Critical Path Method

THE CRITICAL PATH METHOD (CPM)…
CPM basically is a technique that separates planning and scheduling. It
also clarifies the inter-relationship time and cost.
CPM evaluates all the possible alternative plans for project and
associates each plan with a schedule.
It is a technique for finding the ordered sequence of all the activities
forming a project so that the project is completed on the shortest possible
time coincident with the lowest cost.
Each possible plans established by listing every activity related to the
project. Then their inter-relationship is established in step by step order by
drawing an arrow diagram to show what must precede each activity.
What must follow it and what can run concurrently with it

In CPM, each arrow represents a job capacity. It has no dimension but
shows the direction of the time work flow for the activity (time flows from
the tail of the arrow to the head) for each plan, the cost related to the
duration. As the pace of a project is forced, its cost will rise. Conversely, if it
is allowed to drag, the cost will rise again because of continuing overhead
expenses.

ARROW DIAGRAM FOR SMALL BUILDING
6 EVENT NUMBER 25 ACTIVITY DURATION ---- DUMMY ACTIVITY
(finish and clean up
cannot start until the walls
have been insulated)
CRITICAL PATH ACTIVITIES(dark arrow)---------- (as shown it will take 51
days to complete the building)

1. Planning the CPM
In preparing CPM, the contractor is required to perform the planning
phase since he is the only knowledgeable about his cost and methods
of doing business in the best possible time for the best possible cost.
There are Five inputs which can be produced:
A. A NETWORK (arrow diagram) defining the activities in the project.
B. DURATION estimates of activities
C. COST estimates of Activity for Cost Monitoring and Cash requirement
Calculation
D. RESOURCE ESTIMATES for resource requirement calculations such as
men money, materials and equipment. The schedule produced for a
project assumes that enough manpower and equipment is available to
get the cities done

E. TRADE (Responsibility) INDICATORS for activity grouping such as
subcontractors.
Subcontractor is primarily concerned with activities appear in their
order of sequence as the structure is put together – and those responsible
for various activities throughout the project must review the schedule to
determine when they must act.
A. THE NETWORK (arrow dia.)
is usually arrived at by all persons who have anything to do with the
project. All subcontractors and suppliers should be asked to review the
network carefully to make certain that the activities pertaining to their
work is accurately and realistically described.

ELEMENTS OF NETWORK DIAGRAMMING
NETWORK INTERPRETATION
Activity B cannot start until the job A is
completed.
The no. at the tail of any arrow must be
less than the no. at the head arrow
Activity C cannot start until both job A
and job B are completed
Activity B and activity C cannot start
until both job A and job B are
completed

Both activity A and B must be
completed before jobs C and D can
start.
Both jobs A and B must be completed
before activity C start.
Job D depends only on job B, and not
on job A(E, here is called DUMMY)

In the CPM, Scheduling the wall footing may be done by phases and the
activities involved are well defined as to what come first and what can
be done simultaneously.

1. EVENTS:
an event is a point in time signaling the beginning or end of one or
more activities. It is the point which denotes the completion of all
preceding activities and the beginning for all succeeding dependent
activities.

NOTES:
a) Keep in separate classification activities performed by different tradesman such as
plumbers, carpenters, masons etc.
b) Divide the project with respect to its structural elements. For example, the roof
assembly would be separated from wall construction, which in turn would be separated
from the foundation.
c) Divide the contract for assignment of responsibility. As an example, the painting sub-
contractor’s activity functions shall not be lumped with that of the resident flooring sub-
contractor.
d) Work for similar nature performed is different locations throughout the project should be
considered separately as should these operations performed at the same time but at
considerably different locations within the project.
e) It is required that all numbered activities be grouped in a line with one of the numbered
phases. It does not, however, follow that all activities which fall on the line with a
particular phase start at exactly the same time.

As long as they finish at the same time within 15 days.

2. DUMMY
“not more than one activity may have the same Even Number”
It is sometimes necessary to use a “Convector” type of activity that
doesn’t really represent work, but merely helps to observe the rule
stated above. This type of activity is usually referred to as a “Dummy”
this special activity is drawn dotted line and indicates that no work is
involved in that activity. The dummy involves no duration and no cost. It
serves only as a dependency connector or sequence indicator.

A rule one must follow is that every number must be used and the
number at the tail of any arrow must
COMMON ERRORS
1. WAGON WHEEL
Here you can start set forms only when pre-fabrication of forms is
finished. A dummy is made from 3 to 4 since you cannot start to set
the forms if layout and excavate is not finished.

2. WATERFALL ERROR
The error here lies in the fact that as shown, pour cap, Bent #4
cannot start until after pour footing bent #3 has been completed.
The dummy 15 to 16 cannot occur until 13 has, because of the
dummy from 13 to 15.

b. Duration Estimate
This stage requires the planner to estimate the amount or time that will
be necessary to complete each activity. The simplest way to make the
duration estimate is to determine to “normal’ amount of time needed to
finish the activity with normal sized crew or with the normal amount of
equipment.
Start with the longest duration for each activity and then ‘speed up”
those that will shorten the project.
Duration estimates are made on an individual basis. No consideration
of often activities can be made. The duration estimate is used to
calculate the schedule for a project. It is also used to find those activities
that are controlling the amount of time needed to get the project done.
These are the critical activities and collectively they make up the
“CRITICAL PATH”.

 CRITICAL PATH
The critical path is the longest path in time through the Network. Since these critical
activities are added to determine the total duration of the project, and delay of one of
these activities will proportionately delay the job and conversely any speed up will
decrease the total duration time.
duration 10 days
duration 10 days
(4 days delay)
duration 10 days
(2 days advance)

Path 1 – 2 -4 -7 has a total of 24 days
Path 1 – 5 -7 has a total of 18 days
Path 1 – 3 -6 -7 has a total of 32 days
This then is the CRITICAL PATH, the longest number of days and is the path controlling the projects
length.

Activity 6 to 8 cannot start until activity 2-6 and 3-6 are completed. This critical path longest
duration of 30 days is activity 1-3-6-8-10.
If it is required that the amount of time needed to complete the project be shortened, these
are the activities upon which to concentrate. Non critical activities are strictly dependent
upon the completion of the critical items, so spending up non critical activities is of no value at
all, in terms of project duration.
Since the critical activities are usually less than 30 of the total activities, a large percentage of
the activities in a project have extra time available since they are, in a waiting for the critical
items to be completed.
An important point to keep in mind when using PERT/CPM is that there is not necessarily only
one critical path. There may be several
c. COST ESTIMATES
Time and peso estimates- A necessary part of the project network is the assignment of time
and pesos for each activity displayed. These ingredients are the basis of calculations to
determine when the project will be accomplished and what the total direct cost will be. It is
important that at these time and pesos estimates be as accurate as possible, and made by
persons responsible for the individual task.

When reducing the time required for a
project from normal to crash, the cost will
usually increase.
Two estimates are required for PERT/CPM
1. time and money, it would take to do the activity under normal work and
manpower conditions.
2. time and money it would take to do the activity on a crash basis or in a shorter
than normal time.

d. RESOURCES ESTIMATE
It is important that all parties concerned with the development and approval of the
construction network be aware that the PERT/CPM which indicate completion within the
specified time can become very meaningless if the resources to implement the plan are
not available. Imagine if you require 4 painters to paint the exterior in three days but
become aware that there are only two paint brushes available.
In addition to resource consideration at the beginning of the project, particularly the
optimum loading and leveling of manpower, the contractor must continually review the
plan to detect significant changes which could prudently require immediate re planning
and reallocation of resources. He may wish to hire more men, order overtime, change the
priority of work, or bring additional equipment to the site.
having the network as a guide for interpreting the relative importance of the activities
and their resource requirements assist the field supervision in making maximum use of its
available manpower. Thus, the tendency to continually shift men from one job to another,
from one foreman to another, is lessened and this result in greater labor productivity and
lower labor cost.

The assignment of peso values and costs to the various activities on the network produces
several benefits:
1) It will allow the contractor to quickly produce a projected cash flow analysis, showing
the expected rate of expenditure and income.
2) If the peso value portion is made available to the owner or contracting agency, it
provides a projection of expected progress payments;
3) If the peso value portion shows both the curve based on the earliest start of each
activity and the curve based on the latest start of each activity, the owner can make
a decision concerning the optimizing of funds, utilization, interest minimization and a
related realistic schedule determination.
The role of resources – men, money, materials and equipment – is of major importance in
the determination of a meaningful construction plan and realistic construction schedule.
The schedule produced for a project assumes that enough manpower and equipment is
available to get the activities done as schedule.

In a project of average size, several hundred activities can be expected. The actual
performance of these activities, however, will be the responsibility of several different
individuals activities affecting his portion of work, and will not necessarily be very much
concerned about the general contractor’s relations with concrete supplier.
In the produced schedule, the individual activities appear in their order of sequence – as
the structure is put together – and those responsible for various activities throughout the
project must review the schedule to determine when they must act. On the same day,
activities will probably be scheduled involving several subcontractors and suppliers.
it is desirable to be able to single out all the project’s activities in such a way that all the
activities for a subcontractor, for example, can be grouped. This is the purpose of the
Trade Indicator – here again the computer can act easily on this question. In this way, an
electrical sub-contractor or need not made through all activities in the project, but could
quickly and easily find all the activities for which he is responsible.

II. SCHEDULING
The three most important aspects of any projects are :
1. The over all length
2. What the immediate problems are
3. What might occur in the near future to cause delay
A. CRITICAL PATH – the project is now in network form and it contains a time estimate for
each activity. The next step is to determine the total amount of time required to complete
the project. This is determined by tracing each on the network, adding up the times of the
activities and making the path which takes the longest elapsed time. The longest path is
the “Critical Path”. Since the project cannot possibly be completed until the path is
completed. The activities on this path are in turn, the critical activities of the project and
any delay in their completion would result in a stretch out of the project. There may be
more than one critical path.

Activity 6 to 8 cannot begin until activities 2 to 6 and 3 to 6 are completed. These activities
portray the availability of a construction crew and receipt of necessary false work before
construction begin.. This may not seem a difficult problem but suppose this crew and false
work were utilized in another phases of the project a phase lagging.

B. SLACK OR FLOAT
Float – used by CPM system
Slack – used by pert system
A term for those activities which do not fail on the critical path. These activities have
scheduling leeway that can be used without adverse effect on the project.
As shown in the previous figure, the longest time from event 1 to 6 is thirteen weeks. The
difference in time between path, 1-3-6 indicates a total leeway of three weeks in path 1-2-
6. this “float” available may or may not be attributed to any one activity in this path but
can be divided equally or assigned to any of the activities on this path.
It can be seen, therefore, that event 2 can be accomplished
as early as 6 weeks from the start of the project, but also as
late as 9 weeks, and still not become critical or cause delay
of event 6 the men, material, equipment and money tied up
in these activities then become resources from which the
project manager or supervisor may draw to improve the
condition of the critical path activities.

C. SCHEDULE ANALYSIS
as the computer is producing the range of schedules, based on the activities time cost
data, it also stores all of the necessary information for each activity processed, when the
PERT/CPM user has selected the schedule. These details would indicate when each
activity was to start and finish in order to get the project done in the time allotted.
EARLY START – is the earliest point in time that can activity can
start. that all activities before it have been finished, this is not
necessarily the point in time that the activity will start; it is,
however the earliest time that it can start, if the network has
been correctly drawn.
EARLY FINISH – is merely the duration of the activity after its early start. This is not necessarily
the point in time that the activity will be over. A “finish” date in PERT/CPM is defined as the
first day upon which no further work is to be done for an activity. It is then the first day after
physical completion of the activity.

LATE START – It was pointed out that many activities can stand by until the critical acitivities
are finished. However, there is a limit to the amount of time these activities can be
ignored. The limiting point in time is called the activity must start if the project is to get
done in time.
LATE FINISH – is the date that the activity must be finished if the project is not be delayed. It
is the duration after the LATE START. It also the day after the physical, completion of the
activity.

For NON-CRITICAL activities, there is a difference between the earliest starting date and
the latest. This difference is called FLOAT
Two types of float”
a. FREE FLOAT
D, E and F is the CRITICAL PATH B starts when A is completed after 4 days C starts when B
is completed after 10 days B and C had not free float since they have early starts.
F can only start when (E) is finished which is after 20 days. So the non-critical activities of
ABC or 14 days and Activities of D, E or 20 days has given Activity C a FREE FLOAT of 6
days.

b. TOTAL FLOAT
Is the amount of Float that is shared by all activities on a non-critical path.
the 6 days float in the example above is shared by activities A, B, and C if the activity A
which is 4 days only uses the float, it becomes 10 days when activity B and C becomes
critical activities.

Critical Path Method

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