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CONSTRUCTION PLANNING
 Planning can be defined as ‘drawing up a method
or scheme of acting, doing, proceeding, making,
etc., developed in advance.
 Construction projects involve using different
resources—human, equipment and material,
money, etc., and at all times.
 The task of a construction planner is to draw up
plans for optimum utilization of all these resources
and to ensure appropriate preparedness at all
times.
 construction of a large project involves diverse
agencies—government regulators, clients/owners,
designers, consultants and contractors.
 it is important to ensure proper coordination to
ensure that the agencies do not work at cross-
purposes, and that the common goal is served.
 It should be noted that plans are drawn up at each
of the stages or phases of a project, though
different terminologies are used at times depending
upon the stage of the project
 Ex:- feasibility plan, preliminary plan etc.
 initially when the project is at the inception stage,
the plan could be referred to as a feasibility plan,
while in the engineering and execution stages,
terms such as preliminary plan and construction
plan, respectively, are commonly used.
 Some of the activities involved in construction
planning are:
Defining the scope of work:
 Since all activities involve consumption of different
resources to different extents, it is important that the
scope of work involved is properly and, to the extent
possible, completely defined. Any addition, deletion, or
modification in the scope could have serious
repercussions in terms of time of completion and cost
etc.
 For example, if felling trees and getting environment
clearances is added (at a later date) to the scope of a
contractor who has been awarded a job for construction
of roads, it would obviously cause difficulties.
Identifying activities involved:
 This part of planning is very closely linked to defining
the scope, and involves identifying activities in a
particular job.
 Since different activities involved consume different
physical resources to varying extents, it is crucial that
these activities are exhaustively listed, along with the
resources required.
 For example, though different agencies may be
concerned with ‘environmental impact assessment’, it is
important for them to identify the tools or parameters
each will be using so as to plan effectively.
Establishing project duration
 This can be done only with a clear knowledge of the
required resources, productivities and interrelationships.
 This information is used to prepare a network and other
forms of representations outlining the schedules.
 Duration for an activity normally depends on amount of
resources allocated to it and can be increased or
decreased.
Defining procedures for controlling and assigning
resources:
 It is important that the planning document prepared is
followed by others involved in the execution of the
project, or in its individual phases.
 Thus, the procedures to be followed for procurement
and control of resources for different activities—
manpower, machines, material and money—are also
laid down.
Developing appropriate interfaces:
 The planner needs to devise an appropriate system for
management information system (MIS) reporting.
 Tools such as computers and formats for reporting are
widely used, and it may be noted that several software
are readily available to aid the planner
Updating and revising plans:
 a construction plan needs to be continuously updated
and revised during monitoring
 the planner should clearly understand the product to be produced
in terms of scope and expected performance, the input required
and the process involved, including the issues in quality control
and tolerances at different steps.
 At the same time, the time and productivity aspects involved in
the different activities should also be understood, besides the
interdependence of activities.
 The planning should also identify milestones and targets for the
different agencies to facilitate proper monitoring during execution.
 Inclusion of features identifying risks associated with a project,
and the appropriate responses for mitigation enhance the quality
of the project plan.
TYPES OF PROJECT PLANS
 Schedule, cost, quality and safety can be identified
as specific items on which the success of any
(construction) project is evaluated.
 Thus, at times it makes sense to have different
plans for each of these criteria—and draw up
(separately) a time plan (or schedule), cost plan,
quality plan and safety plan.
 depending upon the nature and stage of the project,
one may also need to deal with a plant and
equipment plan, a maintenance plan and a staff
deployment plan.
TIME PLAN
 Time is the essence of all construction projects, and
contracts often have clauses outlining awards
(bonus payments) or penalties (as liquidated
damages) for completing a work ahead or later than
a scheduled date.
 While effort is made to ensure timely completion of
work, it should be noted that some of the common
reasons for delays could be a sluggish approach
during planning, delay in award of contract,
changes during execution, alterations in scope of
work, delay in payments, slow decision-making,
delay in supply of drawings and materials, and
labour trouble.
 Several reasonably well-established techniques are
available and commonly used for time planning (or
‘scheduling’) activities—for example, critical path
method (CPM), programme evaluation and review
technique (PERT), precedence network analysis
(PNA) etc.
 The choice of the method to be used in a particular
case depends on the intended objective, the nature
of the project, the target audience, etc.
MANPOWER PLAN
 This plan focuses on estimating the size of
workforce, division in functional teams and
scheduling the deployment of manpower.
 It may be noted that manpower planning also
involves establishing labour productivity standards,
providing suitable environment and financial
incentives for optimum productivity, and grouping
the manpower in suitable functional teams in order
to get the optimum utilization.
MATERIAL PLAN
 The material plan involves identification of required
materials, estimation of required quantities, defining
specification and forecasting material requirement,
besides identification of appropriate source(s),
inventory control, procurement plans and
monitoring the usage of materials.
CONSTRUCTION EQUIPMENT PLAN
 Modern construction is highly mechanized and the role
of heavy equipment in ensuring timely completion of
projects cannot be over-emphasised. Machines are
used in modern construction for mass excavation,
trenching, compacting, grading, hoisting, concreting,
drilling, material handling, etc. Induction of modern
equipments could improve productivity and quality,
besides reducing cost. At the same time, it should be
borne in mind that heavy equipments are very costly
and should be optimally utilized in order to be
productive. It is also important that the characteristics of
equipment are kept in mind when drawing up an
equipment plan.
FINANCE PLAN
 Given the fact that large construction projects require huge
investments, and a long time to complete, it is obvious that
all the money is not required at any one point in time.
 Contractors fund their projects from their working capital, a
part of which is raised by the contractors using their own
sources (e.g., bank loans secured against assets,
deployment of resources from their inventory).
 Whereas the rest comes from a combination of avenues
such as mobilization advance for the project, running-
account bills paid by the client, secured advances against
materials brought at site, advance payments, and credits
from suppliers against work done.
 Thus, a careful analysis needs to be carried out to determine
how the requirement of funds varies with time.
WORK-BREAKDOWN STRUCTURE
 ‘Work-breakdown structure’ (or WBS), or simply
‘work breakdown’, is the name given to a technique
in project management in which the project is
broken down into manageable parts.
 WBS represents ‘a task-oriented “family tree” of
activities and organizes, defines, and graphically
displays the total work to be accomplished in order
to achieve the final objectives of the project.’
 This provides a central organizing concept for the
project and serves as a common framework for
other exercises such as planning, scheduling, cost
estimating, budgeting, configuring, monitoring,
reporting, directing and controlling the entire
project. Thus, it should be intuitively clear that for a
complex project, greater care is required in
formulating a successful WBS.
 A work-breakdown structure (usually triangular in
shape) progresses downwards in the sense that it
works from pursuing general to specific
objectives—much like a family tree, it provides a
framework for converting a project’s objectives into
specific deliverables.
 In cases of complex projects the power and utility of
the WBS method in effective management of the
work is clearly demonstrated
METHODOLOGY OF WBS
 A project is split into different levels from top to bottom
 The WBS does not go into the details of activity at the
operational level. The term ‘subprojects’, ‘work
packages’, and ‘tasks’ are used interchangeably
 The tasks are broken down into activities that are the
lowest level of a work-breakdown structure.
 It should be borne in mind that once this breakdown is
exhaustive, operations such as development of the time
schedules, resource allocation and project monitoring
become simplified.
PROJECT PLANNING TECHNIQUES—
TERMINOLOGIES USED
Event and Activity
 Event is a point in time when certain conditions
have been fulfilled, such as the start or completion
of one or more activities. An event consumes
neither time nor any other resource. Hence, it only
expresses a state of system/project.
 Activities take place between events. Activity is an
item of work involving consumption of a finite
quantity of resources and it produces quantitative
results. An exception to this rule is the dummy
activity
 Ex: activity i-j. The start (node i) and the completion
(node j) of this activity can be considered as events.
Dummy Activity
 This activity does not involve consumption of
resources, and therefore does not need any time to
be ‘completed’. It is used to define interdependence
between activities and included in a network for
logical and mathematical reasons.
 Network
Precedence:
 This is the logical relationship implying that an activity
needs one activity (or more activities) to be completed,
before this activity can start.
 For example, in order to be able to start plastering, the
brickwork needs to have been completed
 It is a common practice in most construction projects to
represent the precedence of activities in the form of a
table, called the precedence table.
 For preparing the precedence table, a list of activities
that should precede a given activity is given.
 It should also be mentioned that this concept (of
precedence) is sometimes referred to as ‘dependence’.
NETWORK LOGIC
DURATION OF AN ACTIVITY
 Duration of an activity (i, j) is denoted by D(i, j). This
is the length of time required to carry out an activity
(i, j) from the beginning to its end.
 Depending upon the activity and the level of detail,
the duration may be expressed in days, weeks, or
months.
 a duration cannot be really fixed or given as a final
number, and as such remains only an estimate,
based on past experience with productivity, etc
START AND FINISH TIMES
 In principle, an activity can be started as soon as
the groundwork involved has been completed, but
the client or contractor may (be able to) wait for
sometime before starting the activity without
affecting the overall project completion.
 Similarly, depending upon the starting time and the
duration, the activity may be completed at different
times.
 Earliest start time of an activity: This is the earliest,
that the activity (i, j) can be started, i.e., all the necessary
preconditions are met. Earliest start time of an activity (i,
j) has been denoted by EST(i, j)
 Earliest finish time of an activity This is the earliest,
that an the activity (i, j) can be completed. Earliest finish
time of an activity (i, j) has been denoted by EFT(i, j)
Mathematically, the relationship can be expressed as
EFT(i, j) = EST(i, j) + D(i, j)
 Latest finish time of an activity: This is the latest
time that an activity needs to be completed in order that
there is no delay in the project completion. Latest finish
time of an activity (i, j) has been denoted by LFT(i, j)
 Latest start time of an activity This is the latest time
when an activity must be started, in order that there is
no delay in the project completion. Latest start time of
an activity (i, j) has been denoted byLST(i, j)
Mathematically, the relationship can be expressed as:
LST(i, j) = LFT(i, j) − D(i, j)
FORWARD AND BACKWARD PASS
 The forward pass moves from the ‘start’ node
towards the ‘finish’ node, and basically calculates
the earliest occurrence times of all events.
 Considering that the project starts at time zero, the
earliest occurrence time at each node is found by
going from node to node in the order of increasing
node numbers, keeping in mind the logical
relationships between the nodes as shown by the
connecting arrows.
 The earliest occurrence time for any node can be
estimated from the (maximum) time taken to reach
that node from the different incoming arrows.
 he backward pass is made in a similar manner to
that of the forward pass, except that the process is
carried out in reverse through the nodes, starting
from the end node and finishing at the start node.
 the late occurrence time for different nodes can be
found out, depending on whether there is a single
outgoing arrow from a node
 For the end node the late occurrence time is
considered same as the earliest occurrence time.
 The late occurrence times for these nodes can be
simply determined as Li = Lj − D(i, j)
 In case if multiple arrows reaching same node,
 Li = Mjin[Lj − D(i, j)], where the minimization is over
all nodes j that precede node i.
 for some events (nodes) in the network, the two
values (E and L) will be the same if the latest
project completion time is taken as the earliest
project completion time.
 These events are called critical events and the path
is called critical path.
FLOAT OR SLACK TIME
 The time period by which an activity can be delayed
without adversely affecting project completion.
 Total float in an activity Total float of an activity
is the amount of time by which the start of the
activity may be delayed without causing a delay in
the completion of the project. This is calculated as
TF(i, j) = LST(i, j) − EST(i, j)
Or
TF(i, j) = LFT(i, j) − EFT(i, j)
The values of TF(i, j) calculated from above equations
are referred to as start float and finish float
respectively.
 In terms of event times, the TF(i, j) can be defined
as the late occurrence time Lj of the succeeding
event minus the early occurrence time Ei of the
preceding event minus the duration of the activity
defined between these events.
Thus,
TF(i, j) = Lj − Ei − D(i, j)
 Free float Free float is the amount of time by which
the start of an activity may be delayed without
delaying the start of a following activity.
 Free float is defined as the earliest occurrence
time Ej of the following event minus the earliest
occurrence time Ei of the preceding event minus the
duration of the activity defined between these events.
 Free float for an activity (i, j) is denoted by FF(i, j) and
is calculated from the following expression: FF(i, j)
= Ej − Ei − D(i, j)
 Independent float Independent float is the amount
of time by which the start of an activity may be
delayed without affecting the preceding or the
following activity.
 Independent float is defined as the earliest
occurrence time Ej of the following event minus the
latest occurrence time Li of the preceding event
minus the duration of the activity defined between
these events.
 Independent float for an activity (i, j) is denoted by
IF(i, j) and is calculated from the following
expression: IF(i, j) = Ej − Li − D(i, j)
 Interference float:
It is defined as the difference in total float and free
float.
In other words, Interference Float =
TF(i, j) − FF(i, j)
Critical Path:
The ‘critical path’ is defined as one that gives the
longest time of completion (of the project).
Construction planning - Construction Technology and Project Management

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Construction planning - Construction Technology and Project Management

  • 2.  Planning can be defined as ‘drawing up a method or scheme of acting, doing, proceeding, making, etc., developed in advance.  Construction projects involve using different resources—human, equipment and material, money, etc., and at all times.  The task of a construction planner is to draw up plans for optimum utilization of all these resources and to ensure appropriate preparedness at all times.
  • 3.  construction of a large project involves diverse agencies—government regulators, clients/owners, designers, consultants and contractors.  it is important to ensure proper coordination to ensure that the agencies do not work at cross- purposes, and that the common goal is served.  It should be noted that plans are drawn up at each of the stages or phases of a project, though different terminologies are used at times depending upon the stage of the project  Ex:- feasibility plan, preliminary plan etc.
  • 4.  initially when the project is at the inception stage, the plan could be referred to as a feasibility plan, while in the engineering and execution stages, terms such as preliminary plan and construction plan, respectively, are commonly used.
  • 5.  Some of the activities involved in construction planning are: Defining the scope of work:  Since all activities involve consumption of different resources to different extents, it is important that the scope of work involved is properly and, to the extent possible, completely defined. Any addition, deletion, or modification in the scope could have serious repercussions in terms of time of completion and cost etc.  For example, if felling trees and getting environment clearances is added (at a later date) to the scope of a contractor who has been awarded a job for construction of roads, it would obviously cause difficulties.
  • 6. Identifying activities involved:  This part of planning is very closely linked to defining the scope, and involves identifying activities in a particular job.  Since different activities involved consume different physical resources to varying extents, it is crucial that these activities are exhaustively listed, along with the resources required.  For example, though different agencies may be concerned with ‘environmental impact assessment’, it is important for them to identify the tools or parameters each will be using so as to plan effectively.
  • 7. Establishing project duration  This can be done only with a clear knowledge of the required resources, productivities and interrelationships.  This information is used to prepare a network and other forms of representations outlining the schedules.  Duration for an activity normally depends on amount of resources allocated to it and can be increased or decreased.
  • 8. Defining procedures for controlling and assigning resources:  It is important that the planning document prepared is followed by others involved in the execution of the project, or in its individual phases.  Thus, the procedures to be followed for procurement and control of resources for different activities— manpower, machines, material and money—are also laid down.
  • 9. Developing appropriate interfaces:  The planner needs to devise an appropriate system for management information system (MIS) reporting.  Tools such as computers and formats for reporting are widely used, and it may be noted that several software are readily available to aid the planner Updating and revising plans:  a construction plan needs to be continuously updated and revised during monitoring
  • 10.  the planner should clearly understand the product to be produced in terms of scope and expected performance, the input required and the process involved, including the issues in quality control and tolerances at different steps.  At the same time, the time and productivity aspects involved in the different activities should also be understood, besides the interdependence of activities.  The planning should also identify milestones and targets for the different agencies to facilitate proper monitoring during execution.  Inclusion of features identifying risks associated with a project, and the appropriate responses for mitigation enhance the quality of the project plan.
  • 11. TYPES OF PROJECT PLANS  Schedule, cost, quality and safety can be identified as specific items on which the success of any (construction) project is evaluated.  Thus, at times it makes sense to have different plans for each of these criteria—and draw up (separately) a time plan (or schedule), cost plan, quality plan and safety plan.  depending upon the nature and stage of the project, one may also need to deal with a plant and equipment plan, a maintenance plan and a staff deployment plan.
  • 12. TIME PLAN  Time is the essence of all construction projects, and contracts often have clauses outlining awards (bonus payments) or penalties (as liquidated damages) for completing a work ahead or later than a scheduled date.  While effort is made to ensure timely completion of work, it should be noted that some of the common reasons for delays could be a sluggish approach during planning, delay in award of contract, changes during execution, alterations in scope of work, delay in payments, slow decision-making, delay in supply of drawings and materials, and labour trouble.
  • 13.  Several reasonably well-established techniques are available and commonly used for time planning (or ‘scheduling’) activities—for example, critical path method (CPM), programme evaluation and review technique (PERT), precedence network analysis (PNA) etc.  The choice of the method to be used in a particular case depends on the intended objective, the nature of the project, the target audience, etc.
  • 14. MANPOWER PLAN  This plan focuses on estimating the size of workforce, division in functional teams and scheduling the deployment of manpower.  It may be noted that manpower planning also involves establishing labour productivity standards, providing suitable environment and financial incentives for optimum productivity, and grouping the manpower in suitable functional teams in order to get the optimum utilization.
  • 15. MATERIAL PLAN  The material plan involves identification of required materials, estimation of required quantities, defining specification and forecasting material requirement, besides identification of appropriate source(s), inventory control, procurement plans and monitoring the usage of materials.
  • 16. CONSTRUCTION EQUIPMENT PLAN  Modern construction is highly mechanized and the role of heavy equipment in ensuring timely completion of projects cannot be over-emphasised. Machines are used in modern construction for mass excavation, trenching, compacting, grading, hoisting, concreting, drilling, material handling, etc. Induction of modern equipments could improve productivity and quality, besides reducing cost. At the same time, it should be borne in mind that heavy equipments are very costly and should be optimally utilized in order to be productive. It is also important that the characteristics of equipment are kept in mind when drawing up an equipment plan.
  • 17. FINANCE PLAN  Given the fact that large construction projects require huge investments, and a long time to complete, it is obvious that all the money is not required at any one point in time.  Contractors fund their projects from their working capital, a part of which is raised by the contractors using their own sources (e.g., bank loans secured against assets, deployment of resources from their inventory).  Whereas the rest comes from a combination of avenues such as mobilization advance for the project, running- account bills paid by the client, secured advances against materials brought at site, advance payments, and credits from suppliers against work done.  Thus, a careful analysis needs to be carried out to determine how the requirement of funds varies with time.
  • 18. WORK-BREAKDOWN STRUCTURE  ‘Work-breakdown structure’ (or WBS), or simply ‘work breakdown’, is the name given to a technique in project management in which the project is broken down into manageable parts.  WBS represents ‘a task-oriented “family tree” of activities and organizes, defines, and graphically displays the total work to be accomplished in order to achieve the final objectives of the project.’
  • 19.  This provides a central organizing concept for the project and serves as a common framework for other exercises such as planning, scheduling, cost estimating, budgeting, configuring, monitoring, reporting, directing and controlling the entire project. Thus, it should be intuitively clear that for a complex project, greater care is required in formulating a successful WBS.
  • 20.  A work-breakdown structure (usually triangular in shape) progresses downwards in the sense that it works from pursuing general to specific objectives—much like a family tree, it provides a framework for converting a project’s objectives into specific deliverables.  In cases of complex projects the power and utility of the WBS method in effective management of the work is clearly demonstrated
  • 21. METHODOLOGY OF WBS  A project is split into different levels from top to bottom  The WBS does not go into the details of activity at the operational level. The term ‘subprojects’, ‘work packages’, and ‘tasks’ are used interchangeably  The tasks are broken down into activities that are the lowest level of a work-breakdown structure.  It should be borne in mind that once this breakdown is exhaustive, operations such as development of the time schedules, resource allocation and project monitoring become simplified.
  • 22. PROJECT PLANNING TECHNIQUES— TERMINOLOGIES USED Event and Activity  Event is a point in time when certain conditions have been fulfilled, such as the start or completion of one or more activities. An event consumes neither time nor any other resource. Hence, it only expresses a state of system/project.  Activities take place between events. Activity is an item of work involving consumption of a finite quantity of resources and it produces quantitative results. An exception to this rule is the dummy activity  Ex: activity i-j. The start (node i) and the completion (node j) of this activity can be considered as events.
  • 23. Dummy Activity  This activity does not involve consumption of resources, and therefore does not need any time to be ‘completed’. It is used to define interdependence between activities and included in a network for logical and mathematical reasons.  Network
  • 24.
  • 25. Precedence:  This is the logical relationship implying that an activity needs one activity (or more activities) to be completed, before this activity can start.  For example, in order to be able to start plastering, the brickwork needs to have been completed  It is a common practice in most construction projects to represent the precedence of activities in the form of a table, called the precedence table.  For preparing the precedence table, a list of activities that should precede a given activity is given.  It should also be mentioned that this concept (of precedence) is sometimes referred to as ‘dependence’.
  • 27. DURATION OF AN ACTIVITY  Duration of an activity (i, j) is denoted by D(i, j). This is the length of time required to carry out an activity (i, j) from the beginning to its end.  Depending upon the activity and the level of detail, the duration may be expressed in days, weeks, or months.  a duration cannot be really fixed or given as a final number, and as such remains only an estimate, based on past experience with productivity, etc
  • 28. START AND FINISH TIMES  In principle, an activity can be started as soon as the groundwork involved has been completed, but the client or contractor may (be able to) wait for sometime before starting the activity without affecting the overall project completion.  Similarly, depending upon the starting time and the duration, the activity may be completed at different times.
  • 29.  Earliest start time of an activity: This is the earliest, that the activity (i, j) can be started, i.e., all the necessary preconditions are met. Earliest start time of an activity (i, j) has been denoted by EST(i, j)  Earliest finish time of an activity This is the earliest, that an the activity (i, j) can be completed. Earliest finish time of an activity (i, j) has been denoted by EFT(i, j) Mathematically, the relationship can be expressed as EFT(i, j) = EST(i, j) + D(i, j)
  • 30.  Latest finish time of an activity: This is the latest time that an activity needs to be completed in order that there is no delay in the project completion. Latest finish time of an activity (i, j) has been denoted by LFT(i, j)  Latest start time of an activity This is the latest time when an activity must be started, in order that there is no delay in the project completion. Latest start time of an activity (i, j) has been denoted byLST(i, j) Mathematically, the relationship can be expressed as: LST(i, j) = LFT(i, j) − D(i, j)
  • 31. FORWARD AND BACKWARD PASS  The forward pass moves from the ‘start’ node towards the ‘finish’ node, and basically calculates the earliest occurrence times of all events.  Considering that the project starts at time zero, the earliest occurrence time at each node is found by going from node to node in the order of increasing node numbers, keeping in mind the logical relationships between the nodes as shown by the connecting arrows.  The earliest occurrence time for any node can be estimated from the (maximum) time taken to reach that node from the different incoming arrows.
  • 32.  he backward pass is made in a similar manner to that of the forward pass, except that the process is carried out in reverse through the nodes, starting from the end node and finishing at the start node.  the late occurrence time for different nodes can be found out, depending on whether there is a single outgoing arrow from a node  For the end node the late occurrence time is considered same as the earliest occurrence time.
  • 33.  The late occurrence times for these nodes can be simply determined as Li = Lj − D(i, j)  In case if multiple arrows reaching same node,  Li = Mjin[Lj − D(i, j)], where the minimization is over all nodes j that precede node i.  for some events (nodes) in the network, the two values (E and L) will be the same if the latest project completion time is taken as the earliest project completion time.  These events are called critical events and the path is called critical path.
  • 34. FLOAT OR SLACK TIME  The time period by which an activity can be delayed without adversely affecting project completion.  Total float in an activity Total float of an activity is the amount of time by which the start of the activity may be delayed without causing a delay in the completion of the project. This is calculated as TF(i, j) = LST(i, j) − EST(i, j) Or TF(i, j) = LFT(i, j) − EFT(i, j) The values of TF(i, j) calculated from above equations are referred to as start float and finish float respectively.
  • 35.  In terms of event times, the TF(i, j) can be defined as the late occurrence time Lj of the succeeding event minus the early occurrence time Ei of the preceding event minus the duration of the activity defined between these events. Thus, TF(i, j) = Lj − Ei − D(i, j)
  • 36.  Free float Free float is the amount of time by which the start of an activity may be delayed without delaying the start of a following activity.  Free float is defined as the earliest occurrence time Ej of the following event minus the earliest occurrence time Ei of the preceding event minus the duration of the activity defined between these events.  Free float for an activity (i, j) is denoted by FF(i, j) and is calculated from the following expression: FF(i, j) = Ej − Ei − D(i, j)
  • 37.  Independent float Independent float is the amount of time by which the start of an activity may be delayed without affecting the preceding or the following activity.  Independent float is defined as the earliest occurrence time Ej of the following event minus the latest occurrence time Li of the preceding event minus the duration of the activity defined between these events.  Independent float for an activity (i, j) is denoted by IF(i, j) and is calculated from the following expression: IF(i, j) = Ej − Li − D(i, j)
  • 38.  Interference float: It is defined as the difference in total float and free float. In other words, Interference Float = TF(i, j) − FF(i, j) Critical Path: The ‘critical path’ is defined as one that gives the longest time of completion (of the project).