By Issa Bass
 

The objective of a project is either to solve an existing problem or to start a new venture. In either case a carefully planned and organized strategy is needed to accomplish the specified objectives. The strategy includes developing a plan which will define the goals, explicitly set the tasks to be accomplished, determine how they will be accomplished, estimate time and the resources (both human and material) needed for their completion.

How projects are planned and managed will seriously impact on the profitability of the ventures that they are intended for and the quality of the products or services they generate.

Most project management plans are subdivided into four major phases: the feasibility study, the project planning, the project implementation and the verification or evaluation. Each one of these phases requires strategic planning.

Since all the tasks included in a project cannot be executed at the same time because of their interdependence, a critical path needs to be determined when scheduling of the activities.

The three major tools that are used for the purpose of planning and scheduling the different tasks in project management are the Gantt chart, the Critical Path Analysis (or Method) and the Program Evaluation and Review Technique.

But before any scheduling starts, it is essential to accurately estimate the time that every task might require. A good scheduling must take into account the possible unexpected events and the complexity involved in the tasks themselves.

This requires a thorough understanding of every aspect of the tasks before developing a list.

One way of creating a list of tasks is a process known as the Work Breakdown Structure (WBS). It consists in creating a tree of activities that take into account their lengths and contingence.  The WBS starts with the project to be achieved and goes down to the different steps necessary for its completion. As the tree starts to grow, the list of the tasks grows.

Once the list of all the tasks involved is known, based on experience or good wit, an estimation of the time required can be made and milestones determined.

Knowing the milestones of a project with certainty is extremely important, because they can affect the timeliness of the project completion as a whole, and delays in project completions can have serious financial consequences and above all they can cost companies market shares. In a global competitive market, innovation is the driving force that keeps businesses alive, and this is more obvious in high tech industries. Most companies have several lines of products and each one of them is required to put out a new product every year or every six months. If for instance DELL's Inspiron or Latitude fails to put out new products on time, it is likely to lose profit from the forgone sales (the loss is proportional to the products' Time-To-Live) and market shares to its competitors.

The Gantt chart

Gantt charts (named after the American social scientist, Henry L. Gantt, its author) are effective for scheduling complex tasks. They help arrange the different events in synchronism and associate each task with its owner and its estimated beginning and ending time.

The charts also allow the project's team to visualize the resources need to complete the project and the timing for each task, it therefore shows where the task owners must be at any given time in the execution of the projects. The team working on the project should know whether it is on schedule or not by just looking at the chart.

The chart itself is divided in two parts. The first parts shows the different tasks, the tasks owners, the timing and the resources needed for their completion; the second part graphically visualizes the sequence of the events.

The following chart summarizes a project scheduling for a building construction.

The horizontal bars on the calendar side of the chart depict the beginnings and the ends of the scheduled tasks.

Some tasks cannot start until the preceding ones are finished. The main disadvantage of a Gantt chart is that it does not take into account the interdependence between the tasks. It shows the sequence and the beginning and the ends of the tasks but does not indicate whether one task has to wait for the end of a preceding one.

The Critical Path Analysis is another tool used for complex projects and it does take into account the interdependence of the tasks

Critical Path Analysis (CPA)

Not only does the CPA take into account the interdependence of the critical tasks, but in addition it considers the possibility of performing different tasks in parallel, and the tasks that can be performed at the same time or wait. It also helps monitor the execution of the tasks as they are being implemented. The CPA identifies the tasks that need to be completed on time and the ones that can wait for the whole project to meet its deadline. It helps estimate the Critical Path, the project duration and the slack time for every activity.

The CPA resembles the tree in the Work Breakdown Structure (WBS) with the difference that it takes into account the timing of the tasks. It is a web of activities linked by arrows between every two nodes.

The first step in creating a CPA diagram is to list the tasks including their duration and the order in which they have to be completed.

In some case, the project team might itself be in need to complete the project before the time predicted by the CPA, which creates a need to reduce the time spent on some activities.

The following table contains the information needed to create and display the Critical Path for a fictitious project.

Based on this information, we can determine the Critical Path, the project duration and the slack time for H.

Task A is the first on the list, no other task can start until it is completed. Tasks B and C come next, they are contingent on task A. task E, G and H are on the same path as C, while task D and F are on the same path and depend on B.

The letters on the diagram represent the different activities and the numbers beside them represent the time it will take to accomplish the tasks.

The diagram shows that there are two paths to the project: ABDF and ACEGH. The duration for ABDF is 20 day and the duration for ACEGH is 18 days. Since ABDF is the longest path, it is also the Critical Path. The earliest that the task H can start is within 16 days.

The advantage of the Gantt chart over the CPA is the graphical visualization of the tasks along with their timing, the task owners, the start time and end times. The advantage of the CPA over the Gantt chart is the sequence of events that takes into account the interdependence of the tasks.

The CPA is a deterministic model because it does not take into account the probability for the tasks to be completed sooner or later than expected, the time variation is not considered.

Program Evaluation and Review Technique (PERT)

The PERT is just a variation of the CPA with the difference that it follows a probabilistic approach while the CPA is a deterministic model.

Once the critical tasks have been identified, their timing estimated, the sequence of events determined and a list of activities established, we can evaluate the probability for the different tasks to be accomplished on time and the shortest possible time for each of them.

The completion of each task is said to follow a Beta distribution with the expected length of the project being

E(p) =
Where
LgT   stands for Longest time
ST  Stands for Shortest time
lt  Stands for likely time

The estimated standard deviation

The completion of the whole project follows a Normal distribution.

Based on the information bellow, find the critical path for the project, the project completion time, the probability of finishing it on time and the probability of finishing it at least 1 day earlier.

Solution:

The critical path has the longest duration. It is critical because any delay in any task will cause a delay for the whole project. In this case, we have two paths ABDF which will last 20 days and ACEGH which will last 17 days. So the critical path is ABDF.

The estimated variance for the critical path is 0.029 + 0.11 + 0.25 + 0.11 = 0.499 with a standard deviation of .

Completing the project at least 1 day earlier means completing it in 19 days or less. The probability for such an event to take place is found using Normal distribution

1.42 corresponds to 0.9222 on the Normal table. Since we have a negative sign, the area we are looking for will be on the right side of 0.9222 under the normal curve which is equal to 0.0778.

About the author
Issa Bass is the managing editor of SixSigmaFirst. He can be reached at issa@sixsigmafirst.com

Tell us what you think about this article. Send a note to the Editor.

http://www.mindtools.com/pages/article/newPPM_04.htm