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Networks and pert / cpm critical path method

Anonim

The PERT / CPM was designed to provide several useful pieces of information for project managers. First, PERT / CPM exposes the "critical path" of a project. These are the activities that limit the duration of the project.

In other words, to get the project done early, the critical path activities must be done early. On the other hand, if an activity on the critical path is delayed, the project as a whole is delayed by the same amount. Activities that are not on the critical path have a certain amount of slack; that is, they can be started later, and allow the project as a whole to stay on schedule. The PERT / CPM identifies these activities and the amount of time available for delays.

networks-and-pert-cpm-critical-path-method

INTRODUCTION

Large-scale one-time projects have been around since ancient times; this fact is attested by the construction of the pyramids of Egypt and the aqueducts of Rome. But only recently have operational researchers been scrutinizing the managerial problems associated with such projects.

The project management problem arose with the Polaris armaments project, beginning in 1958. With so many components and sub-components together produced by various manufacturers, a new tool was needed to program and control the project. The PERT (Program Evaluation and Review Technique) was developed by scientists from the Naval Office of Special Projects. Booz, Allen and Hamilton and the Weapons Systems Division of the Lockheed Aircraft Corporation. The technique proved so useful that it has gained wide acceptance in both the government and the private sector.

Around the same time, the DuPont Company, in conjunction with Remington Rand's UNIVAC Division, developed the Critical Path Method (CPM) to control the maintenance of DuPont chemical plant projects. CPM is identical to PERT in concept and methodology. The main difference between them is simply the method by which time estimates are made for project activities. With CPM, activity times are deterministic. With PERT, the times of the activities are probabilistic or stochastic.

The PERT / CPM was designed to provide several useful pieces of information for project managers. First, PERT / CPM exposes the "critical path" of a project. These are the activities that limit the duration of the project. In other words, to get the project done early, the critical path activities must be done early. On the other hand, if an activity on the critical path is delayed, the project as a whole is delayed by the same amount. Activities that are not on the critical path have a certain amount of slack; that is, they can be started later, and allow the project as a whole to stay on schedule. The PERT / CPM identifies these activities and the amount of time available for delays.

The PERT / CPM also considers the resources required to complete the activities. In many projects, limitations in manpower and equipment make scheduling difficult. The PERT / CPM identifies the moments of the project in which these restrictions will cause problems and according to the flexibility allowed by the slack times of the non-critical activities, allows the manager to manipulate certain activities to alleviate these problems.

Finally, PERT / CPM provides a tool to control and monitor the progress of the project. Each activity has its own role in it and its importance in the completion of the project is immediately apparent to the project manager. The activities of the critical path, therefore, allow to receive most of the attention, since the completion of the project, depends heavily on them. Non-critical activities will be manipulated and replaced in response to the availability of resources.

Background.

There are two origins of the critical path method: the PERT method (Program Evaluation and Review Technique) developed by the United States Navy in 1957, to control the execution times of the various activities that make up space projects, due to the need to complete each of them within the available time intervals. It was originally used by the Polaris project time control and is currently used throughout the space program.

The CPM method (Critical Path Method), the second origin of the current method, was also developed in 1957 in the United States of America, by an operations research center for the firm Dupont and Remington Rand, seeking the control and optimization of operating costs through proper planning of project component activities.

Both methods provided the administrative elements necessary to form the current critical path method, using control of execution times and operating costs, to seek that the total project is executed in the shortest time and at the lowest possible cost.

Definition.

The critical path method is an administrative process of planning, programming, execution and control of each and every one of the component activities of a project that must be developed within a critical time and at optimal cost.

Applications.

The field of action of this method is very wide, given its great flexibility and adaptability to any large or small project. To obtain the best results, it should be applied to projects that have the following characteristics:

  1. That the project is unique, non-repetitive, in some parts or in its entirety. That all or part of the project must be executed, in a minimum time, without variations, that is, in critical time. That the cost of lowest possible operation within an available time.

Within the scope of application, the method has been used for the planning and control of various activities, such as construction of dams, opening of roads, paving, construction of houses and buildings, repair of ships, market research, settlement movements, regional economic studies, audits, university career planning, distribution of operating rooms times, factory extensions, planning of itineraries for collections, sales plans, population censuses, etc., etc.

DIFFERENCES BETWEEN PERT AND CPM

As stated before, the main difference between PERT and CPM is the way the time estimates are made. E1 PERT assumes that the time to perform each of the activities is a random variable described by a probability distribution. CPM, on the other hand, infers that the times of the activities are known in a deterministic way and can be varied by changing the level of resources used.

The time distribution that PERT assumes for an activity is a beta distribution. The distribution for any activity is defined by three estimates:

  • the most likely time estimate, m, the most optimistic time estimate, a; and the most pessimistic time estimate, b.

The shape of the distribution is shown in the following Figure. The most likely time is the time required to complete the activity under normal conditions. Optimistic and pessimistic times provide a measure of the uncertainty inherent in the activity, including equipment breakdowns, labor availability, material delays, and other factors.

With the defined distribution, the mean (expected) and standard deviation, respectively, of the activity time for the Z activity can be calculated using the approximation formulas.

The expected completion time of a project is the sum of all the expected times of the activities on the critical path. Similarly, assuming that the time distributions of the activities are independent (realistically, a strongly questionable assumption), the project variance is the sum of the variances of the activities on the critical path. These properties will be demonstrated later.

In CPM only an estimate of time is required. All calculations are made with the assumption that the uptime is known. As the project progresses, these estimates are used to monitor and monitor progress. If any delay occurs in the project, efforts are made to get the project back on schedule by changing the allocation of resources.

Methodology.

The Critical Path Method consists of two cycles:

  1. Planning and Scheduling.

1.1.- Project definition

1.2.- List of Activities

1.3.- Sequence Matrix

1.4.- Time Matrix

1.5.- Activities Network

1.6.- Costs and pending

1.7.- Network compression

1.8.- Time, resource and financial limitations

1.9.- Elasticity matrix

1.10.- Probability of delay

  1. Execution and Control.

2.1.- Project approval

2.2.- Work orders

2.3.- Control charts

2.4.- Reports and analysis of progress

2.5.- Decision making and adjustments

Definition of the project

In every activity to be carried out, precise and clear knowledge of what is going to be carried out, its purpose, feasibility, available elements, financial capacity, etc. is required. This stage, although essential for the execution of the project, is not part of the method. It is a previous stage that must be developed separately and for which the Critical Path Method can also be used. It is an investigation of viable and available objectives, methods and elements.

Activities list

It is the relationship of physical or mental activities that form interrelated processes in a total project. In general, this information is obtained from the people who will intervene in the execution of the project, in accordance with the assignment of responsibilities and appointments made in the Project Definition.

The activities can be physical or mental, such as constructions, paperwork, studies, inspections, drawings, etc. In general terms, Activity is considered to be the series of operations carried out by a person or group of people continuously, without interruptions, with determinable initiation and termination times. This list of activities serves as a basis for the people responsible for each process to prepare their execution budgets.

Example:

  1. Maintenance and production managers. Preparation of the partial expansion project Cost calculation and budgeting Approval of the project Unpacking of new machines Placement of old and new machines Installation of machines General tests General start-up Review and cleaning of old machines.Painting of old machines. Painting and cleaning of the building.
  1. Electrical engineer. Preparation of the electrical project Calculation of costs and budgets Approval of the project Installation of a new transformer Installation of new lighting Installation of switches and starters
  1. Contractor Engineer. Preparation of the project of dead work Calculation of costs and budgets Approval of the project Foundation of the machines New floors Placement of new windows

Sequence Matrix

There are two procedures to know the sequence of activities:

a.- By background

b.- By sequences.

By background, those responsible for the processes will be asked which activities must be completed to execute each one of those that appear on the list. Special care must be taken that each and every one of the activities has at least one antecedent except in the case of being initial activities, in which case their antecedent will be zero (0).

In the second procedure, those responsible for the execution will be asked what activities should be done at the end of each one of those that appear on the list. For this purpose we must present the sequence matrix starting with activity zero (0) that will serve to indicate only the starting point of the others. The information should be taken one by one of the listed activities, without overlooking any of them.

In the column of "annotations" the programmer will make all the indications that help him to clarify situations of sequences and presentation of the network. These annotations are made at discretion, as this matrix is ​​only a working paper.

If a matrix of antecedents is made, it is necessary to later make a matrix of sequences, since it is the latter that is used to draw the network. This matrix is ​​not definitive, because subsequent adjustments are generally made in relation to the existence and availability of materials, labor and other execution limitations.

Times Matrix

In the study of times, three quantities estimated by those responsible for the processes are required: the average time (M), the optimal time (o) and the worst time (p).

The mean time (M) is the normal time needed to carry out the activities, based on the personal experience of the informant. The optimal time (o) is the one that represents the minimum possible time regardless of the cost or quantity of material and human elements that are required; it is simply the physical possibility of doing the activity in the shortest time. The lousy time (p) is an exceptionally long time that could occur occasionally as a result of accidents, lack of supplies, involuntary delays, unforeseen causes, etc. Only the time in which the problem presented is remedied should be counted and idle time should not be counted.

Time can be measured in minutes, hours, days, weeks, months and years, on the condition that the same measurement is used for the entire project. The above times will be used to average them using the PERT formula, obtaining a resulting time called standard (t) that is influenced by the optimal and the worst at the same time.

That is, standard time equals the optimal time, plus four times the average time, plus the worst time, and this sum divided by six (6). This formula is calculated to give the mean time a higher ratio than the optimal and worst influencing times. This ratio is four (4) to six (6).

Both the sequence matrix and the time matrix are brought together in a single so-called information matrix, which serves to build the measured network.

Activities Network

The graphic representation of the activities that show their events, sequences, interrelations and the critical path is called a network. Not only is the method called critical path, but also the series of activities counted from the beginning of the project to its completion, which have no flexibility in their execution time, so any delay suffered by any of the activities in the series would cause a delay in the whole project.

From another point of view, critical path is the series of activities that indicates the total duration of the project. Each of the activities is represented by an arrow that begins at one event and ends at another.

An event is called the moment of initiation or termination of an activity. It is determined in a variable time between the earliest and the latest possible, of initiation or termination.

The events are also known by the names of nodes.

The initial event is called i and the final event is called j. The end event of an activity will be the start event of the next activity.

The arrows are not vectors, scalars, nor do they represent any measure. The shape of the arrows does not matter, as they will be drawn according to the needs and convenience of presentation of the network. They can be horizontal, vertical, ascending, descending, curved, straight, broken, etc.

In cases where there is a need to indicate that an activity has an interrelation or continuation with another, a dotted line, called a league, will be drawn between the two, which has a duration of zero.

The league can sometimes represent a waiting time to be able to start the next activity.

Several activities can end in an event or start from the same event.

  1. Leave events loose when finishing the network. All of them must be related to the initial event or the final event.

Procedure to Plot the Measured Network

To draw the measured network, graph paper is used with the scale indicated at the top with the units of time chosen, in a reasonable interval for the execution of the entire project. As at this moment the duration of the same is not known, since one of the objectives of the network is to know it, this interval is only approximate.

The network is then started by drawing the activities that start from event zero. Each of them must be drawn in such a way that event j ends, according to the standard duration, in the time indicated on the upper scale. Now we will show the initiation of activities 1, 2, 3, and 4 with a duration of three, two, three and five days respectively.

In the case of the expansion of the factory, the initial activities are those shown in the figure below, since the three activities that start from scratch each last three days.

Next, the progressive numbering of the sequence matrix should not be taken to draw the network, but the activity terminals, from top to bottom and from left to right, as the events j appear.

In the previous case, we look for the sequences of activity 1, after 12 and at the last of 18. In their order, we look for the sequences of 2, 13 and 19. If an activity has zero duration, draw vertically, either ascending or descending, in such a way that it does not occupy time within the network.

Strictly speaking, an activity cannot have zero duration time, since it would not exist; However, some activities are so short in duration that it is negligible and it is not convenient to consider a unit of time. For example, if the unit is working for a day and the duration of the activity is five or ten minutes, there is no reason for this activity to be assigned a work day. In the case that is developed, the approval of the budgets is supposed to take from half an hour to an hour for their execution; but since the unit taken in the project is one day, the execution time is considered zero.

According to the annotations of the sequence matrix, activities 3, 14 and 20 must be simultaneous, so we need a common event to finish all three. Due to the need for construction, activity 14 will only be indicated with the number in parallel to activity 3, which also has zero duration. It can also appear parallel to activity 20.

In this type of network there is no need to indicate the activities with arrows, but only with lines, except for the links that will indicate the direction of continuity.

To continue with the drawing of the network, it must be remembered that activities 3, 14 and 20 converge to the common event and therefore we must look for the sequences of these three activities, which will logically start from the same event. We continue to lengthen terminals 15,4,21 and 9, in precisely this order, in accordance with the method adopted.

Thus we find that after activity 15 follows activity 16 with a duration of six days; after activity 4 follows activity 5 with a duration of six days; after activity 21 there follows activity 23 with a duration of three days and also activity 5 with a duration of six days; and after activity 9 follows activity 10 with a duration of two days.

When an activity is a sequence of two or more previous activities, it must be placed on the network after the most advanced antecedent activity.

For this reason, it is convenient to make the network with a pencil to be able to erase the activities and easily change places. In this way, it is necessary to modify the diagram of the previous figure, since activity 5 is later than 4 and 21; We remove it from the place that ends earlier and place it after the 21 that appears earlier. However, so that the sequence of 4 is not lost with 5, a link is placed between the two.

We look for the continuation of the terminals of activities 16, 5, 23 and 10, finding that they are respectively 17 with two days; the 6 with four days; 22 with four days and 11 with twelve days.

The activities after 17, 6, 22 and 11 are respectively 6 with four days; 7 with six days and none for 11, so in the network we only place a link between the end of 17 and the start of 6 to indicate continuity and another between the end of 22 and the start of 7 with the same object of continuity. Now we place the sequence of 6 only, since we have already seen that 11 is the end of the process. The sequence of activity 6 is 7 with six days and the sequence of activity 7 is 8 with duration of zero. Since there is no other activity after the network terminals, it must be considered that the project has been completed, so the duration of the project is 26 days.

By virtue of the fact that no single events should be left, a link is placed between the 11 terminal and the final event of the project, leaving the entire network as follows and in which the following particularities are appreciated:

  1. The activities that have zero duration are indicated vertically, either ascending or descending, such as those corresponding to activities 3, 20 and 8. Activity 14 with zero duration is not drawn on the network for construction reasons and is only indicated together with activity 20 that has the same characteristics. Activities that are sequential to two or more previous activities are drawn after the antecedent that has the highest date in its final event. Like activity 5, which is a sequence of activities 4 and 21. Activity 4 ends on day 6 and 21 ends on day 10. Activity 7 is a sequence of activities 6 and 22 and is placed in front of the one with the most recent date. discharge at the end, that is, activity 6.This same activity 6 is after activities 17 and 5 and is placed after activities 5 for the reason already given. The links that appear in the graph mean the following: activity 5 is a continuation of activity 4; 6 is a continuation of 17; 7 continues from 22 and 11 will end at the end of the project The critical path is the series of activities that begin in event i of the project and end in event j of the same, without suffering interruption due to what they indicate the size o duration of the project, and is represented by activities 12, 13, 21, 5, 6, 7 and 8 drawn with a double line.The critical path is the series of activities that begin in event i of the project and end in event j of the same, without suffering interruption for what they indicate the size or duration of the project, and is represented by activities 12, 13, 21, 5, 6, 7 and 8 drawn with double line.The critical path is the series of activities that begin in event i of the project and end in event j of the same, without suffering interruption for what they indicate the size or duration of the project, and is represented by activities 12, 13, 21, 5, 6, 7 and 8 drawn with double line.

The above network can be drawn with colors to indicate different responsibilities: for example, the responsibility of the electrical engineer is drawn in red, that of the civil engineer in green, and that of the plant engineer in blue.

Costs and Pending

In this step, the costs of each activity carried out in standard time and in optimal time will be requested. Both costs must be provided by the persons responsible for the execution, in accordance with the budgets already supplied by them. These costs should be noted in the information matrix.

Activities Normal Limit
A. From the Plant Engineer
1. Project 600.00 800.00
2. Cost 100.00 100.00
3. Approval - -
4. Unpacking 200.00 200.00
5. Placement 600.00 800.00
6. Installation 1,400.00 2,800.00
7. Testing 6,100.00 6,300.00
8. Start - -
9. Review 2,100.00 2,800.00
10. Machine Painting 960.00 960.00
11. Building Painting 3,160.00 3,520.00
15,220.00 18,280.00
B. From the Electrical Engineer
12. Project 6,000.00 6,500.00
13. Cost 100.00 100.00
14. Approval - -
15. Transformer 18,600.00 19,000.00
16. Lighting 8,900.00 9,300.00
17. Switches 4,100.00 4,400.00
37,700.00 39,300.00
C. Of the Contractor Engineer
18. Project 4,000.00 4,600.00
19. Cost 100.00 100.00
20. Approval - -
21. Foundation 3,400.00 3,800.00
22. Floors 2,800.00 3,200.00
23. Windows 1,900.00 2,200.00
12,200.00 13,900.00
Total of the Three Budgets 65,120.00 71,480.00
Buy New Machinery 80,000.00 80,000.00
Totals …………………………. 145,120.00 151,480.00

In the previous table we see the budgets with the normal cost for the activities carried out in standard time and the limit cost for the activities carried out on optimal time.

The totals in the normal cost column indicate the direct costs of the project executed in standard times, however the limit cost totals do not indicate a real cost, since it will not be necessary for all activities to be carried out in optimal time, but just some of them.

Network Compression

Compressing a network will help us determine which activities will be optimized in time.

Time Limitations

The normal execution time of the network must be determined and if it cannot be done in the available interval, the network must be compressed to the necessary time, calculating the increased cost.

The optimal execution time will indicate whether or not the project can be done within the specified period.

Resource Limitations

It is possible in any project to have the case of having limited human or material resources, so that two activities must be carried out during the same period with different personnel or different machinery, it cannot be executed and in this way there would only be more to wait for finish one activity to start the next.

In the following project the following limitations appear:

  1. Activities 11 and 12 must be carried out with the same machine, so it is necessary to finish one in order to start the other Activities 2 and 4 must be carried out with the same personnel Activities 8 and 9 must also be undertaken with the same machine.

For the solution of this problem, a measured network without limitations must first be made, then it will be studied on that same network, which activities of the limited ones must be carried out first and which ones later. Once the decision is made, the adjustment is made in the sequence matrix and the corresponding network is drawn with those adjustments.

Here we can see that for convenience it is better to do activity 11 before 12; activity 4 before 2 and activity 9 before 8; therefore we add the sequences corresponding to activities 11, 2 and 8 in the information matrix:

With these adjustments, the network that would contain the resource limitations could already be drawn, allowing optimization studies to be carried out in time and costs; We will show this in the following drawings after talking about the financial limitations.

Economic Limitations

The optimal cost will be determined to know if the project can be done with the available economic resources. If there is the possibility of doing it, the most favorable total time will be sought for the needs and objectives of the project; otherwise, the project will simply have to wait until it has the minimum financial resources to carry it out.

Elasticity Matrix

In order to make effective and quick decisions during the execution of the project, it is necessary to have at hand the data of the probabilities of delay or advance of work of each one of the activities, that is, their elasticity.

Let us first examine the procedure for calculating the clearances provided by the possibility of delaying an activity without consequences for other jobs.

Slack is the freedom that an activity has to extend its execution time without harming other activities or the total project. There are three classes of clearances:

  1. Total clearance; does not affect the completion of the project; Free play; does not modify the termination of the process; and Independent clearance; it does not affect the completion of earlier activities or the initiation of subsequent activities.

Total slack is important to the project manager, who is responsible for completing the project on time; free play is of interest to the head of execution of a process because of his responsibility for it; and the independent slack is information that is useful to the person who will coordinate the project work.

To calculate the clearances, the approved network is measured in the forward direction, as the first reading and then in the opposite direction as the last reading. The first reading will be indicated for each event within a circle and the last reading will also be indicated for each event within a square. It starts with the zero time indicated on the initial event and the standard duration of each activity is added, accumulating in each event.

When two or more activities converge in an event, the longest duration will be taken to make the event indication. For example, in activities 4 and 2 lasting two and six days respectively, the duration greater than six will be noted, which added to time four above will give a time of ten in the referred event. Note these same indications in the events found on the 15th, 19th and 21st.

When you have a league that indicates completion of the process, the same amount accumulated in the final event will be run towards the initial event. When the league does not indicate process termination, but only continuity between two processes, the accumulated quantities should not be modified even if the league has different start and end dates.

Then the last reading begins in the final event, scoring the same amount of 21 within a square; then the duration of each activity is subtracted and the difference is indicated in the following event.

When two or more activities converge in an event, the lower reading of them should be noted in this. In the initial events of the end-of-process leagues, the same amount recorded in the final event must appear, but in the continuity leagues the lesser amount of the activities that converge will be placed.

In the figure it can be seen that in each activity of the network there are four readings; the first and last of event i and the first and last of event j. Where:

P i Means the earliest the activity can start.

U i Means the latest it can be started.

P j Means the earliest it can be finished.

U j Means as late as it can be finished.

The difference between the earliest start date and latest finish date produces the longest available time slot and this is based on the project count.

Subtracting the duration t from this interval produces the total slack:

The difference between the earliest start date and the earliest end date indicates the available interval depending on the process, And by subtracting the duration t from this interval, the free slack remains:

The difference between the latest start date and the earliest finish date indicates the shortest possible time interval and is based on previous and subsequent activities, and by subtracting the time t from this interval the independent slack is obtained:

The readings of the events and the results of the application of the backlash formulas are passed to the information matrix.

In column 6 the standard time t was changed to the scheduled execution time e. The expansion percentage (column 15) is calculated by dividing the number of days of total slack by the standard time of each activity.

The activity class (column 16) is graded by taking the previous percentage from lowest to highest, being the zero-percentage critical class those that require the most attention and control.

The days that activities can be compressed (column 19) are obtained by subtracting the optimal time from the standard time. The compression percentage (column 20) is equal to the days compressed divided by the standard time of each activity.

The standard deviation (column 21) that represents the probability of being late or early on average is equal to the worst time minus the optimal time divided by 6.

By definition it represents 68% security. If greater security is desired in the result, the equivalent of two standard deviations will be taken from 95% and if 99% security is desired in the duration of the activity, three standard deviations will be taken.

In this way, we can observe that activity 5 has a standard time of six days and a standard deviation of one day. This means that it can be run between five and seven days with 68% security; between four and eight days with 95% security; and between three and nine days with 99% security. The greater the interval that is mentioned for the execution, the greater the certainty of hitting it.

The standard deviation of the project is equal to the sum of the standard deviations of the critical path:

This deviation will be the delay probability of the entire project. Of course it is the same probability of advancement of the same.

If there are several critical paths within the project, the largest deviation of them will be taken as the standard deviation of the project.

In the previous case the critical path is given by:

This means that the project will run between

that is, between 21 and 25 days, with 68% security. There is no probability of advancement in this project since its execution time is already compressed. The standard deviation can be designated as tolerance in the development of the project.

Lag Probabilities

To determine the probability that an activity or the entire project will be delayed, the amount of standard deviation corresponding to the desired days of delay is calculated and the following table is prepared:

PERT charts

The PERT graph is an original graph of unmeasured networks that contains the data of the activities represented by arrows that start from an event i and end in an event j.

At the top of the arrow the identification number is indicated, generally the event numbers (ij). The standard duration (t) of the activity appears within a rectangle at the bottom. In the upper half of the event the progressive number is noted, in the lower left quarter the last reading of the project and in the lower right quarter the first reading of the project.

This graph has the advantage of informing the earliest and latest start and end dates of each activity, without having to resort to the slack matrix.

Let's see how the factory expansion is presented by means of a PERT chart.

EXECUTION AND CONTROL OF THE PROJECT

Project approval

When the people involved in the execution of the project are fully satisfied with the times, sequences, costs and distribution of human and material resources, it must be approved. At this time the work program should be completed with the following:

  1. The list of activities The general budget The specifications of the activity The designation of positions and responsibilities and the organization of command The network of activities The limiting conditions of work The work procedures The necessary equipment The plans and itinerary and schedule diagrams The information matrices

Work orders

Work orders are prepared based on activity specifications, limiting conditions, work procedures, necessary equipment and process, itinerary and schedule schemes, as well as the help of the information matrices.

In them, the precise indications must be given so that the activity is carried out by the person or group of persons responsible, in accordance with the general plans, in time, in the quantity and of the desired quality.

Control charts

In project control, it is necessary to accurately determine both the progress of each of the activities and that corresponding to the total project. An effective form of control is the use of graphs that allow the development of activities to be visually monitored, and for this purpose, two types of graphs will be used:

  1. The progress graph The performance graph

The progress graph contains, in addition to the network, a strip at the bottom that shows the percentage of progress achieved in each unit of time.

The ordinates found in the time divisions mark the schedule for each activity, for each process and for the entire project.

To calculate the programmed percentage of progress, we proceed as follows:

  1. The total percentage of progress (1.00) is divided by the number of activity days that the project has. This number is the sum of column "e" of the information matrix (66).

F (Da) = = 0.0151

Naturally, if the unit of time does not represent days but hours, the unit of progress will be Ha (hours-activity).

  1. The units of advance (Da) that appear on the network on each scheduled day are counted. In each of the first four days we found 3 activities; in the fifth and sixth there are 4 activities; From the seventh to the tenth, we find 3 activities, etc. The units of progress are accumulated on each day that has passed, and the units of progress accumulated are multiplied by the progress factor calculated in part a.

In this way and for our base example, the following results are obtained:

The amounts that appear in column 4 of this table are entered at the bottom of the advance grid. It is enough to indicate two decimal places.

If greater precision in the drawing is desired and the size of the graph allows it, divisions can be made in the daily sections to show the progress of one by one percent.

Note that the scales are different in the sections that contain unequal amounts of (Da).

With the above, the progress graph is ready to receive the information.

Let us now prepare the performance graph that will help us to observe the pace or speed of work at the same time as the partial goals that are being achieved over time.

In the ordinate we present a scale with percentages and in the abscissa the days of the project duration plus the calculated tolerance.

This graph shows the final goal that is on the line of 100% efficiency and the coordinate of the final time of the project.

Now we can calculate the progress made daily in the project and present it in the previous graphs. Project progress is the sum of the progress achieved by each of the component activities.

The following table shows the daily reports of real progress in each activity.

This information is processed in the project progress table shown below:

The columns of this table are filled as follows:

  1. At the time of receiving the actual progress information: The day of the information is noted The numbers of the reported activities are expressed. A T will be entered first to indicate the activities previously completed. The percentages, as per one, of the work carried out until the day of the information, for each of the activities scheduled on the day indicated, the accumulated total is noted. of the activities previously completed. After making the previous annotation, the following columns are calculated: Indicate the scheduled days of execution for each activity reported in accordance with column e of the information matrix. In the base example, the array is in the table above.The reciprocals of the above times are determined to indicate the volume of work or load that corresponds to each day. For example, if an activity must be done in 3 days, each day corresponds to 1/3 of work, that is, in decimal 0.33. The reciprocal is obtained by dividing the unit by the number of days programmed and expressing this result in decimals. The days elapsed in each activity are indicated according to the program, and not with the days elapsed in the advance. Verify that these quantities are not greater than those indicated in column 3 of the table, since it is not possible to program more than 100% of the work of an activity Multiply the values ​​in columns 4 and 5 to obtain the percentage of work that must be fulfilled according to the program, for each activity, on the day of the information.This corresponds to the daily work load for the days elapsed in the reported activity. The total progress factor per activity (fa) is calculated by multiplying the factor of the progress unit (Da) by the number of days programmed in column 3 of this box. In our example, we must remember that Da = 1.00 / 66 = 0.0151. This column indicates the progress of the project with the work carried out in its entirety of the indicated activity. The previous percentage of progress in the project is adjusted with the actual percentage of the activity. To do this, multiply the percentage of activity in column 7 by the percentage in column 8. Since the progress of the project is the sum of the partial progress achieved by the activities,The amounts that appear in column 9 corresponding to the activities in operation and the accumulated total in column 10 for the activities already completed are added. This sum represents the actual progress of the project as of the day of the information. Now the scale of progress programmed in the progress graph is consulted to know the percentage that corresponds to the day of the information. Once found, it will be indicated in this column. This data can also be found in column 4 of the table. The percentage of project performance, productivity, speed or efficiency is equal to the amount of progress achieved. Divided by the programmed progress percentage. In this column, the result of dividing the amounts that appear in column 11 by the amounts in column 12 is noted.

The following annotations are made in the progress graph:

  1. The scheduled day, according to column 1. Fill in or color the rectangle corresponding to this day. The progress of the three activities in operation, as indicated in column 7. For activity 1 the scheduled work is 0.33 according to column 6, so the coordinate marks this amount. As the work achieved is the same programmed, the advance reaches the same coordinate. If this had not been the case, the annotation would have been made up to the proportional part. The progress of the project according to column 11. The lower band must be filled in with color to make this annotation. Join the programmed percentage and that achieved in the zone of deviations. If there is no angle it means that it is working according to the programmed; otherwise it may indicate delay or advance.The angle measurement is not related to the percentage of lag or lead because the scale of advance is uneven. It is only a visual wake-up call for noncompliance with the program.

Note that the coordinate corresponding to the scheduled days has different values ​​for the activities and for the project. Furthermore, you can present different values ​​for each activity. The values ​​taken for each activity must be consulted in the project progress table and the project values ​​must be observed in column 12 of said table.

Next we will proceed to make the annotation in the performance graph:

  1. Enter in the lower strip the day elapsed, according to column 1 of the project progress table. Enter the efficiency percentage according to column 13.

If there is a deficiency, an area will appear that must be colored below the 100% level.

  1. Indicate the percentage of progress, according to the amount that appears in column 11 of the table. The advance zone must be colored.

The progress of the project suffered a delay of 0.2426 - 0.2155 = 0.0271 (2.71%), reducing its efficiency or performance to 89% of the program, due to some of the activities being delayed. Activity 4 did not start because the machinery did not arrive at the warehouse. Activity 9 corresponds to the critical process. It has maximum control of progress and was performed on schedule. Activity 15 is late; I must advance; it had to advance 30% and only reached 10%. Activity 21 was also delayed although very little, perhaps it is only an error of assessment of the supervisor. Anyway, the delay is recorded.

The project suffered a greater delay as a consequence of not having started activity 4. Now the delay is 0.3032 - 0.2488 = 0.544 (5.44%) with an efficiency of 83%. Activity 9 is carried out according to the program. Activity 15 with a strong delay and activity 21 with a small delay.

The project delay was reduced, thanks to the initiation of activity 4. We now have 0.3487 - 0.3246 = 0.0241 (2.41%) behind with 93% efficiency. Critical Activity 9 continues according to schedule. Activities 15 and 21 accelerated the pace of work. The 21 managed to reach the scheduled quota.

Again, although small, a reduction in project delay was achieved. Activities 4 and 15 were finished. Activities 9 and 21 were executed on time. Activity 16 cannot be indicated due to the delay of 15.

The project is almost on time, since its efficiency reaches 99%. Activities 9 and 21 were completed and activity 16 is late. Activity 21, on the other hand, was finished, but ahead of the program.

This allows starting activities 5 and 23, which are sequential to activities 4 and 21, already completed.

The project has a small delay: 0.4852 - 0.4731 = 0.0121 (1.21%) with 97% efficiency. Activity 5 started one day early. On the other hand, 23 could not be started early, so the initiation will be normal. Activity 10, which is critical, was performed normally. Activity 16 continues with a strong delay due to the lack of materials.

The project work rate was maintained at 97% efficiency. Activity 10 was finished on time. Activity 5 is normally executed one day in advance of the program. Activity 16 is still late. Activity 23 on time.

The project presents the same small delay. Activities 5 and 11 run on time. Activities 16 and 23 late.

He sped up the project slightly with one point. The same situation in general, as in the previous day.

The project continues with the same slight delay. Process A was completed in its entirety.

Activity 22 is the only one delayed.

The same comment as the day before.

Process B was completely finished. The project on time.

The project on time.

The project and activities on time.

Processes C and D were completed. The project was completed on schedule.

Now let's see how the progress and performance graphs of the project were:

EXECUTION AND CONTROL OF PROCESSES

By virtue of the fact that each of the component processes of the project is led by different people who have the responsibility of starting and finishing their activities on time, it is necessary that they have their control chart where they can observe both the progress of their process and their performance.

This graph is similar to the performance graph used in the project.

A diagram of the activity sequences can be added to the top showing where the total slacks are located, so that the person in charge of the process has a precise idea of ​​their time availability.

We also need a process progress table with the following data and it is filled in as follows:

  1. With the original information from the supervisor: Write down the day of the information Indicate the number of the reported activity Express, in terms of one, the progress of the same The previous data is then processed in the following columns: Take the percentage from column 9 of the project progress table and write it down in this column Make the conversion with the factor (fa) previously calculated Write down the accumulated total of completed activities Sum of columns 5 and 6 that respectively represent the progress of the activity in operation and the accumulated total of activities completed in the process. This column indicates, therefore, the total progress in the process on the day of the information. Calculate the scheduled daily progress,dividing the unit by the total number of days of duration of the component activities of the process and accumulating said result Divide the progress achieved by the programmed progress to measure the performance of the process. Column 7 between column 8.

Let's see, in the base example, how the activities of process A are carried out.

Process A

This process will consist of five activities that last 15 days. If we remember that the value of the project progress unit (Da) is equal to = 0.01515, then this process represents the 15 x 0.01515 = 0.2272 (22.72%) of progress in the project. As this quantity 0.2272 represents 100% progress of the process, then the conversion factor of the percentage of progress from project to process (fa) will be:

0.2272: 1.00:: n: fa

fa = n = 4.39 n.

In this way, the percentage that appears in column 9 of the project progress table and transferred to column 4 of the process progress table, can be converted, with this factor, into the progress achieved in the activity based on this process.

This process A consists of five activities with a duration of 15 days. Your programmed advance unit will therefore be

Da = = 0.0667

As only one unit of advance is worked per day, this will be the daily accumulated advance that is programmed in column 8 of the process advance table.

Process B

This process consists of five activities with a total duration of 17 days, so its contribution to the progress of the project is 17 x 0.01515 = 0.2576.

The conversion factor (fa) from the percentage of progress of the project to the percentage of progress of the process is:

Fa = = 3.88

The unit of daily progress of this process will be:

Da = = 0.05882, What accumulated will be used to make the annotations in column 8 of the progress table of the process.

Process C

Process C is made up of six activities with a total duration of 17 days and, therefore, the conversion factor (Fa) and the daily advance factor (Da) programmed are the same as those of process B above.

Fa = = 3.88

Da = = 0.05882, The programmed advance count was interrupted on day 6 with 0.3533 until day 11, when it continues with activity 5.

Process D

This process D, with activities 9, 10 and 11, has, like the two previous processes, a duration of 17 days, so the conversion and progress factors are the same.

Fa = = 3.88

Da = = 0.05882, The process progress chart appears in the process progress chart table D.

EVALUATION PROCEDURE

When activities are carried out ahead of the scheduled dates, they generally do not modify their direct costs and, instead, indirect costs do decrease. In general terms, we can say that the results of the budgets benefit by completing the activities before the scheduled date. The decision to advance the activity following the one finished in advance is also simple and the possibility of doing so should only be investigated in terms of having the human and material resources required at that time.

When it comes to delays, evaluation and decision are not so simple because, as a general rule, costs change, sequences are disrupted and time availability is lost, so there is a need to have an evaluation procedure that allows determining all the consequences of a delay in a project activity.

The delays must be absorbed by the slack and in the event that these do not exist, they must be neutralized by means of compressions in the activities.

SLEEVE ABSORPTION

Multiply the scheduled execution time e therefore by one of the amount of work remaining to be done. The result is the time it takes to finish the activity normally. The time available is subtracted from the previous time and the difference represents the delay, which must be absorbed by the total slack. If this is not possible, proceed as follows:

COMPRESSION ABSORPTION

The optimal time is multiplied or therefore by one of the volume of work pending execution. The product represents the time required to complete the activity under optimal conditions, that is, with maximum acceleration. If this time is less than the available time, it means that the project will not be delayed, but if it is greater, the difference will be the amount of time that the project will delay, except that an activity after the delayed activity can be compressed within the process.

EVALUATION TABLE

All activities that are delayed or the scheduled start or end times are changed in any way should be analyzed using an evaluation chart such as the following:

The columns of this table will be filled with the following data:

  1. Note the day of the information Indicate the numbers of the activities that undergo variations in the program Percentage of work advanced by the activity per day that is reported, expressed as per one Percentage of work pending to be performed, equal to the amount minus the amount noted in column e. Execution time e programmed by the activity, according to the approved network. Real time elapsed since the scheduled date for its initiation. The normal time required to complete the activity is equal to the product of multiplying the execution time (5) therefore by one of missing work (4). The time available to execute the activity is the difference between the scheduled time (5) and the elapsed time (6). The remaining time is equal to the time needed (7) minus time available (8).Write down the total slack days calculated for the activity. Determine the number of slack days that will be needed to cover the missing time in column 9. Full days will always be used to cover fractions of missing time. It is convenient to make the modification in the information matrix. The amount of time used to absorb the delay will be increased to the available time 8 in the following days until the end of the activity. The available slack is the difference between the original amount (19) and the used slack (11). Record the time The optimal time required is equal to the product of multiplying the so much by one of missing work (4) by the optimal time (13). If when compressing the activity,the time required (14) to complete the activity is less than the time available (8) a zero will be entered in this column; Otherwise, the difference represented by the remaining time to finish the activity even after its compression will be noted. Note the slope of the activity, taken from the information matrix. The compressed time is equal to the programmed time (5) minus the time optimal (13). Enter the same amount that appears in column 4. The cost of the compression of the activity is equal to the product of multiplying the slope (16) by the compressed time (17) and by the volume of work that is missing to perform (18). This cost will be increased to the normal cost to obtain the total cost of the activity. If there is time shortage (15) after compressing the delayed activity,a subsequent activity must be used in the same process. In this case, the number of the affected activity must be noted in this column Note the slope of the affected activity taken from the information matrix Enter the scheduled time of the affected activity according to the information matrix Determine the amount Necessary understanding of the affected activity to absorb the missing time in column 15. The maximum compression of the affected activity should be obtained from the information matrix. In the event that this compressed time is not sufficient, one or more other activities of the same process must be compressed and if they are not available, this missing represents the amount of time that will delay the completion of the entire project.The cost of compressing the affected activity is equal to the product of multiplying the slope (21) by the compressed time (23). The total cost resulting from the compressions is equal to the sum of columns 19 and 24. Record in this column the modifications to be made to the program. The following symbols are suggested:
  1. HT-2 (14)

Take two days of total slack to complete activity 14.

  1. HT-1 (18) (23) (25)

Take one day of total slack to finish activity 18 and subtract one day of total slack, in the information matrix, from activities 23 and 25.

  1. Co-1 (5)

Compress activity 5 one day. In any case, the activity will be carried out in optimal conditions to speed up the missing work. The indicated time is only used for programming, but it is difficult to indicate the degree of acceleration, so it is preferable to apply the maximum.

  1. Co-2 (7) (15)

Compress the missing work for activity 7 into two days and the same amount for activity 15. In this case, activity 15 will start two days after the scheduled date to finish on the scheduled day.

  1. Co-1 (10) 3 (12)

Compress activity 10 one day and activity 12 three days.

Conclusions

PERT and CPM have been applied to numerous projects. Starting with their initial application to the Polaris project and to the maintenance of chemical plants, today they (and their variants) are applied to the construction of roads and buildings, and to the development and production of high-tech items such as airplanes, space vehicles, ships and computers.

PERT was developed for projects where there was uncertainty in the timing of the activities (usually because the project had never been tried before and therefore there were no databases, for the timing of the activities). This led to the probabilistic approach that was taken. While in PERT the time estimates and their distributions have been controversial, the PER'I 'has been a useful tool for project management. The main disadvantage is that it is not functional for large projects, due to the three estimates of time required for each activity and the limited capacity of current computers to store this vast amount of data. Additionally, the cost of updating and maintaining project information over time in such dynamic environments,it can be excessively prohibitive.

On the other hand, CPM was developed to handle repetitive or similar projects (eg, chemical plant maintenance). Obviously, a great deal of experience is gained over time in such circumstances, even though two projects may not be the same. This experience led to the analysis of collision techniques used in CPM networks.

While CPM and PER'I 'are essentially the same, their nuances make each more applicable than the other in different situations. In both methods the essential information desired is the critical path and the clearances. These allow the project manager to make informed decisions, based on the principle of management by exception, about the plans and projects of the current work and to monitor the progress of the project.

Bibliography

  • MONTAÑO, Agustín. Initiation to the Critical Path Method. 1972. Editorial Trillas, SA Mexico. DF México.MOSKOWITZ, Herbert and Gordon P. Wright. Operations research. 1982. Prentice Hall Hispanoamericana, SA Naucalpan de Juárez. México.TAHA, Hamdy A. Operations Research, An Introduction. 1989. Ediciones Alfaomega, SA Mexico. DF Mexico.

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The following video-lesson clearly explains how to create a CPM-PERT diagram, good material to complement what has already been stated in the document.

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Networks and pert / cpm critical path method