CHAPTER THREE

THE PLANNING PHASE

As mentioned in the previous chapter, the Planning Phase is the most important of the three phases. It is here that the contractor decides and describes how his project will be built.

These decisions are described in several ways. The devices used for description are called input data or just "inputs" for short. The contractor can develop al1 those inputs described in earlier chapters, but only the Arrow Diagram and the Duration Estimates are essential. Cost Estimates and Resource Estimates are entirely optional. All inputs, their production and effect, will be discussed in detail in this chapter.

THE ARROW DIAGRAM An arrow diagram must be drawn to identify, in a graphic form, the

individual items of work, services or tasks -. referred to in CPM as ACTlVlTlES - that are involved in accomplishing the project. Also, of equal importance, the arrow diagram must show how each activity depends upon others during the sequence of construction.

In substance, the arrow diagram graphically describes the sequence of activities and their inter-relationships within the project.

EVENT.

ACTlVlTY m FIGURE 3-1

In an arrow diagram, both arrows and circles are used to describe the sequence of work. An arrow represents an activity, and a circle represents an EVENT. An event is the starting point of an activity and occurs only when al1 the activities preceding it (which means al1 the arrows leading to the circle) have been completed.

In figure 3-1, the starting point for the arrow marked ACTlVlTY is the occurrence of event number two. Event number (3) does not occur until the work represented by the arrow (2) to (3) and the work represented by the arrow from (5) to (3) has been completed - and this means entirely completed. This means then that the work represented by the activity from (3)

to (4) cannot start until (2) - (3) and (5) - (3) have been finished. If this does not accurately describe the situation, the arrow diagram must be redrawn.

Because everything that happens in CPM is based on dependency situations (¡.e., one activity dependent upon others), the arrow diagram must be a meaningful description of the project. If it is not, less than satisfactory results will be obtained from CPM. In almost every case of difficulties or dissatisfaction with CPM, the cause can be traced to a faulty or unrealistic arrow diagram. Everything in an arrow diagram has significant meaning, and for this reason the basic principles must be understood and applied completely.

PRlNClPLE NUMBER 1 The first principle of arrow diagram development that must be understood is

that everything in the diagram has meaning. Within this principle, the following rules must be learned and applied.

1. Every arrow represents an item of work and is referred to as an acrivity. POUR FOOTINGS

b

2. An EVENT is the starting point of an ACTlVlTY shown as a circle. The circle usually has a number in it called the Event Number

POUR FOOTINGS b

3. An ACTlVlTY depends upon and cannot begin until the completion of al1 preceding ACTIVITIES.

DIG a INSPECT FOOTINGS POUR FOOTINGS b

ORDER 6, DELIVER REBARS - As illustrated above, POUR FOOTINGS depends upon the completion of

DIG B INSPECT FOOTINGS and ORDER 8 DELIVER REBARS.

4. All activities that start with the same event depend upon and cannot begin until the completion of al1 ACTIVITIES THAT ENTER THAT EVENT.

DIG 8, INSPECT FOOTlNGS POUR FOOTINGS

ORDER 8 DELIVER REBARS POUR RAMP b

In the case illustrated above, POUR FOOTINGS and POUR RAMP depend upon the completion of the two activities that enter their common starting event. In other words, it is impossible to POUR FOOTINGS or to POUR RAMP until DIG & INSPECT FOOTINGS and ORDER 8 DELIVER REBARS have both been completed. The diagram indicates that al1 the footings (not just

some) must be dug and inspected, and al1 necessary rebars must be on hand before either of the two activities starting with event (9) can begin.

INSTALL STORM D R A l N

O B T A I N PERMITS

CLEAR 6 STRlP

PRELIMINARY SURVEY

INSTALL SANITARY SEWER

FIGURE 3-2

In this illustration (Figure 3-21, al1 three activities that start with event (10) must wait until al1 activities that enter event (10) have been entirely completed. None of the three can start until both OBTAIN PERMITS and PRELIMINARY SURVEYhave been finished. If one of the three leaving (10) does not depend upon the completion of both those entering (101, the arrow diagram is misdrawn and the schedules produced from it will not be realistic.

PRlNClPLE NUMBER 2 A second principle is that an acriviry has a single definire startingpoinr anda

single definire ending poinr. Placing an arrow in a diagram, must satisfy two basic questions:

1. "What activities must be completed before this one can start?" This indicates the event from which to start the activity.

2. "What activities cannot be started if this one is not completed?" This indicates into which event the activity should enter.

Suppose, for example, the following arrow diagram (Figure 3-3) has been drawn.

SET WALL POINTS BLOCK WALLS

EXCAVATE POUR FTGS. BOILER RM. BOILER RM.

FTGS. 8 PADS

UNDER FLOOR PLBG. BOILER RM.

FIGURE 3-3

As shown, excavating for the footings and pads for the Boiler Room is the first activity followed by placing the concrete footings and pads. At event (3) and as a result of the completion of the previous activities, several independent work items then can commence.

Suppose, however, that it is desired to add an activity to indicate delivery of concrete block for the walls of the boiler room. The first question asked about this new activity should be, "What must be finished before the block can be

ordered and delivered?" Actually, there is nothing in the diagram that -if not accomplished - would hold up the ordering and delivery of block. The starting point for this activity would then be event (1).

The second question to be asked about the new activity is, "What cannot proceed until this activity is completed?" The answer is, of course, BLOCK WALLS, BOILER ROOM. The termination point for this new activity then is EVENT (41, and the results of the analysis described above would look like this (Figure 3-4):

ORDER 8 DELIVER BOILER RM. BLOCK c SET WALL POINTS BLOCK WALLS

EXCAVATE POUR FTGS. BOILER RM.

/ BOILER RM.

FTGS. & PADS 1 8 PADS BOILER RM.

UNDER FLOOR PLBG. BOILER RM.

FIGURE 3-4

PRlNClPLE NUMBER 3 A third principle is that the arrow diagram does not describe time

relationshlps but rather dependency relationshlps. Generally, the arrow diagram is not drawn on a time scale. That is, the length and direction of an activity arrow has no relationship to the amount of time required to accomplish the work represented by it. Likewise, two activities starting with the same event do not necessarily occur at the same time; however, they are independent. They rnay or may not go on at the same time. The time that an activity takes place is decided in the Scheduling Phase, not by the arrow diagram. The arrow diagrarn merely defines the dependency situations that exist. In the illustration involving the concrete block for the boiler room walls, for example, the activity ORDER & DELIVER BOILER ROOM BLOCK starts with Event (l), as does EXCAVATE FOOTINGS B PADS, etc. This does not mean that both activities must be underway at the same time. They might but probably won't. The only thing indicated is that these two activities are independent.

PRlNClPLE NUMBER 4 It is very important to realize that the arrow diagram is hardly ever drawn by

a single person. Because the accomplishment of the schedule produced from the arrow diagram is affected by a large number of people, al1 persons who have anything to do with rhe project must be consulred when creating the arrowdiagram. All subcontractors and suppliers should be asked to review the arrow diagram carefully to make certain that the activities pertaining to their work are accurately and realistically described. This principle applies also and equally to the production of duration estimates for the activities.

OTHER RULES AND CONVENTIONS Notice in the illustrations, thus far, that the events are al1 numbered. This

makes it possible to uniquely identify an activity - and its position in the diagram. An activity is identified by using the event number at its tail (called the activity's "1") and the event number at its head (called the activity's "J"). In the boiler room illustration, POUR FOOTINGS & PADS - BOILER ROOM could be referred to as ACTlVlTY (2)-(3) and identified in that fashion.

So that an activity can be uniquely identified by its " 1 " and "J" numbers, a rule must be established and observed in the creation of the arrow diagram. The rule can be stated as follows:

"NOT MORE THAN ONE ACTlVlTY MAY HAVE THE SAME ' 1 ' AND THE SAME 'J'."

In order to observe this rule, it is sometimes necessary to use a "connector" 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 as a dotted line and indicates that no work is involved in that activity.

CLEAR L A N D y cLEAR LAND y STAKEOUT STAKEOUT

Wrong Way Right Woy

FIGURE 3-5

Figure 3-5 illustrates this rule and the use of the dotted-line (dummyi activity. The dotted-line activity represents the dummy and involves no duration and no cost. It serves only as a dependency connector of sequence indicator.

When using a computer for scheduling, the numbers used for "1's" and "J's" need follow no particular system. That is, the numbers for the events can be chosen at random. The event number at the tail of an activity arrow does not have to be less than the event number at the head of the arrow.

For example, if the schedule for the project diagram shown below is to be produced by computer, the numbering of the events illustrated presents no problem. The only rule that must be followed in numbering the events for

computer scheduling is that the same number may not be used twice. This is so that the computer will not get dependencies confused.

However, if one plans to produce a schedule by hand, care must be taken to make sure of two things:

1. Every number must be used, and 2. The number at the tail of any arrow must be less than the number at the

head of that arrow. The arithmetic necessary for the manual production of a schedule will be

explained in a later chapter. At that time, it will be explained why these two rules have to be observed. The computer can work its way around these difficulties and so the rules need not be followed for it. This difference between the computer and manual approach to the Scheduling Phase becomes important when new activities must be added to an already numbered diagram. Since the rules must be followed, the whole job will require renumbering if the schedule is developed manually.

When numbering a network for computer manipulation, the numberer must keep two things in mind. One, it will probably be necessary at some time during the life of the project to revise or change the network in some fashion. Second, much time can be wasted looking for I-J identified activities if no systematic approach has been made.

Because of this, some system is usually followed in numbering a network. Anything will work as long as it alleviates the two problems above described. A simple approach is to number consecutively moving from top to bottom and then from left to right, skipping al1 numbers ending in 3, 6, or 9.

It is always wise to refrain from numbering the diagram until it has been completed, reviewed and approved.

Another rule governing the creation of the arrow diagram, whether scheduled manually or with the computer, is that a project will have only one starring event and only one ending event. When nothing must be done prior to the start of an activity, the arrow representing that activity starts with the project's starting event. When nothing depends upon the accomplishment of an activity, its arrow ends with the project's ending event. One always knows, because of this rule, where an activity belongs in the network.

It must be kept firmly in mind that restricting the arrow diagram to one starting event and one ending event does not at al1 limit the number of starting or ending activities.

Because the Arrow Diagram is the CPM user's graphic description of how he plans to do his work, care must be taken to ensure clarity. For this reason diagrams are usually drawn horiz~ntally from left to right with no activities moving "backwards," and al1 event connections easily identified. In the illustration following, the network does not make clear that more than two activities enter event number 7.

INSTALL WELLPOINTS CONNECT DEWATERING

INSTALL DISCHARGE

The proper technique to be used in this situation follows:

INSTALL WELLPOINT CONNECT DEWATERING

INSTALL PUMPS

INSTALL DISCHARGE

Another bad networking practice is the unnecessary use of "phantom" connectors andlor failure to adequately identify both the source and destination thereof. Following is an illustration of properly used phantoms.

INSTALL WELLPOINTS CONNECT DEWATERING

TO EXCAVATE FROM FOOTlNGS

DELIVER PUMPS

Phantom connectors are usually presented in some way different from the normal event graphics in order to firmly and clearly identify them as unusual.

The arrow diagram is the single most important piece of input information, and serious effort must be expended on its production. The arrow diagram makes up about 80% of the Planning Phase and even if only this is done, substantial benefits will be obtained frorn CPM.

The creation of a realistic, accurate, and meaningful arrow diagram requires a complete and detailed analysis of the job described. This disciplined approach to the planning of a job provides the planner with insights about the project unattainable in any way other than actually accomplishing it. The detailed investigation necessary to produce a good arrow diagram also pinpoints problem areas, allowing the planner sufficient time to make proper preparation prior to arriving at this point of construction.

The creation of a realistic arrow diagrarn requires that the project planner be intimately acquainted with the project and the organization accomplishing it. One can obtain assistance in the production of an arrow diagram, but one can never entirely divorce himself from the proceedings.

ARROW DIAGRAM CONSTRUCTION PROBLEMS This section will be devoted to problems requiring the production of arrow

diagrams. Before attempting to draw diagrams for the projects described later in this section, the reader would do well to review the previous section, particularly the pages in which the arrow diagram and the principles guiding its creation are discussed in detail. If CPM is to be used successfully, the arrow diagram upon which CPM is based must be properly drawn. For the arrow diagram to be properly drawn, the principles upon which its creation are based must be completely and thoroughly understood.

The major items to be kept in mind when creating an arrow diagram are: 1. Everything in the arrow diagram has significant meaning. 2. An activity hasa single definite starting point and a single definite ending

point. 3. The arrow diagram describes dependency relationships rather than time

relationships. Remember that when an arrow, representing an activity, is placed into the

diagram, two questions are asked about it - 1. What activities must be completed before this one can start? This

determines the event that starts the activity. 2. What activities cannot start until this one has been completed? The

answer to this question indicates at what event the activity ends. There is also an unwritten rule one should keep in mind as the diagram is

drawn. It can be stated as follows: AN ARROW DIAGRAM IS DRAWN WlTH A PENCIL THAT HAS A LARGE

ERASER!

BASlC PROBLEMS. Problem 1. To illustrate arrow diagram generation with an actual problem,

suppose that it was desired to install a drainage ditch in the backyard of a

house. Assume for this problem that only one man was going to work on this project. Draw a diagram for this one-man project including only the following activities:

1. DIG DlTCH 2. PLACE GRAVEL IN BOTTOM OF DlTCH 3. OBTAIN DRAlNTlLE 4. INSTALL DRAlNTlLE AND BACKFILL Make the following assumptions about these activities: A. There is no need to order or deliver gravel. There is a supply in the

driveway. B. OBTAIN DRAlNTlLE does not require the effort of the one man doing

this project. It is a "delivery" type activity. The first activity possible in this project is DIG DlTCH - so an activity

indicating this would be drawn.

DIG DlTCH

After the ditch had been dug, the placing of the gravel would follow, and the diagrarn would show this as follows:

--O PLACE GRAVEL IN DlTCH

After the gravel is in, the draintile could be installed. However, in order for this to happen, the draintile must have been obtained. This means that the activity OBTAIN DRAlNTlLE must end at the beginning of INSTALL DRAlNTlLE AND BACKFILL. This will be at Event (3) and the diagram would look iiKe this:

INSTA11 DRAlNTlLE

& BACKFILL

OBTAIN DRAlNTlLE /

The question remaining is where does OBTAIN DRAlNTlLE start? One must further ask what activities must be accomplished before this one can start. It turns out that nothing need be done in order to start this activity and it thus starts with Event (1 1. The complete solution is beluw.

DIG DlTCH PLACE GRAVEL I N INSTALL DRAlNTlLE

DlTCH & BACKFILL

\ OBTAIN DRAlNTlLE /

Problem 2. To create a slightly more complicated problem, consider the situation that would exist if the work described in problem 1 had been performed in the street in front of the house rather than in the backyard.

If this were the case, it would be necessary to add to the list of activities given for 1 the following:

5. OBTAIN PERMIT TO BLOCK STREET 6. BLOCK STREET 7. OBTAIN TRENCHER 8. ORDER AND DELIVER PAVING MATERIAL 9. PAVE STREET For this problem, the following assumptions are made in addition to those

already mentioned in problem 1 : C. The permit is only necessary to block the street. There is no doubt that it

will be obtained. D. OBTAIN TRENCHER is a delivery type activity just as OBTAlN

DRAlNTlLE was in problem 1. The solution to this problem would start with the first activity that can take

place. In this problem, four independent activities can be shown as starting the project. Which one goes where is not at al1 important. In the beginning, below, it may appear that al1 four activities are expected to start or take place at the same time. This is definitely not the case. The person drawing the

OBTAIN TRENCHER /

OBTAIN PERMIT

OBTAIN DRAINTILE

ORDER & DELIVER

PAVING MATERIAL

diagram must realize and remember at al1 times that the arrow diagram does not describe time relationships but rather only dependencies. This diagram, so far, states only that OBTAIN TRENCHER, OBTAIN PERMIT, OBTAIN DRAINTILE, and ORDER AND DELIVER PAVING MATERIAL are independent; that is, they can start at any time whether other activities have started or not. When these activities take place will be determined in the scheduling phase.

The next item that can be placed into the diagram is BLOCK STREET. The only thing that must be done before this activity can start is OBTAIN

OBTAIN TRENCHER

Y OBTAIN DRAINTILE

ORDER (L DELIVER PAVING MATERIAL

PERMIT. This new activity then starts with Event (2). The assumption that obtaining the permit was only a formality makes it

possible to show OBTAIN TRENCHER, OBTAIN DRAlNTlLE and the PAVING MATERIAL ACTlVlTY as starting with Event (1). If this assumption had not been made, a prudent decision would have been to start these activities at Event (2) so as to avoid spending money without beinci sure of the results.

After the street had been blocked, DIG DlTCH could start. However, because the ditch isto be dug through the pavement, the trencher would have to be on hand. The arrow diagram indicating this would appear as shown in Figure 3-6.

From this point until the final activity, the diagram would be con- structed as it was for problem 1, as shown in Figure 3-7.

The final activity would be the repair to the damage caused by tearing up the street. In order to pave, however, the paving materials would have to be on hand. This situation is described by making the event that -starts PAVE STREET (6) and making the same event the end point for ORDER AND DELIVER PAVING MATERIAL. The final solution to this problem is illustrated in Figure 3-8.

OBTAIN TRENCHER

BLOCK STREET

OBTAIN DRAlNTlLE

\ ORDER 6 DELIVER PAVING MATERIAL

FIGURE 3-6

OBTAIN TRENCHER

INSTALL DRAlNTlLE

OBTAIN DRAlNTlLE

FIGURE 3-7

25

OBTAIN TRENCHER 1 7

\ ORDER L DELIVER PAVING MATERIAL

FIGURE 3-8

An important point to remember about arrow diagrams is that the assumptions made about the activities are as imporrant as the activities themselves. They should always be written down so as to be remembered.

Problem 3. Create an arrow diagram for a reinforced concrete equipment foundation project to be built partially below ground level. Assume that al1 necessary tools, equipment and materials íincluding concrete) are on the job site, and that there is no limit to the number of workers. A rented backhoe is used to excavate. Use only the following activities:

1. LAY OUT AND EXCAVATE 2. FINEGRADE 3. PREFABRICATE FORMS 4. PREFABRICATE REBAR 5. SET FORMS 6. SET REBAR AND ANCHOR BOLTS 7. ADVISE AVAlLABlLlTY OF BACKHOE 8. POUR CONCRETE For this problem assume that FlNE GRADE must be done before the forms

are set. One would start the arrow diagram with three independent activities.

Remember that the diagram does not indicate that these three items are underway at the same time. I t only shows that they are not dependent on the completion of any other activities.

PREFAB REBAR

PREFAB FORMS

LAY O U T & EXCAVATE

After the layout and excavation had been completed, two activities could be started. FlNE GRADE would depend upon the completion of this activity, and of course, the backhoe could not be made available until the completion of this phase of work. The diagram would grow like this:

PREFAB REBAR - PREFAB FORMS

LAY OUT B EXCAVATE FlNE GRADE

\ ADVISE AVAlLABlLlTY OF BACKHOE

Again, the diagram is nor stating that FlNE GRADE and that ADVISE AVAILABILITY OF BACKHOE occur simultaneously, but rather that they both depend upon -cannot start until- the completion of LAY OUT AND EXCAVATE.

After FlNE GRADE had been completed, and when PREFAB FORMS was finished, SET FORMS could start. At its conclusion, and after PREFAB REBAR had been completed, it would be possible to SET REBAR and ANCHOR BOLTS and then finally POUR. The final arrow diagram would look like this:

PREFAB REBAR

PREFAB FORMS

BOLTS

FlNE GRADE

\ ADVISE AVAllABlLlTY O F BACKHOE

DUMMIES Occasionally, it is necessary to use a "connector" type activity to indicate

a dependency relationship without causing confusion. This type of activity, which does not represent work and which has a duration of zero, is called a DUMMY activity and is shown on the arrow diagram as a dotted line.

There are two reasons for using dummies. These two reasons can be illustrated by altering problem 3 above. Suppose that instead of having a single activity called SET REBAR AND ANCHOR BOLTS, it was desired to make two activities: one called SET REBAR and the other called SET ANCHOR BOLTS. Suppose that both depended upon PREFAB REBAR and SET FORMS and that both had to be completed before the POUR. The affected part of the diagram would appear as below:

SET REBAR

\ SET / ANCHOR BOLTS

From a dependency point of view, there is nothing wrong with this kind of description. However, confusion results from having more than one activity with the same 1-J numbers. It is not clear which is activity (4145). Earlier in this chapter a rule was established to avoid this situation. It was stated that not more than one activity may have the same 1-J combination. So as not to break this rule, one of the two "non-unique" activities must be changed into two, one of which is a dummy:

SE1 REBAR SET FORMS 9 .o o POUR

\ L SET

ANCHOR BOLTS

If this diagram is examined closely, the following points become clear: 1. Event (5) occurs when SET REBAR and SET ANCHOR BOLTS have

been completed. 2. Since the DUMMY from (4) to (7 ) activity has zero duration, it is

completed at the same point in time that Event (4) occurs. 3. For this reason, Event (7) occurs when SET FORMS is finished and

PREFAB REBARS is finished, and SET ANCHOR BOLTS can start at this time.

4. This is exactly the same dependency statement that was made in the incorrect solution above in which two activities from (4)-(5) appeared.

The first reason for using a dummy then is to maintain the uniqueness of rhe 1-J identificarion system.

The second reason for using a dummy is somewhat more complex. A connector type activity is sometimes needed to describe dependencies in such a way that non-dependent activities are not shown as dependent. This can be illustrated also with the diagram from problem 3 on page 27.

If the problem were changed by eliminating the assumption that FlNE GRADE had to precede the setting of the forms, one would be tempted to produce an arrow diagram that looked like Figure 3-9.

PREFAB REBAR

SE1 REBAR, ETC.

FlNE GRADE

ADVISE AVAlLABlLlTY O F BACKHOE

FIGURE 3-9

This approach, however, is incorrect because it is not possible to SET FORMS unless at least the excavating has been completed. Another solution - which is also incorrect- might be to combine event number (2) and went (3). Event (3) would then appear as in Figure 3-10.

PREFAB FORMS SE1 FORMS

ADVISE AVAllABlLlTY OF BACKHOE

FIGURE 3-10

The error in this arrow diagram exists because FlNE GRADE and ADVISE AVAlLABlLlTY OF BACKHOE do not depend upon the completion of PREFAB FORMS as indicated, but rather only on LAY OUT AND EXCAVATE.

The correct solution is one in which SET FORMS is indicated as depending upon both PREFAB FORMS as well as on LAY OUT AND EXCAVATE, and in which FlNE GRADE and ADVISE AVAlLABlLlTY OF BACKHOE depend only on LAY OUT AND EXCAVATE. The proper way to show this situation is by using the first solution with a DUMMY from (2) to (3), as illustrated in Figure 3-1 1.

Because the DUMMY from (2) to, (3) has a zero duration, it is finished when Event (2) occurs. It merely transfers, then, the dependency relationship - the sequence - desired to Event (3).

The second reason for using a DUMMY is to establish a dependency or sequence wirhout con fusing non-dependent activities.

PREFAB FORMS SET FORMS

l

LAY OUT 6 EXCAVATE FlNE GRADE

\ ADVISE AVAllABlLlTY OF BACKHOE

FIGURE 3-11

DUMMY PROBLEM Problem 4. Go back to the very first problem in this chapter. There it was

assumed that only one man would work on the job. If the job is broken into segments to show how several crews would get the job done, the activity list would be almost doubled. Assume for this problem that each of those original activities will now be done each in two phases. That is, approximately half the ditch will be dug before the "gravel crew" will start placing gravel, and the gravel will be in half the ditch before

the crew installing the draintile can start work. The activity list would then consist of the following items:

1. OBTAIN DRAlNTlLE 2. DIG DlTCH FlRST HALF 3. DIG DlTCH SECOND HALF 4. PLACE GRAVEL FlRST HALF 5. PLACE GRAVEL SECOND HALF 6. INSTALL DRAlNTlLE FlRST HALF 7. INSTALL DRAlNTlLE SECOND HALF It must be assumed for this problem that the first half of each job will be

finished before the second half starts. Assumed also is that OBTAIN DRAlNTlLE is a delivery type of activity and that the ditch will be backfilled as part of the INSTALL DRAlNTlLE operation.

The initial activities would be drawn in as follows:

DIG DlTCH FlRST HALF DIG DlTCH SECOND HALF

\ GRAVEL FlRST HALF

\ OBTAIN DRAlNTlLE

This arrangement of activities indicates that when DIG DlTCH FlRST HALF is complete, two activities can start - DIG DlTCH SECOND HALF and GRAVEL FlRST HALF. Independently, OBTAIN DRAlNTlLE can occur any time after the start of the project.

When the gravel is in the first half of the ditch and if the draintile is on hand, the draintile can be installed. The diagram would grow to look like this:

\ \ OBTAIN DRAlNTlLE LAY TlLE FlRST HALF

When the second half of the ditch had been dug, the gravel could be placed. However, the assumption was made that the first half of any job would have to be completed before starting the second half. This causes a problem insofar as the present version of the diagram is concerned. It is desired to show that GRAVEL SECOND HALF depends upon DIG DlTCH SECOND HALF and GRAVEL FlRST HALF. Tying this new activity to the ditch digging operation is no problem, but difficulties arise when GRAVEL FlRST HALF is considered. The problem is caused by the fact that GRAVEL FlRST HALF has been tied into Event (3). If the end of GRAVEL FlRST HALF is connected to the

beginning of GRAVEL SECOND HALF, and a dummy is about the only way this could be done, a serious sequence error is committed.

\ OBTAIN DRAlNTlLE

The diagram, as it appears above, indicates that GRAVEL SECOND HALF cannot start until OBTAIN DRAlNTlLE has been completed. That is, the diagram states that it is impossible to place grave1 unless draintile is on hand. No such assumption was made, so this is incorrect.

The problem is solved by rearranging the diagram as originally created and splitting GRAVEL FlRST HALF into two paths. Dummy activities are, of course, required to do this. The final solution to this expanded drainage ditch problem appears below.

GRAVEL

SECOND HALF 9 SECOND HALF \ /

FlRST HALF '-=-% \ OBTAIN DRAlNTlLE INSTALL DRAlNTlLE INSTALL

DRAlNTlLE FlRST HALF SECOND HALF

ADVANCED PROBLEMS Problem 5. It is desired to create an arrow diagram for the steps necessary

to be taken in the production of a hollow metal door and frame assembly. TL,d activities involved in this project are as follows:

1. MAKE DOOR 2. INSTALL LOCK IN DOOR 3. PUT HINGES ON DOOR 4. ASSEMBLE DOOR FRAME COMPLETELY 5. INSTALL DOORBELL ON FRAME 6. HANG DOOR 7. CLEAN UP SlTE There are several assumptions that must be considered in this project.

These are: A. The frame is complete prior to bell installations. B. The lock is installed prior to hanging. C. The hinges must be on the door before hariging. D. The door frame must be assembled prior to the hanging. E. The part of the lock that is in the frame, and the part of the hinges that is

part of the frame, is taken care of when the frame is assembled. F. Clean up is the final activity. G. There are no space or manpower limitations. The solution to this problem looks like this.

CLEAN UP

ASSEMBLE DOOR FRAME

Note that there are two dummy activities in this diagram-one for each of the two reasons discussed earlier. Activity (3145) exists so that the 1-J's remain unique for INSTALL LOCK and for INSTALL HINGES. Activity (4)-(5) shows that HANG DOOR rnust wait until ASSEMBLE DOOR FRAME has been completed but INSTALL BELL does not depend on anything except ASSEMBLE DOOR FRAME.

Problern five can be made sornewhat more complex by adding just three new activities. These are:

8. DELIVER BLUEPRINTS FOR FRAMEAND DOOR 9. DELIVER LOCK HARDWARE

10. DELlVER HlNGE HARDWARE Note that the blueprints are for the frame and the door only. They are no+

needed to obtain the lock and the hinges. When the arrow diagran: r for this problern is drawn, the dependencies must be checked very carefully. It is very easy to mistakenly indicate that the installation of the hinges depends upon the lock delivery andlor that the installation of the lock depends upon the hinge delivery.

The solution to this problem can be found at the end of this chapter. Problem 6. Prepare an arrow diagram for the road separation bridge

structure project described below. The arrow diagrarn is to be for the bridge structure only; the roadway is not included. Create the activities for this project from the major areas of activities indicated below. Assume for this project that there is only one concrete pouring crew. This means that it will be impossible to place into the final diagram a concrete pouring type of activity without linking it in some fashion to al1 other pours. This restriction makes it irnpossible to have an independent pour.

FIGURE 3-12

32

SLAB A SLAB B I SLAB C

CONCRETE CAP

FORMED CONCRETE

PlLES BENTS

-

-

>

Other restrictions exist for various areas of operation. The major areas of activity in this ~ro iect and the restrictions that exist are indicated in the diagrarn (Figure 3-12) and the table (Figure 3-13).

Operation Restriction

MOVE IN

PREPARE SlTE

PROCURE PILES

DRlVE PILES ONE AT A TIME

EXCAVATE FOOTINGS ONE AT A TIME

FORM FOOTINGS ONE AT A TIME

POUR FOOTINGS ONE AT A TIME

FORM CAPS ON PlLE BENTS* TWO SETS OF FORMS AVAILABLE.

FORMS PUT IN PLACE ONE SET AT A TIME

POUR CAPS ON PlLE BENTS ONE AT A TIME

CURE AND STRIP CAPS ON PILE BENTS

FORM FRAMED CONCRETE BENTS* ONE SET OF FORMS, REUSED

POUR FRAMED CONCRETE BENTS ONE AT A TIME

CURE AND STRlP FRkMED CONCRETE BENTS

FORM SLABS

ONE SET OF FORMS FOR END SLABS.

ONE SET OF FORMS FOR CENTER SLAB.

FORMS PUT IN PLACE ONE AT A TlME

POUR SLABS ONE AT A TIME

CLEAN UP AND MOVE OUT

" The caps on the concrete bents arc formcd ai-id pourcd with the bcnt. FIGURE 3-13

A solution to this problern can be found at the end of this chapter. Because of the rnany restrictions in this problem, the arrow diagram will contain numerous durnmies.

COMMON ERRORS Two errors of arrow diagram construction are frequently made. If the

diagram drawer is on the lookout for these two types, his diagram will be greatly improved.

The first error is called the wagon wheel. Refer to page 29 where dummies were being discussed. The illustration there contains a wagon wheel at event number (3): It looks like this:

PREFAB FORMS SET FORMS

LAY OUT L EXCAVATE FlNE GRADE

\ ADVISE AVAlLABlLlTY O F BACKHOE

This is called a wagon wheel because it has a number of arrows entering the event and a number of them leaving. It is an error because not every activity that leaves Event [31 depends upon the cornpletion of al1 activities that enter Event [31. Remember that Event (3)-which is the starting point for al1 activities that leave that event-does not occur until al1 activities entering it have been completed. The correct approach appears below.

PREFAB FORMS SET FORMS

I

LAY OUT 6 EXCAVATE FlNE GRADE

\ RETURN BACKHOE

One should look ven/ critically at every event that has more than one activity arrow entering and more than one leaving. One must ask of every activity leaving such an event, "Must this activity wait until every one of those entering have been completed?" If the answer is "yes," the actívity can stay with the event; if the answer is "no," adjustments must be made.

The second type of error is related to the wagon wheel but is slightly more difficult to spot. It could be called the water-fall error because generally it will look like Figure 3-14.

This is part of the solution to the three-span bridge project described earlier in this chapter. It is incorrect. Notice that there is a dummy from Event (13) to event (15). This dummy exists to show that POUR CAP, BENT # 1 cannot take place until after POUR FOOTING, BENT # 3 has been completed. This is legitimate because the shortage of crews made it necessary for pours in that problem to be linked together.

Notice further that activity (15)-(16) restricts FORM CAP, BENT #4. This is also permissible because the restrictions described stated that the caps had to be formed one at a time. The error exists, however, because FORM CAP, BENT #4cannotsrart untilafterPOUR FOOTING, BENT #3 has

been completed. The dummy from (15)-(16) cannot occur until (13) has because of the dummy from (13) to (15).

POUR F O O T I N G , BENT # 3 FORM BENT $ 3

\

FORM CAP, BENT # 1 POUR CAP, BENT # 1

DRlVE PILES, BENT # 4 FORM CAP, BENT # 4

FIGURE 3-14

The difficulty in this "water-fall" of dependencies is that Event (15) is a wagon wheel. This is not immediately obvious, however, because one of the activities entering is a dummy activity and tends to be overlooked. The correct arrangement of the activities in this example is as follows:

POUR FOOTING, BENT # 3 FORM BENT * 3

DRlVE PILES, BENT # 4 FORM CAP, BENT # 4

This illustration does not agree completely with the solution to Problem 6 that appears at the end of this chapter. This is because the complete solution involves more activities than appear here. The illustration above is correct for the activities involved.

DURATION ESTIMATES The next stage of input development involves the element of time. This

requires the planner to estimate how long it will take to complete each activity or the duration time of each activity. This is necessary in order to produce the CPM Schedule for the project. The arrow diagram describes how the activities fit together; the duration estimates indicate how long each will take.

Duration estimates can be made in a variety of ways. The simplest way is to determine the "Normal" time to finish an activity with a normal sized crew with the normal amount of equipment. In addition to this simple approach, the CPM user has the ability to examine a range of durations for the activities so as to produce more than one schedule for the project, starting with the longest duration for each activity and then "speeding up" those that will shorten the project. The mechanics of making duration estimates and the purpose for this range of estimates will be discussed in the next chapter.

It must be emphasized that when duration estimates are made, they are made on an individual activity basis. That is, no consideration of other activities can be made. Remember that the planning phase-in which the duration estimates are made-is entirely separate from the scheduling phase.

If the arrow diagram has been properly drawn, the duration estimates produced for most of the activities will be relatively small. If the bulk of the activities are assigned durations greater than 5, the arrow diagram is probably not indicating realistic dependencies.

COST ESTIMATES The user of CPM can submit, asan input, cost estimates for all, or for some,

activities in the project. It must be emphasized that he does not have to submit cost data. However, with this information included in the input data, CPM can produce Cost Status Reports, Cash Requirement Predictions, Requisition Backup Reports, and Payment Documents.

These reports will be discussed in detail in later chapters. Here they will be described only briefly, and only in terms of the necessary input information.

The Cost Status Report is produced in the Control Monitor Phase and is discussed and illustrated in more detail in Chapter 5. It indicates to the project manager the relationship of his project's actual costs incurred to costs estimated for work in place.

The Scheduling Phase of CPM sets up a schedule for the project, and as the project proceeds, information is submitted to the computer showing which activities have been completed. If information as to how much each activity was expected to cost had also been submitted to the computer, it would be able to calculate how much money should have been spent to that point in time.

If the computer was able to calculate how much should have been spent, the "Cost" status of the project could be determined by comparing this estimated total against the amount of money that was actually spent.

In order for this report to be produced, information must be developed for the computer, showing how much each activity will cost when complete.

1 J Activity ~ --

Category .

Amount

1 2 EXCAVATE FTGS & PADS BOILER 15-Excavation $ 455.30 ROOM 46-Gen Labor 60.00

2 3 POUR FTGS & PADS - BOILER ROOM

11-Concrete 1,488.08 12-Conc Labor 375.60 46-Gen Labor 45.00

The cost estimates can be submitted in a form similar to that shown above. In the example, it is indicated that activity (1)-(21, EXCAVATE FTGS €t

PADS-BOILER ROOM, will cost $445.30 for excavation and $60.00 for general labor. Also indicated is that (2)-(3) POUR FTGS & PADS-BOILER ROOM will cost $1,488.08 for concrete, $375.60 for concrete finishing (labor) and $45.00 for general labor. By indicating the type of expense involved in getting each activity done, it is possible fo find out the cost status of any desired category. If this were not desired, just one cost per activity could be indicated.

The "Cash Requirement Prediction" uses the same input information as the Cost Status Report with a slight variation. The Cost Status of a project is based on activities reported as finished. The Cash Requirement Prediction assumes that al1 activities will be completed as scheduled during each calendar week of the project.

One additional feature exists in the "Cash Requirement Prediction." It is possible to indicate to the computer whether a cost for an activity is an expense item or an income item. When supplied with this kind of information, the computer can predict how much money will be required to pay for completed activities and how much income the completion of those activities will produce.

Requisition Backup Reports and Payment Documents - described and illustrated in later chapters - facilitate both the administration of payments from the owner to the contractor and payments from the contractor to his subs. It is possible to "factor" the costs assigned each activity by a percentage common to al1 activities assigned to each what the subcontractor will be paid out of what the contractor gets paid when each activity is completed.

RESOURCE ESTIMATES The schedule produced for a project assumes that enough manpower and

equipment is available to get the activities done as scheduled. This is not always the case, and in a large or cornplex project, i t rnight not be obvious that a deficiency exists. So that the project manager can determine how many people and how much equipment will be required, he can be provided with a "Resource Analysis" for the project.

This report will be discussed and illustrated in following chapters. Briefly, it indicates the amount of various kinds of resources required for the accomplishment of each activity. The types and amount of resources are supplied the computer in a form like that illustrated below.

I 1 Activity Resource Required ~

1 2 EXCAVATE FTGS & PADS- BACKHOE 2 BOILER ROOM LABORERS 4

ENGINEER 1

2 3 POUR FTGS & PADS- CEMENT FlNlSHERS 6 BOILER ROOM LABORERS 4

FOREMEN 1

In the preceding illustration, EXCAVATE FTGS B PADS-BOILER RM is indicated as requiring two backhoes, four laborers, and one engineer. The next activity is described as needing six concrete finishers, four laborers and one supervisor. Al1 activities in the project would be described in the same way, and the computer would calculate how many backhoes would be necessary on every day of the job along with how many laborers, how many concrete finishers and so on through every type of resource required.

\ COMPLETE FRAME INSTALL

DOORBELL

Solution to Problem 5 [Chapter 31