PERT/CPM

Introduction

The reticular analysis enables design and planning of a project, at all levels of details, regarding the duration of each activity, the order of priority, the review of the program when changes or delays happen and finally the cost of the project.

The methods of reticular analysis which are used to optimize the design and planning of a project are Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) . These methodologies were developed independently of each other in late 50s. Researchers have used PERT method for handling problems with stochastic activities' times while they have used CPM method for problems with deterministic times.

Essentially, this difference resulted because these two methods encountered problems of different nature during the period they were developed. There were also differences in the way in which the two methods depicting activities with a network form.

In PERT networks, the activities were represented with edges while in CPM networks, the nodes symbolized the activities.

In any case, these differences do not exist anymore. The way of representation of the activities is based on the user's selection while the methodology is merged in a common method which is called PERT/CPM method. According to this, all the networks which are obtained by this method, they are called PERT/CPM networks.

History

In 1958, James E. Kelly of Remington Rand and Morgan R. Walker of DuPont, apply for the first time the CPM to support the planning of construction and maintenance of industrial chemical production complexes. The cases of use of CPM method are presented mainly in construction works, in construction of airplanes and in large shipbuilders.

Application

PERT/CPM network representation

There are two methods for representing the PERT / CPM networks.

• The first method is the Activity On Arrow (AOA) where each activity is represented by a unique edge, whereas the nodes represent the starting and finishing events of the activity which is enclosed by the edge defined by two nodes. In a PERT / CPM network, the lengths of the edges are not necessarily proportionate to the duration of each activity. The relative sequence of the activities is reflected by the fact that the starting node of an activity, i.e. an edge which starts at a node, can be both the finishing node of all activities (edges) that lead to it. So, all the activities which are leaded to a node must be completed before beginning an activity whose edge starts from the same node. In each edge it is noted the symbol of the corresponding activity and its duration. This representation is called PERT / CPM network on an AOA type.
• The second method is the Activity On Node (AON) where each activity is represented by a single node, while the sequence relationship that has been recorded in the table of the immediately previous activities is reflected by the edges which connect the nodes-activities. Each activity (node) which is associated with a subsequent activity through an edge is a prerequisite and must be completed before starting the next activity. At each node we note the duration and the name of each activity. This representation is called PERT/CPM network on an AON type.

Usage

Discussion

The key questions that can be answered and moreover the general the information which can be acquired by the project manager and by extension, the execution group by constructing the PERT/CPM network are the followings:

• The graphical representation of the activities and in particular, accurate graphical representation of the sequence of prerequisite activities.
• The estimation of the total time that the work will last.
• The identification of the critical activities. In other words, all these activities that must not be delayed because then, the completion of the project will be delayed.
• The identification of non-critical activities. In other words, all these activities which have delay margins without affecting the project.
• For each non-critical activity, the slack time can be detected. In other words, this is the maximum possible margin delay of an activity without charge of the total time of the project.
• The identification of the probability of the project completion within a certain period of time and in particular in cases where the duration times of activities are estimations.
• The ability to monitor the temporal evolution of the project, the allocation of resources and the possibility of revising the program by changing times, identifying new critical activities and reallocating resources.
• The definition of the possibility to reduce the project completion time (crashing), by the determination of the required resources and the activities which need to be fed.