performed. The control, on the hand takes place
during the work on the project. Gradually as resources get used and
completion times are obtained, project management techniques can be used
to reallocate, if necessary, the rescues, according to the revised
criticality rankings of the jobs
remaining to be done.
The
process of planning and executing a project by synchronising various
constituent activities to achieve its accomplishment within the desired
timelines and available resources is called project management.
According
to UK Association of Project Management, ‘it is a process of planning,
organizing, monitoring and controlling of all aspect s of a project and the
motivation involved to achieve the project objectives safely and within the
agreed time, cost and performance criteria.’
Constructing
the Network
A project network is a directed graph that consists of finite
collection of elements called events (or nodes) together with a subset of
the ordered pairs (i, j,) of nodes called activities (or jobs or tasks or
operations). In other words, a network is the graphical representation of
logically and sequentially connected arrows and nodes representing
activities and events of a project.
(Also called arrow diagrams) diagrams show the operations/activities to
be performed to complete a job, the sequence and inter-relationship of
various activities involved.
In networks, an activity is a clearly identifiable and manageable operation
or an element of work entailed in the project and it is represented by an
arrow. An event (or node), is the and/or finish of an activity or group of
activities. Others terms used are junction, milestone or stage. In general
milestone is reserved for particularly significant events that require
special monitoring. An activity arrow (i, j,) extends between two nodes,
the tail node (or event), i, represents the start of an activity and the
head node (event) j, represents the completion of an activity as shown
below:
Activities may also be termed
jobs, tasks or operations. Activities which must be completed before a
certain other activity starts are called the predecessor activity starts
are called successors activities.
Predecessor activity: Activities that must be
completed immediately prior to the start of another activity called
predecessor activities.
Successor activities: Activities that cannot be
started until one or more of the other activities are completed, but
immediately succeed them are called successor activities.
Concurrent activity: Activities which can be
accomplished at the same time are known as concurrent activities.
Path: An unbroken chain of activity
arrows connecting the initial event to the final event via other events is
called a path.
RULES OF NETWORK CONSTRUCTION.
1. Each defined activity is
represented by one and only one arrow in the network. Therefore, no single
activity can be represented more than once in the network. These arrows should
be kept straight and not curved.
2. Before an activity can be
undertaken all activities preceding it must be completed. Thus, a network
should be developed on the basis of logical or technical dependencies
between various activities of the project. The discipline of networking
requires that the project be considered in a thorough and analytic manner
and the predecessor-successor relationships between the various activities
clearly laid.
3. The arrows depicting various
activities are indicative of the local precedence only. The length and
bearing of the arrows are of no significance, although arrows in network
diagrams should be drawn to show time flow left to right i.e. in the
forward direction.
4. The arrow direction indicates
the general progression in time. Each activity must start and end in a
node (or event). The tail of an activity represents the point in time at
which the “activity start” occurs and the node marking this start is
called the tail event for this event. The head of an activity represents the
point in time at which the “activity completion” occurs and the node
marking this termination is called the head event for that activity.
5. When a number of activities
terminate at one event, it indicates that no activity emanating from that
event may start unless all activities terminating there have been
completed.
6. Events are identified by
numbers. Each event identified by a number higher than that allotted to
the event immediate preceding one. ie., events should be numbered such
that for every arrow there is an event number before and after. In
assigning numbers to the events, care should be taken that there is no duplication
of event numbers in a network. The event numbered 1 denotes start of the
project and is called initial node (or event) while the event carrying the
highest number denotes the final event in the network. A network
should have only one initial and one terminal node
7. The activities are identified
by the numbers of their starting and the ending events. An event which
represents the joint completion of more than one activity is known as a
merge event, while an event which portrays the initiation of more than one
activity is called the burst event.
8. Parallel activities between two events,
without intervening events, are prohibited. Thus two or more activities
cannot be identified by the same beginning and ending events. By
implication, any two events should not be connected with more than one
arrow. When two or more activities in a project have the same head and
tail events, dummy activities are needed in constructing the network. The
figure on the left is the wrong way to represent the two activities while
the figure on the right shows the correct representation
of the two activities using a dummy.
9.
10.
DUMMY ACTIVITY: Dummy activities are usually
shown by arrows with dashed lines. Dummy activities are also very useful
in establishing proper logical relationships in the networks which cannot,
otherwise, be adequately represented.
11. Looping is not permitted.
12. Dangling is not permitted.
Numbering
the events (Fulkerson’s Rule)
After the network is drawn in a logical sequence, every event is
assigned a number which is placed inside the node circle. The number
sequence should be such so as to reflect the flow of the network. The rule
devised D R Fulkerson is used for the purpose of numbering and involves
the following steps.
1. The initial event has all
outgoing arrows with no incoming arrow is numbered 1.
2. Delete all the arrows coming out of node 1. This will convert
some more nodes (at least one) into initial events. Number these events
2,3 …
3. Delete all the arrows going out from these numbered events to
create more initial events. Assign the next numbers to these events.
4. Continue until the final or terminal node, which has all arrows
coming in with no arrow going out, is numbered.
CRITICAL
PATH :
The critical path in a network
diagram is the longest continuous chain of activities (i.e. a path along
which it takes the longest
duration) through the network starting from first to the last event and
is shown by thick line or double lines. All activities lying on this
critical part are called critical activities, as any delay in their
execution will lead to a delay in the completion of the entire project.
NETWORK CRASHING
Project Time & Cost in Networking
Introduction:
For completing a project
various activities have to be completed which requires lot of money.
Hence, the project manager always
remains conscious of time as well as costs involved. CPM assumes
direct relationship between time and cost and uses time-cost trade-off
concept, which is its unique feature. This concept relates to the fact
that on a crash basis, it will cost a little more but even this increase
in cost may prove economical in various ways. As such the project manager
will keep in mind the time-cost consideration before taking decisions
regarding the project and its different activities.
CRASHING: is employed when project
manager want to shorten the project completion time by spending extra
resources (more money). In real life, it is always possible to employ more
resources. For example, the activity of laying tiles which requires team
of mason assisted by a labourers. By increasing the number of mason and
labourers the activity duration can be shortened or crashed. But this
to has limitation by increasing the mason and labourers would not reduce
the duration any more since they are liable to jam up. Concerned
specialists would have to estimate the crashing limit for each activity as
also the extra money for crashing each activity. Crash time is the minimum
activity duration to which an activity can be compressed by increasing the
resources and hence by increasing the direct costs.
Time-cost
optimisation algorithm
The process of shortening a project duration is called crashing
and is usually achieved by adding extra resources to an activity.
Project crashing involves the following steps:
NETWORK CRASHING
Step I: Find the critical path
and identify the critical activities. List all possible paths starting and
duration of each path.
Step II: Calculate the cost slope
for the different activities by using the formula.
Cost slope = Crash cost - Normal cost
Normal time - Crash time
The crash slope indicates the extra cost required to expedite an activity
per unit time.
Identify the activities on critical path which have cost slope less than
the indirect cost.
Step III: Crashing the activity
having minimum cost slope i.e. Less than the indirect cost. Redraw the
network diagram with the crashing time. And find out the critical path if
there is no change. This means that the network cannot be further crashed.
This is the optimum network.
Step IV: Calculate the total cost of the
project before and after crashing. Check whether crashing reduces the cost
of project. By calculating the difference of before and after crashing
Total cost without crashing
Direct cost + indirect cost
Total cost after crashing
Direct cost + indirect cost
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