Project Management

The Numbers Group

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Introduction to Project Management

Project management was first used to manage the US space program. It's practice has now been expanded rapidly through the government, the military and the corporate world. Here is the main definition of what project management is:

  1. Project management is no small task.
  2. Project management has a definite beginning and end. It is not a continuous process.
  3. Project management uses various measurement tools to accomplish and track project tasks. These include Gantt and Pert charts.
  4. Projects frequently need resources on an add-on basis as opposed to organizations who have full-time positions.
There are three main points that are most important to a successful project:
  1. A Project must meet customer requirements.
  2. A Project must be under budget.
  3. A Project must be on time.

There are four phases a project goes through.

The role of the project manager in project management is one of great responsibility. It's the project manager's job to direct and supervise the project from beginning to end. Here are some other roles:
  1. The project manager must define the project, reduce the project to a set of manageable tasks, obtain appropriate and necessary resources, and build a team or teams to perform the project work
  2. The project manager must set the final goal for the project and must motivate his workers to complete the project on time.
  3. A project manager must have is technical skills. This relates to financial planning, contract management, and managing creative thinking and problem solving techniques are promoted.
  4. No project ever goes 100% as planned, so project managers must learn to adapt to change.
There are many things that can go wrong with project management. These are commonly called barriers. Here are some possible barriers:
  1. Poor Communication
  2. Disagreement
  3. Failure to comply with standards and regulations.
  4. Inclement weather.
  5. Union strikes.
  6. Personality conflicts.
  7. Poor management
  8. Poorly defined project goals


What is a Goal?

According to the New Comprehensive International Dictionary of the English Language a goal is a point toward which effort or movement is directed. The objective point that one is striving to reach

All goals should be SMART Goals



Agreed Upon



Project Life Cycle

In Contemporary Systems Analysis, 5th Edition published by Business and Educational Technologies, Marvin Gore and John Stubbe wrote that the Project Life Cycle includes the following Phases and activities:

A. Study Phase

  1. User Need
  2. Initial Investigation
  3. User Review
  4. System Performance Design
  5. Candidate Review
  6. Study Phase Report

B. Design Phase

  1. General System Review
  2. Processing Requirements Identification
  3. Data Base Design
  4. Control Requirements
  5. Output Design
  6. Input Design
  7. Software Selection
  8. Equipment Selection/Acquisition
  9. People
  10. Reference Manual Identification
  11. Plans
  12. Design Specifications Preparation
  13. Design Phase Report Preparation

C. Development Phase

  1. Implementation Planning
  2. Computer Program Design
  3. User Review
  4. Equipment Acquisition and Installation
  5. Coding and Debugging
  6. Computer Program Testing
  7. System Testing
  8. Reference Manual Preparation
  9. Personnel Training
  10. Changeover Plan Preparation
  11. Development Phase Report Preparation
  12. User Acceptance Review

D. Operation Phase

  1. System Changeover
  2. Routine Operation
  3. System Performance Evaluation
  4. System Changes/Enhancements

Project Management Tools


Good project management deals with three factors: time, cost and performance. Projects are successful if they are completed on time, within budget, and to performance requirements. In order to bring the many components of a large project into control there is a large toolkit of techniques, methodologies, and tools. These techniques provide the tools for managing different components involved in a project: planning and scheduling, developing a product, managing financial and capital resources, and monitoring progress. However the success of a project will always rest on the abilities of a project manager and the team members.


This tool is related to planning and scheduling a project. Basically it is a functional decomposition of the tasks of the project. The total work of the project is broken down into the major subtasks. It starts with the end objective required and successively subdividing it into manageable components in terms of size and complexity: program, project, system, subsystem, components, tasks, subtasks, and work elements.


It should be product- or task-oriented and should include all the necessary effort which must be undertaken to achieve the end objective. Because it defines the work required to achieve an objective and help to show the required interfaces, a WBS is useful for complex projects. However, it has got an important drawback: it does not show the timing of activities. In order to overcome this drawback, another tool can be used.


Developed by Harry Gantt in 1916, these charts give a timeline for each activity. They are used for planning, scheduling and then recording progress against these schedules.


Basically there are two basic types of Gantt Charts: Load Charts and Project Planning Charts.

* Load Charts:
This type of chart is useful for manufacturing projects during peak or heavy load periods. The format of the Gantt Load Chart is very similar to the Gantt Project Planning Chart but, in this case, uses time as well as departments, machines or employees that have been scheduled.

* Project Planning Chart
It addresses the time of individual work elements giving a time line for each activity of a project. This type of chart is the predecessor of the following tool: PERT. As it can be seen in the figure, it is really easy to understand the graph, but in developing it you need to take into consideration certain precedence relationships between the different activities of the project. On the chart, everyone is able to see when each activity starts and finishes but there is no possibility to determine when each activity may start or if we can start a particular activity before finishing the immediate predecessor activity. Therefore, we need somehow know the precedence relationships between activities. This is the main reason for using the following tools instead of using exclusively Gantt Charts.

PERT/CPM (Critical path Method)

Both methods show precedence relationships explicitly. Although the two methods were developed independently during the fifties, they are surprisingly similar. Both methods, PERT and CPM, use a graphic representation of a project that it is called "Project Network" or "CPM diagram", and it is used to portray graphically the interrelatioships of the elements of a project and to show the order in which the activities must be performed.


In order to represent a project network, two basic elements are used:

A cycle, called "node", represents an event. An event describes a checkpoint. It does not symbolize the performance of work, but it represents the point in time in which the event is accomplished.

An arrow, called "arc", represents an activity.

The network will try to reflect all the relationships between the activities.

Two simple rules govern the construction of a project network:

  1. Each activity must be represented by only one directed arc or arrow.
  2. No two activities can begin and end on the same two nodes or cycles.

Another element to represent a project network is a "dummy activity". To explain it, we will consider the following example:

The temptation is to represent these relationships as:

But then we have broken the second rule earlier mentioned. To show that activities A and B precede C, whereas activity B precedes activity D, we use a dummy activity as shown in the figure:

To construct a project network, first of all, we need a list of activities showing the precedence relationships between the different activities involved, a list as the following example:


Because each activity must have a unique pair of starting and ending nodes, we must use a dummy activity to draw the first four activities, as shown in the figure. Constructing a project network, is a trial-and-error process. It usually takes two or three attempts to produce a neatly constructed network. After constructing the network, the duration of each activity should be shown in parenthesis. But, what is this for? With this representation we can determine the minimum completion time for the project. We do this by starting at the originating event of the network (node 1) and determining the earliest time we can start an activity, given the activities that precede it and assuming that all the activities start as soon as possible and are completed as soon as possible. For example for the first one, it would be:

Where T=0 is the Earliest Start Time (ES) for activity A and T=1 is the Latest Start Time (EF) for activity A. Continuing this process results in the network:


Notice that in the case of activity D for example, it only starts after both precedence activities B and C are completed. If everything goes as planned, the project will take 15.5 months to complete. However, every activity needs to start as early as possible for the project to be completed in 15.5 months. We can use a similar process to determine which activities we can delay, and by how much, without increasing the completion time of the project. To calculate this, we can define the "Latest Finish Time" (LF), and the "latest Start Time" (LS) for each activity, for example:

Continuing with this process we can obtain


Now we have a project network with the earliest and the latest start and finish times, where:

Then I can calculate how much I can delay an activity. That is the "Slack Time." To determine it, we can use either or two equations:

Slack Time: LS-ES

Slack Time: LF-EF

The slack represents how long we can delay the activity without delaying the entire project. The activities that have zero slack lie on a path through the network. This path is called the "Critical Path," and the activities are called "Critical Activities." If you delay these activities, you will delay the entire project. Every project has at least one critical path, but there can be more than one. Another procedure to determine the critical path is just noticing which is the largest path through the network, in this case A-B-D-G-H-I-K-L.


Both tools lead to the same end: a critial path and critical activities with slack time equal to zero. The differences between these tools come from how they treat the activity time. PERT treats activity time as a random variable whereas CPM requires a single deterministic time value for each activity. Another difference is that PERT focuses exclusively on the time variable whereas CPM includes the analysis of the Time/Cost Trade-off.


We have a high degree of uncertainty in regard to the completion time of many activities. It makes sense in the real world that you do not really know how long a particular activity will take, specially talking about certain activities such as research and development. In this case, we can look at the project completion time in a probabilistic fashion and for each activity we can define:

  1. Optimistic time estimate: an estimate of the minimum time an activity will require.
  2. Most likely time estimate: an estimate of the normal time an activity will require.
  3. Pessimistic time estimate: an estimate of the maximum time an activity will require.

These three estimates are considered to be related in the form of unimodal probability distribution: m. What we need in any case is a specific duration for each activity taking into consideration these three estimates. This can be possible calculating the expected or mean activity time for each activity as

With the expected time for each activity we can determine which is the critical path. Using three assumptions, we can conclude that project completion time or critical path completion time has a normal distribution. Using this, we can determine probabilities, using completion time as a normal random variable, mean and standard deviation.

P(Completion Time <= 15.5 months) = P ( z <= 15.5 - mean/ standard deviation) =

Other Useful Sites for Obtaining Information

Project Management Institute

      Home Page:

To Download Project Management Book of Knowledge:

Listing of Articles about Project Management:

Examples of Project Management Training Opportunities:
      Project Management Service Bureau:
      Paul S. Adler & Associates:
      LCT, Incorporated:
      CHM & Co. Pty Ltd:

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