Ihab Saad – Tegrity Lecture Arrow Diagramming Method
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Welcome to another class in construction scheduling, and today
we're going to start talking about one of the scheduling techniques,
which is the activity on arrow, also known as Arrow Diagramming
Method. So sometimes it's referred to as AOA activity on arrow, or
sometimes also referred to as ADM Arrow Diagramming Method. So
what's the Arrow Diagramming Method? How does it work? What are
these calculations? This is basically what we're going to be
discussing in this lecture. We're
going to have an introduction to what this scheduling technique is
and what's the advantage of the scheduling technique. We're going
to talk about the network diagram and some common issues related to
its use network calculations, which is basically used to
establish the dates for the network. And then we're going to
discuss another elaboration or another iteration in improvement
of scheduling techniques, which is called the time scaled network.
And then finally, we're going to talk about units of time.
The activity on aeronnetwork is the first developed networking
method. We started talking about scheduling techniques. We talked
about a checklist, basically write down all the activities that you
need to do, and it's not necessarily in order. It does not
show any dependency among these activities, and it does not show
any duration for these activities. So it's just a matter of listing
the activities, and once you've done each one of them, you check
it with a check mark. So at the end, it can be used as a planning
tool and as a control tool by looking at the checked activities.
But again, as you can see, the drawbacks of this technique. It
does not show duration, does not show dependency or order of the
activities. Another technique was the Gantt chart, or the bar chart,
which was a great development, because now it showed in a
graphical format, the different activities, which showed on two
axes, a vertical axis showing the activities, and horizontal axis is
a time line, showing when does each activity start and finish. So
you can trace a bar or a line representing the duration of the
activity. So the activities are drawn in a scale that shows their
relative duration, however, and that's that technique, by the way,
is still very commonly used today in construction projects and any
other project as well. The main drawback of that technique is that
it does not show the dependency among the activities. Yes, it
shows when each one should start and when each one is expected to
finish or plan to finish, but it does not show what the
interrelationship among these activities? What if one of them
was delayed? How is that going to affect the others? That is not
shown on the Gantt chart? Trying to do that, as we're going to see
by the end of this lecture, by adding links might create
something that's really hard to to read. So someone started thinking
about a new graphical method of representing the activities. How
are we going to develop that schedule? And they started
thinking about the flow of water, for example, from the source until
it reaches your house, how it goes from a large plant through a
smaller one, through pipes and popping stations and so on. And
these pipes start branching from a main pipe to a secondary pipe,
until they reach the very fine pipes that are in your house. And
then finally, once this water is used and you need to collect it
back the used water, it's done in a reverse way, again, from smaller
pipes to larger ones, until they reach the sewage treatment plant.
So we have junctions, we have pipes, we have connections, and
they show the dependency. If, for example, there's no water in this
pipe, then the following one's not going to have any water either. So
the activity on aero is the first developed networking method, like
a network of water distribution or collection. This is basically what
we have. It's also called the IJ, or Arrow Diagramming Method. Why
is it called the IJ? Because each activity is going to be
represented by two nodes, the start node of the activity and the
finish node of the activity, and the activity itself is going to be
the line, or the arrow connecting between these two nodes. So in
this case, the activity is going to be represented by a node i,
representing its start, and a node j, representing its finish. And
the activity itself is ij, the line that bridges between these
two nodes. Each activity is represented by an arrow spanning
between two nodes representing the start and finish events of the
activity.
So the activities are linked from the finish of one activity to the
start of
the next one through a node. Therefore the finish of one
activity, the node representing the finish of one activity, is
exactly the same as.
Is the node representing the start of the activity that follows it.
So activities are stated on the arrow. The name of the activity,
or the description of the activity is going to be mentioned or
written on the arrow, so we know what activity ij means. Nodes have
no duration and use no resources. The node is just a date. It does
not have a duration. It's an event. This is the start event.
This is the finish event. The i node marks the beginning of the
activity, whereas the j node marks its completion. And the network
always remember that very well. The network always flows from left
to right. Therefore, even if you have in these nodes numbers, let's
say node three, five or 712, or whatever. The number itself does
not mean anything. It's just a matter of order. And you can have,
for example, the numbers in reverse order or any other order,
as long as we know that the network flows from left to right.
This is how we read the network as we are progressing. So here, for
example, we have the node i, we have the finished node j, and the
arrow, or the activity itself, representing
whatever description that might be. And underneath the arrow we're
going to put the duration of that activity.
J should be bigger than I when we're talking about dates, then
this date is going to be later than that one or sometimes it
might be the same date as we're going to see very shortly.
Activities are related to each other through nodes. Activity
2030, cannot start until activity 1020 is complete. Here, for
example, we have activity 1020 which is also known as activity A,
and activity 2030 which is also known as activity B. Activity A
has a duration of five days, B has a duration of 10 days. What if
activity 1020 or a has not started, then definitely 2030
cannot start either. So we say in this case that activity 2030
depends on activity 1020,
now can there be more than one activity depending on one? Yes. So
for example, we can have a starting node, node 10, and from
this node we have three activities starting at the same time. So
these activities have the same start date, but they might have
different finish dates. Activity A is going to finish on day 5b, is
going to finish on day 10, and C is going to finish on day 12. So
all of these started from the same node. Similarly, several
activities can merge into one node as well.
So when two or more activities merge into a node, here we have,
for example, activity, 2040, 3040, and 4040,
of course, there should be that. That's a probably a typo. We
should have put here 50 instead of 40, because you should not have 40
and 40 as the start and finish of the same activity. So this is a
typo. This should be either 4050, or 5040,
once the dependencies have been established among the activities
and network diagram can be constructed. That's why the first
effort is not going to be to draw the network. The first effort
first is going to be to analyze the activities, to define what
these activities are, and then to start thinking logically about
their dependencies and about their order of occurrence. Once we have
established that, we can start drawing the network,
the former activity is called a predecessor or preceding activity,
whereas the dependent activity is called the successor or succeeding
activity. So in the previous examples, for example, we had
three nodes, 1020, and 30. Activity. 1020
is a predecessor to activity 2030,
or is also called a preceding activity to activity 2030 and also
activity 2030 is going to be called a successor to activity
1020 or a succeeding activity to activity 1020 so from now on,
we're not going to say the activity before or the activity
after. We're going to use the new lingo, which we're gonna represent
it as either predecessors and successors to a certain activity.
A network should start with a single node and end with a single
node. That's another convention of drawing the network like it flows
from left to right. Another issue here is that it's gonna have one
starting node and one finishing node. So we're going to have
several activities, maybe merging emerging from one node, and
several activities merging into one node at the end.
To look at an example here, activity on arrow network
dependency. So what we have, what you as a project manager, do, is
develop.
Is, and putting them in the logical sequence is looking at
determining the activity resources, what kind of resources
are going to be needed, and the availability rates of these
resources. So these resources can be material, can be equipment, can
be subcontractor, or simply, can be money that's going to pay for
all of the above,
once we have developed the resource pool and the resource
availability, now we can establish a duration for each activity. And
the duration for the activity is going to be very simple. That's
going to be one universal equation used to determine the duration of
the activity. And that's a very simple equation. It's Q divided by
p or q over p, q is the quantity of work for that activity, and P
is the production rate of the resources used in the activity.
What if one activity has more than one resource with different
production rates? The slowest resource the one
with the lowest production rate is going to be the control effect.
So if, for example, I have to place concrete, and placing the
concrete is going to involve mixing the concrete and the batch
plant,
transporting the concrete to the construction site,
pouring the concrete into the bucket of a tower crane, lifting
the concrete to the seventh floor and then placing that concrete
through a group of personnel of people later.
Now, the production of the batch plant can be 200 cubic yards. An
hour of these 200 cubic yards, I can only transport 50 cubic yards.
An hour of these 50 cubic yards an hour, I can only lift
with the tower crane 30 cubic yards an hour. Of these 30 cubic
yards, I can only place and finish 20 cubic yards an hour. Therefore,
we have seen several resources with different production rates.
The controlling production rate is going to be this the lowest one,
the 20 cubic yards an hour. Therefore, if I have 100 cubic
yards to place, it's going to take five hours. 100 divided by 20,
that gives five pounds. So that's going to be the duration of the
activity. Once we have established the durations of the activities.
Now we can start talking about network calculations and the
dates, when should the activity start? When Should it finish? And
so on and so forth. So the objectives here are going to be to
calculate the duration to establish what's called the
critical path, which is, I'm just going to give you a heads up here,
the definition of the critical path is the longest continuous
path through the network. Listen to the two critical words here,
longest and continuous. It has to be, it will be the longest path,
and it has to be a continuous path through the network. And then
we're going to talk about the activity float. We're going to
define what float is. And then talk about two different types of
floats, total float and free float. The calculations are going
to be done in two phases. One is going to be a motion from left to
right, from the beginning of the network to the end, which is going
to be called following the natural flow of the network. Therefore
it's going to be called forward pass. And then once we reach the
end of the network, we're going to go back to the beginning, so we're
going to be retracing our steps backwards, and that's going to be
moving from right to left against the flow of the network. And
that's going to be called the backward pass. The combination of
the forward pass and the backward pass is going to give us the
network calculations to calculate the different dates for the
different activities.
Let's talk about the forward pass. The forward pass establishes the
early start and the early finish dates of each activity and or the
early node times for each activities. Remember, we mentioned
that the nodes represent dates, events, start, event, finish,
event, and each of these events has a date.
So
the earliest start, which means the activity cannot start any
earlier than that,
and the early finish, sometimes also called earliest finish, means
that the activity cannot finish any earlier than that.
So to calculate the early dates, te
i is the early time at the node i of an activity ij. So we have an
activity ij, which is in this case, 3743
so Tei is the earliest time activity, 3743
can start the earliest time event. I, which is 37 can happen. And
similarly, Tej is the earliest.
Possible time for that activity to finish, or the earliest date at
node 43
looking at this network here, we have several activities, several
predecessors to this activity,
and we might have different dates coming to these activities.
So, for example, I have activity 2237
activities 2737
and activity 3237
each one of them might be ending at a certain date.
However, for node 37 to start.
I have to wait for all the predecessors to happen. So if, for
example, this activity here ended on day 10 and this one ended on
day 12 and this one ended on day 14, I cannot start this one at day
10 because these two are not done yet. I cannot start at day 12
either, because this one has not started again and has not finished
yet. So I have to wait until day 14 for all of these to be
concluded in order to start this following activity. Therefore the
earliest start date for node 37 in this case, would be day 14.
If the duration of this activity is five days, then the finish is
going to occur five days after the start. If the start was 14, then
the finish is going to be day 19. It's as simple as that, very
simple math.
So the whole trick here is that when we are talking about the
earliest start is going to be the latest date of
completion of the predecessor activities again, 1012, and 14. We
have to start with 14.
The early start of activity. JK
is going to be basically the same as the finish of activity. Ij,
the early finish is going to be the early start plus the duration.
So what we said here, this is the early start. There's a duration
here, five days. So the early finish is going to be early start
plus duration.
Now, talking about the forward pass, the forward pass establishes
the early start and the early finish. The early start is going
to be designated as es, and the early finish is going to be
designated as EF, dates for each activity and or the early node
times for each activity. It's basically the same thing. So Tei
is the early time at the i node of an activity ij, and Tej is the
early time at its j node.
As we mentioned here,
Tej maximum is equal to the early finishes of all the activities
that terminate at node j. So here, for example, if we have several
activities, then this is going to be the latest of all of these
dates.
The TE of the first node of the network should be zero. So the
start of the network is going to be at Day Zero, not day one. One
of the common mistakes is to start at day one. We're always going to
start at day zero, where nothing has been done. All the
relationships among activities are finished to start. There's no lag
or delay, which means activity 2030, cannot start until activity
1020 has been fully complete. That's one of the drawbacks of the
Arrow Diagramming Method, as we're going to see.
So again, now the same network that we have drawn, what I want
you to do is to add durations to this network and to start, solving
for the early start and the early finish of the different
activities.
And here's an example.
So here we have activity, 1020,
2100,
2050,
1040, and so on. Each activity has a name. So this is activity A,
activity e, activity f, and each activity has a duration. The
duration is going to be underneath the arrow, so activity 1020, or
activity A has a duration of 10 days. Notice that we have some
dummy activity. So we have here, for example, 2050, is a dummy
activity. Therefore we did not put a duration, since the duration is
going to be zero, same here for 9100, and same for 6070, any
activity that does not have a duration is going to be denoted by
a dotted line or dashed line, and that means it's a dummy activity.
Now looking at the calculation.
Here we're going to put a zero at the start of all of these three
activities. So zero at node 10, which means zero at 1020 zero at
1040, and zero at 1030,
at the node 20, we started with zero, and we have a duration of 10
days. Therefore the early finish of activity 1020, is going to be
day 10, which means that at node 20, the date is 10, which means
that any activity that starts after node 20 is going to start
with 10. So here 20 100 is going to start on day 10, and so would
activity 2050,
activity 1040, has four days of duration. Therefore zero plus
four, we're going to have four at the end of node 40
and activity 1038,
days duration. So basically, we're going to have a an early finish of
day eight. Therefore we're going to start here with eight plus 14.
That's 22 we're going to have 22 here and here, 22 plus four,
that's 2622
plus zero, that's 22 and so on and so forth.
I'd like you to keep doing this, noting that if I have two dates on
coming to a node, I take the larger number.
So here we have two merging activities. Here we have two
merging activities. And so we have here, here we have four merging
activities. So the completion of the project at the end after node
110 is going to be the largest number coming from all of these
four activities.
And this is going to be the forward pass that's going to give
us the early dates of the activities to reverse that we're
going to do the backward pass. The backward pass is the exact
opposite of the forward pass. Whatever we did in forward, we're
going to reverse in backward. So in forward, we move from left to
right, adding the durations of the activities.
And in case we had two activities merging into one node, we took the
larger number
on the backward pass, we're going to do the exact opposite, starting
from right to left, subtracting the durations of the activities.
If two numbers merge into one node in the backward pass, we're going
to take the smaller number to proceed backwards. So the backward
pass indicates the earliest dates on which each activity can be
accomplished.
The backward pass provides the late start and late finish dates
for each activity without affecting the overall duration of
the project. These dates are used in conjunction with the early
dates to determine the criticality of each activity and its float, if
any, as we're going to see in a moment.
So the backward pass begins at the terminal or last activity works
backward toward backwards toward the beginning the late finish,
which is the late time at the no K node of activity, JK, the late
start is going to be late finish minus duration, the opposite of
what we did in the forward pass.
The late date at node k is going to be the minimum of the late
starts of all activities following the node k. So if we have two
activities merging into node k, we're going to take the smallest
number, smaller number, and that's going to be transferred backward
the TL, the late dates of the last node of the network should be
equal to the TE of the last node. So if we started the network with
zero in the forward pass, we should end with zero in the
backward pass. That's basically what it is.
We're going to find that some activities have
the same dates,
and some activities have different dates. We're going to see that in
a in a numerical example, in a moment.
So for example, if activity just looking at the numbers, if
activity 5070,
had the start date of
early, start of 15, duration of 10 days, early finish of 25 remember
these numbers 15 and 25 early start, 15, early finish, 25 in the
backward pass. However, we got a different number. We got an early,
late finish of 28
duration, is still 10. Therefore the early start is going to be 18
in the forward pass, it was 15 and 25 in the backward pass, it was 18
and 28 so what we're saying here is that activity, this activity,
can start as early as day 15
or as late as day 18. It can start any time in between these two
days. If it starts on day 15, that's fine. If it starts on day
1617, or 18, that's fine. The project's still going to finish on
time. Therefore, this activity has some flexibility, or some leeway,
and that leeway or flexibility.
We usually call float, or to be more accurate, total float. To the
total float is the leeway or the flexibility, and it's the amount
of time by which a non critical activity can be delayed, without
delaying the project completion. Why are we saying noncritical?
Because, again, if that activity has this flexibility is not
critical. Therefore, what is a critical activity? A critical
activity is one that has the exact same days. The early start is 15,
the early finish is 25 the late start is also 15, and the late
finish is also 25 so looking at the total float, in this case,
it's zero.
It has to start on day 15 has to finish on day 25 in order for the
project to be completed on time. Therefore we call this activity
critical. Therefore the definition of a critical activity is an
activity that has zero total float.
The free float, on the other hand, is a subset of the total float,
which means it can never exceed the total float. It's part of the
total float. A part can, at its maximum, be equal to the whole so
at its maximum, the free float can be equal to the total float, but
it cannot exceed the total float. Therefore, the free float is the
amount of time look at the definition of total float and the
slight difference with free float.
In case of total float, we said amount of time a non critical
activity can be delayed without delaying, the project completion.
In case of free float, we say it's exactly the same first line,
amount of time a non critical activity can be delayed without
delaying. And here's the difference any of its immediate
successors. We're not looking as far as the completion of the
project. We're just looking at the following activity, the immediate
successor. Is it going to be delayed by the delay of this
activity or not? If it's going to be delayed, therefore the free
float is zero, even if the activity has total float. If it's
not going to be delayed, then in this case, the free float has
certain positive value.
The free float, by the way, can never be negative. The minimum
free float is zero. The maximum is going to be the exact amount of
the total float.
So for the calculations, again, the total float is equal to the
late finish minus the early finish. Or it can also be equal to
late start minus early start. So it's always late minus early at
the same end of the activity. If we look at the start side, it's
late start, minus start minus early start. If we look at the
finish side, it's late finish minus early finish. Free float, on
the other hand, is equal to the earliest, early start of the
activity, minus of the success of the successor, minus the early
finish of the activity. So, for example, if our activity has an
early finish of day 25
and the early start of its successor is day 28 How come?
Because there was another activity that ended on day 28 and merged in
the same node. So now we have two activities, one, finishing on day
25 one finishing on day 28 merging in the same node. When should the
successor start? We take the larger number. So we take 28
therefore for the first one that ends on day 25 it has three days
of free float by which it can be delayed without delaying the start
of its immediate successor. That's how free float works.
There's something called interfering float. We're not going
to focus on it, on it too much. It's basically the difference
between the total float and the free float. It's that simple. We
are not going to address it at all. I just wanted to inform you
about it, so if you read about it or hear about it somewhere else,
it has pretty much no practical use, something called the
interfering float.
Now, with the same exercise that we've done before, I'd like you to
draw the network.
We have the dependencies. In the third column, we have the
durations. And now I'd like you to calculate the early start, early
finish, late start, late finish. Total float, free float and
interfering float for that network. So what you're gonna do
after drawing the network and make doing the calculations, you're
gonna draw the table, and in that table you're gonna add these seven
columns, early start, early finish. Late start, late finish.
Total float, free float and interfering float.
Now let's start looking at some of the limitations of the activity on
arrow networks. One of the major limitations that it shows only one
type of relationships, which means one activity has to finish for its
successor to start. You cannot have a lag. You cannot have an
overlap between the activities. Therefore, it's all finished to
start.
And the issue of dummy activities sometimes it might be a little bit
confusing if you're not used to it. So.
So these are some of the limitations, or the main drawbacks
on activity on arrows. And by the way, activity on arrows are no
longer used on a large scale, as we're going to see later on in the
next lecture about another scheduling technique, another type
of networks. This is the one that's more commonly used, but you
have to learn about this one to be able to do the other one as well
as we're going to see that the calculations are pretty much the
same.
The question now is, that's a very important question, by the way.
It's both a legal question and a technical question. Who owns the
float? So if we say that an activity can be delayed by three
days or five days or 10 days, who can delay it? Is it the owner? Is
it the Arctic engineer? Is it the construction manager? Is it the
general contractor? Is it the subcontractor? Is it the supplier,
who can delay the activity, or basically, who can utilize, or who
can use this float?
The second answer is it's on a first come, first served. Basis,
whoever needs it first can use it first,
but each time you use part of the float, you leave less for someone
else. So if, for example, the activity has 10 days of total
float the owner used three, then for all the other parties that are
left, we only have seven days. If the engineer uses four, then we
have only three remaining days. If the contractor used one, then we
have only two days left for subcontractor, suppliers, etc.
So the ownership of float should be carefully examined in every
contract for equitable risk allocation, we're going to say
that the float is a shared property, and it's a property of
the project. Any party involved with the project can use the
float, as long as we still have some of it,
an example of contract provisions.
So the general statement is that the project owns the float, unless
otherwise stated in the contract. Here, for example, is a is an
example contract provision or clause float, sometimes referred
to, also as slack, is defined as the amount of time between the
early start date and the late start date, or the early finish
date and the late finish date of any of the activities in the
schedule float is not time for the exclusive use or benefit of either
of the owner of the contract. Extension of time for performance
required under the contract clauses entitled changes differing
site conditions, termination for default damages, for delay time,
extensions or suspension of work will be granted only to the extent
that equitable time adjustments for the activity or activities
affected exceed the total float or slack
in simple English, the owner is Not going to grant you any
extension of time as long as the activity has flowed,
the owner is only gonna grant you an extension of time if the full
float has been consumed and the activity has become critical, and
that was the fault of the owner or any of his agents. In this case,
the owner is gonna give the contractor an extension of time.
However,
if the contract has been delayed, the activity has been delayed, and
therefore the project has been delayed due to an error of the
general contractor or any of his agents, then in this case, the
owner is not going to give the contractor any extension of time.
On the other hand, the contractor may have to pay liquidated damages
for the delay to the project.
Some contractors submit late start time, thus hiding part of the
float for their own use. So basically, the contract would have
several versions of the same schedule. On one version, they
would give the owner that this activity is going to take 10 days
to finish
on the inside for their own internal use. They know that this
activity is going to take only six days, so they have embedded four
days of total float inside the activity without showing it to the
owner. It is legal, but slightly unethical.
Now, based on the
Arrow Diagramming Method, someone said, Okay, why not add
lines to the Gantt charts showing because we mentioned that the
Gantt chart, or the bar chart, does not show dependencies. So
someone thought, why not show the dependencies through lines
connecting the activities, as we did with the network, and that
should solve the issue. Now we have a graphical representation
drawn to scale. By the way, the network is not drawn to scale, so
the length of the arrow does not represent anything whatsoever. You
can have two activities with exactly the same.
Length on the arrow with two totally different durations, but
in the Gantt chart, they are drawn to scale. So the time scaled
network is a time scaled diagram combining the principal features
of the bar chart and the activity on arrow diagram. The bar chart
that shows the activity is drawn as a bar with a relative length
drawn to scale and the aspect from the activity on arrow showing the
links or the relationships between the activities.
The problem is that once you have a
500 schedule,
500 activity schedule, which is a relatively medium sized schedule,
it's going to be impossible to navigate through the lines. It's
going to be a big spaghetti bowl. The project is plotted on the
horizontal time scale with arrows vectors and nodes representing
activities, and with Arrow lengths representing time. That's the
difference between time scale and arrow. It's seldom used due to its
illegibility for complex projects. Once again, you get to a complex
project, it's very hard to read. That's how it looks. So basically,
we have a time scale like the the Gantt chart, and we have the nodes
like the Arrow Diagramming Method, and then we have here the links
connecting the activities and so on. So again, here we have made
basically about what seven activities. Imagine if that were
500 activities would be totally impossible to read it, especially
when the lines start intersecting and things like that.
That's another representation of that time scale network. And
again, once you have so many activities, going to be really
hard to read it.
For someone who might consider it advantageous over the Arrow
Diagramming, it shows the activity sequence and order and it shows
the relative duration of the activities. The project plan and
schedule can be shown together graphically. Project progress can
be represented graphically as well.
Disadvantages, use of dummy activities may be cumbersome, not
easily modified, very awkward for large and complex projects, and
still allows for only one type of relationships, which is finished
to start. And that's the main drawback of Arrow Diagramming that
so we did not solve it in the time scaled diagram. Therefore, we are
not going to worry at all about the time scale network. We're not
going to discuss it any further. We're just going to put an end to
it right there.
Now, if you want to go through the exercise and draw the timescale
network to see the interaction among the lines linking the
different activities.
And now we come to another sort of a philosophical discussion that
has very practical implications on our schedule,
the units of time. The units of time depend on the type of the
project.
In most of the projects, especially construction projects,
the minimum increment unit of time is going to be a day. Therefore
we're going to say that this activity has a duration of seven
days, nine days, 21 days, etc. However, on some
very unique activities or some very unique projects, you might
have the duration in minutes or in hours rather than days,
especially if the project has a very short duration, or in case,
the liquidated damages are very high. To give you an example
for the resurfacing of the main runway at O'Hare Airport, and
that's a project that took place several years
ago. O'Hare Airport is one of the busiest airports in the world.
The contractor you cannot shut off the the whole airport just to
surface, resurface the the runway. So it was divided into segments,
allowing for parallel runways to be operating temporarily until you
fix the main one. The contractor was given
14 days to finish the project, and
the contractor was only allowed to work from midnight to 6am where
the traffic is less dense than the rest of the day.
The liquidated damages for that project were $25,000
an hour. So if the project is late by one hour, the contractor pays
$25,000.02
hours, $50,000 so imagine the contractor cannot plan based on
days. A day is too long. A day is 25 times six hours. That's 150,000
hours. That's $150,000.06
hours, because they only work six hours from midnight to 6am
you cannot even schedule by the hour, because, again, $25,000 is a
big chunk. So the activities were drawn by the minute. This activity
is going to take 12 minutes. This one's.
Want to take 15 minutes. It's one seven minutes and so
on. So in turn around or plan shut down work, that's another example.
Durations might be set in terms of shifts or even hours and minutes.
If the schedule is conceptual, durations might be staged or
stated in longer units, such as weeks, months or even years. So I
want to develop a new city
now. The new city is going to take seven years to develop, or
something like the Olympic Games. I am planning for the Olympic
Games eight years in advance. I'm not going to say that on such and
such day. I'm going to install the light switch in the dressing room
of the swimming pool, for example. I cannot do that at the very
beginning, but I would say that the swimming pool should start in
such on such and such date and finish on such and such date,
without putting much detail in between. I just want some
milestones or major events. So in this case, the duration might be
in months or even in weeks.
For most typical construction schedules, we're going to use days
as a unit of time.
CPM days
are work days plus one.
So the CPM day is also referred to as the morning of the project
workday, and also known as the ordinal dates. And that brings us
back to the discussion, why do we start the project on day zero and
not on day one?
And if an activity has a duration of seven days and starts on day
zero, it ends on zero plus seven. That's seven days. Shouldn't the
following activity start the following day? Because we have
reached the end of day seven, we cannot do anything yet, so we're
going to wait until the morning of day eight. Therefore the start of
the following activity is going to be on day eight. That's going to
be really confusing, because when you look at one activity ending on
day seven, the following one starting on day eight, where did
they they go? So from now on, we're always gonna discuss we're
gonna always calculate it based on the start of the day.
If we start on the morning of Day Zero, add seven days, let's count
together zero, that's day. 01234567,
how many is that?
Eight?
So let's do it again.
0123456,
basic, basically, we miscounted. Let's do the counting again. We
start on day zero with the duration of seven days. So
0123456,
how many fingers? Seven fingers. What's the last number? I counted
six. So how come zero plus seven is six? No zero plus seven is
seven. But we're saying that this is the end of day number six,
which is the same as the beginning of day number seven. So we're
always going to count from the beginning of the days. So end of
day six same as beginning of day number seven. Therefore zero plus
seven is seven. We ended the activity on the beginning of day
number seven. We're going to start it successor on the beginning of
day number seven. So the number at the end node is seven. The number
of the start of the following node is also seven.
So make sure you all you always measure from the start of the day
to the start of the following day.
Now these numbers that we are calculating are in workdays,
because we did not include any holidays, any weekends. However,
sometimes the schedule, or most of the time the schedule, is
represented in calendar days,
so we need to make some modification. If I have, for
example, a five
day working week and the activity duration is 10 days, then we're
talking about two weeks. So that's the conversion between calendar
days and work days.
What is a work day?
Unless otherwise specified, the contractor will be permitted. This
is an exemplary contract clause. The contractor will be permitted
to do the work between the hours of 7:45am to 4:30pm
Monday through Friday. Federal holidays that fall within the work
week will not be considered work days prior to the contractor
performing any work during hours other than those specified, the
contractor shall submit an overtime request to the owner's
representative for review and approval. Overtime requests shall
be submitted
no less than 24 hours prior to the time the contractor designs
desires to work.
It so again, if you want to work out of the traditional work week,
out of the traditional work day, you have to submit a request to
the engineer for their proof.
How about the effect of adverse weather conditions?
So if we were supposed to work but there was a storm, for example,
that
forced us to shut down the work.
It may be broadly defined to exclude weekends.
Work Day may be broadly defined to exclude weekends, holidays and
those days on which no work can be performed. So for example,
something like a storm that forced us to close every all the work on
site. Then in this case, it's excluded from the calculations of
the workdays. What constitutes a day on which no work can be
performed, a national holiday weekend, unless stated otherwise,
and other designated non work days for maintenance and other
purposes. So for example, we have the Fourth of July, Christmas Day,
Thanksgiving, sometimes New Year's Day. These are these would be
designated initially as non work days in the calendar of the
project, so that you wouldn't include them in your workday
calculations.
Work days versus calendar days. Now, when the owner says, you have
200 days to finish this project. Are we talking about work days or
calendar days in most of the cases, unless stated otherwise,
we're talking about calendar days. So you have to make that
conversion. You have to retranslate these 200 work leads
200 days into their work equivalent by subtracting all the
holidays and the weekends and so on. In general, if a project is
vulnerable to the weather, or if the weather can dramatically
impact work progress, scheduling with work days is favorable, then
the owner might say, I'm going to give you 200 work days because we
don't know we're going to be working in winter. We might have
some interruptions. I can, I cannot determine the number of the
exact date. So I'm going to give you 200 work days in heavy
construction site work may be a significant component of the
project and susceptible to adverse weather as well as soil
conditions, etc.
Building Construction may be less susceptible to weather, because
once you're done with the skeleton, most of the activities
that take place indoors can be done any time of the day, any time
of the year.
Use of workdays or calendars. The calendar days may be guided by the
contract. So the contract is going to say whether that number of days
is calendar days or work days, if not mentioned, it means calendar
days. Certain project durations may be defined by a specific
calendar date or milestone date, again, that's going to be
specified in the segment or the section in this in the
specifications talking about the schedule,
the work days usually can be converted to calendar days or
calendar days to work days.
Pros and concerns of using work they scheduled is the project on
track? Is the project not on track? We will have to look at
that one once we start performing calculations in the following
lectures.
And now here's a problem for practice. You have to draw a
network and arrow network for the following project. You have the
activities dependencies, or IPAs, and they have, you have the
durations of the activities. You have to now, you are given the
activity as only one designator, which is basically an i j. So you
are given the name on the arrow and not the nodes. You have to
come up with the names of the nodes.
So calculate the duration of the project and calculate early start,
early finish. Late start, late finish, total float and free float
on each activity.
That's basically our discussion for today. You're going to find
some solved examples on the web as well that show you how to solve
these problems. So.