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Managing Business Operations Network analysis & cpm analysis
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Project Management
Project is defined as a huge (mammoth) task which for convenience of management is broken down into smaller elements such that, for each of the smaller elements, one can identify the finite requirements of resources and finite requirements of time. These smaller elements are referred as activities of the project i.e. project essentially comprises of a number of activities e.g. construction of building is a project and electrical work is one of the activities of the project.
Contd…
Slide 1
Project Management
Like the electrical activity, a project will have a number of activities. The first task of the project manager is to define all the activities of the project in terms of time and other dimensions like cost etc. The second task is to establish the inter relation & interdependence of the defined activities. The following are some examples to explain small projects.
Slide 2
Example 1
Activity DescriptionImmediate
predecessorsDuration (weeks)
A Select location - 2
B Obtain speakers - 3
C Make speaker travel plans A, B 2
D Prepare and mail brochure A, B 2
E Take reservations D 3
Christine Philips is in charge of planning and coordinating next spring’s sales management training program for her company. Christine has listed following activities information for this project.
Draw the network diagram; find the critical path and the duration along the critical path.
Slide 3
Activity Description Immediate predecessors
Duration (days)
A Determine output voltages - 5
BDetermine whether to use solid state rectifiers A 7
C Choose rectifiers B 2
D Choose filter B 3
E Choose transformer C 1
F Choose chassis D 2
G Choose rectifiers mounting C 1
H Layout chassis E, F 3
I Build and test G, H 10
A research and development department is developing a new power supply for a console television set. It has broken down the job into the following form:
Draw the critical path schedule, indicate the critical path. What is the time required for completion for the project?
Example 2Slide 4
Categories of Project
The following is an illustrative list of categories of project:i. Complex projects with unknown elements for e.g.
Construction of nuclear power plants ii. Large projects with standard elements for e.g. Construction of
an automobile factory iii. Intermediate project for e.g. layout of machine, implementing
TQM programme, developing new markets etc.iv. Small projects for e.g. installing a new machine, conducting a
market survey etc.v. Turnkey project is one which starts from zero to proceed to a
finished ‘product’. Concept of turnkey is that when the project is finished one turns a key to set the facility in operation, for e.g. Reliance refinery project at Jamnagar is a turnkey project.
Slide 5
Session Objective
Given the activities, their duration and their inter relation,
our objective in this session is:
i. to represent these relation of activities in the form
of a network diagram
ii. to analyze the network diagram using CPM (Critical
Path Method)
Slide 6
Network Diagram
Network diagram is a graphical / pictorial
representation of a series or a sequence of activities in
the logical order of their performance, such that we
establish the inter relation and interdependence of one
activity on all other activities of the project.
Network Diagram comprises of two basic elements:
(i) Activity
(ii) Event (Node)
Slide 7
Elements of Network Diagram
i. Activity: An activity is denoted by an arrow
It signifies the deployment of finite resources over a finite period of time. The tail of the arrow signifies the commencement of the activity and the head signifies the completion of the activity.
ii. Events or Nodes: An event is denoted by a circle
It signifies the status of the project at a point of time. It indicates the start & completion of an activity.
i
Tail Head
where, i={1,2,3,4…. and so on}
Slide 8
A-O-A Convention (i-j convention)
i jA
tij
i < j
Activity A or Activity i-j
Tail event signifies commencement status of the activity.
Head Event signifies completion status of the activity
Arrow signifies deployment of finite resources over a finite period of time.
tij is the duration of the activity
Tail Event Head Event
Slide 9
Good practices of drawing a Network Diagrami. Drawing a network diagram is a trial and error procedureii. The starting event is always one event, irrespective of the number
of starting activities. This event signifies the commencement status of the project
iii. The completion event is always one event, irrespective of the number of final activities. This event signifies the completion status of the project.
iv. The length of the arrow is the convenience of drawing the network diagram. It is no indication of the duration of activity.
v. The arrows must be drawn in the forward direction. Avoid crossing of arrows.
vi. The numbering of events starts with the first event and progressively moves from the left to the right of the network diagram
vii. There is no uniqueness in the final picture of the network diagram.
Slide 10
Good practices of drawing a Network Diagram
These Guidelines are explained with the
following five illustrations of network
diagram:
Slide 11
Analysis of Network Diagram
There are two popular tools used for analysis of Network
Diagram
CPM (Critical Path Method)
PERT (Program Evaluation & Review Technique)
In the following slides, CPM is explained with examples.
Slide 12
Manager’s View of Critical Path Method
Inputs(What information must
be supplied to CPM)
CPM
Outputs(What information results
from CPM that provides for better project management)
1. a complete list of project activities
2. Precedence relationship among activities
3. Estimate of each activities duration
1. Estimated duration of project
2. Identification of critical activities
3. Amount of Float for each activity
Slide 13
Critical Path Method It was developed in 1956 / 1957 by Remington Rand and Du-
pont to help schedule maintenance projects in chemical plants and construction projects.
Critical Path Method is a systematic scientific method based on principle of time estimates to perform a detailed analysis of Network in an application of Project Management
Time estimates in CPM relate to estimating the time for the events of the network diagram. Since the event signifies the status of the project at a point of time, the time estimates in turn signify the status of the project at different points of time. There are two important time estimates; (i) Earliest starting time & (ii) Latest finishing time.
Slide 14
Guidelines for Earliest Start Time (EST)
Earliest Start Time (EST): It signifies the earliest that an activity can start with reference to the commencement status of the project. The following are the guidelines to obtain EST.
i. Earliest starting time for event 1 is taken as zero because event 1 signifies the commencement status of the project i.e. status of the project corresponding to time ‘t = 0’.
ii. For the calculation of EST we start from event 1 and progressively move from left to right in the network diagram (referred as forward pass)
Slide 15
i jtij
Tail Event Head Event
Ei Ej
Ej = Ei + tij
EST of the head event EST of the tail event the duration of the activity= +
iii.Consider two adjacent events
Guidelines for Earliest Start Time (EST)
Slide 16
iv. Consider a merging event (in case more than one activity is merging towards an event).
b d
c
a
Ea
Eb
Ec
Ed
tad
tbd
tcd
Ed = Ea + tad
Ed = Eb + tbd
Ed = Ec + tcd
Take the maximum value
Guidelines for Earliest Start Time (EST)
Slide 17
Latest Finish Time (LFT): It is the latest time by which an activity should finish, otherwise the project completion time will be delayed. The following are the guidelines to obtain LFT.
i. For the last event of the network diagram, LFT = EST (because the last event signifies the project completion status and both EST / LFT signify the project completion time)
ii. For the calculation of LFT, we start with the last event of the network diagram & we proceed progressively from the right to the left of the network diagram (referred as backward pass).
Guidelines for Latest Finish Time (LFT)
Slide 18
iii. For two adjacent events
i jtij
Tail Event Head Event
LiLj
Li = Lj – tij
LFT of the tail event LFT of the head event the duration of that activity= –
Guidelines for Latest Finish Time (LFT)
Slide 19
31
4
2
L2
L1
t12
t13
t14 L3
L4
L1 = L2 – t12
L1 = L3 – t13
L1 = L4 – t14
Take the minimum value
For a bursting event (If there are more than one subsequent activities busting from an event), calculate LFT for each of the head events and take the minimum value
Guidelines for Latest Finish Time (LFT)
Slide 20
Note:
Both EST and LFT for starting event (event 1 of the network diagram) are always zero
Slide 21
Total Float of an Activity
Total Float signifies the maximum permissible delay in performing the activity without delaying the project completion time. The following is the mathematical relation for Total Float
Total Float of Activity LFT (Head Event)
EST (Tail Event)
Duration of Activity= – –
i jtij
Tail Event
Head EventEi
Lj
Total Float of Activityi-j = Lj – Ei – tij
Slide 22
Free Float of an Activity
i jtij
Tail Event Head Event
Ei
Lj
Ej
Li
Free float signifies the maximum permissible delay in commencement of an activity without affecting the commencement of the succeeding activity
Head Event Float = Lj – Ej
Free Float = Total Float – Head Event Float
Slide 23
Definition of Critical Path
If total float of an activity is zero, it means there is no permissible delay in performing the activity i.e. any delay in performing the activity will result in a corresponding delay in the project completion time. Such activities are referred as critical activities.
Path of network is a continuous series or sequence of activities that joins the first event with the last event of the network diagram.
In a network one can enumerate many sequences of activities from starting event to end event. Each sequence will contain different combination of activities with different duration.
Slide 24
Definition of Critical Path
To know the possible time by which the project can be completed, we determine the critical path i.e. the sequence of activities with longest duration. It is known as critical path and any delay in activities lying on this path would cause a delay in the whole project.
Alternately, Critical Path is a continuous series or sequence of critical activities that joins the first event with the last event of the network diagram.
To quicken the process, the activities lying on the critical path should be taken first. The activity lying on non-critical path has some flexibility in their starting time and their delay in start is not likely to affect the final completion date. These are known as slack activities and should be given priority in order of their float value.
Slide 25