OPERATION RESEARCH BBA 4TH CSJMU (PERT & CPM)

                               BBA 4th Semester

         Subject : Operation Research (BBA 406N)

                                      UNIT 5th

                                    PERT & CPM

Project Management (PERT/CPM)

One of the most challenging jobs that any manager can take on is the management of a large-

scale project that requires coordinating numerous activities throughout the organization. A myriad of details must be considered in planning how to coordinate all these activities, in developing a realistic schedule, and then in monitoring the progress of the project. Fortunately, two closely related operations research techniques, PERT (program evaluation and review technique) and CPM (critical path method), are available to assist the project manager in carrying out these responsibilities. They also normally use a software package to deal with all the data needed to develop schedule information and then to monitor the progress of the project. Project management software, such as MS Project in your OR Courseware, now is widely available for these purposes.

PERT and CPM have been used for a variety of projects, including the following types. 

1. Construction of a new plant 

2. Research and development of a new product 

3. NASA space exploration projects 

4. Movie productions 

5. Building a ship 

6. Government-sponsored projects for developing a new weapons system

7. Relocation of a major facility 

8. Maintenance of a nuclear reactor 

9. Installation of a management information system 

10. Conducting an advertising campaign 

Application of PERT/CPM

The Application of PERT/CPM begin by breaking the project down into its individual activities, identifying the immediate predecessors of each activity, and estimating the duration of each activity. A project network then is constructed to visually display all this information. The type of network that is becoming increasingly popular for this purpose is the activity-on-node (AON) project network, where each activity is represented by a node.

PERT/CPM generates a great deal of useful scheduling information for the project manager, including the earliest start time (EST), the latest start time (LST), and the slack for each activity. It also identifies the critical path of activities such that any delay along this path will delay project completion. Since the critical path is the longest path through the project network, its length determines the duration of the project, assuming all activities remain on schedule. However, it is difficult for all activities to remain on schedule because there frequently is considerable uncertainty about what the duration of an activity will turn out to be. 

The PERT three-estimate approach addresses this situation by obtaining three different kinds of estimates (most likely, optimistic, and pessimistic) for the duration of each activity. This information is used to approximate the mean and variance of the probability distribution of this duration. It then is possible to approximate the probability that the project will be completed by the deadline. 

The CPM method of time-cost trade-offs enables the project manager to investigate the effect on total cost of changing the estimated duration of the project to various alternative values. The data needed for this activity are the time and cost for each activity when it is done in the normal way and then when it is fully crashed (expedited). Either marginal cost analysis or linear programming can be used to determine how much (if any) to crash each activity in order to minimize the total cost of meeting any specified deadline for the project. 

The PERT/CPM technique called PERT/Cost provides the project manager with a systematic procedure for planning, scheduling, and controlling project costs. It generates a complete schedule for what the project costs should be in each time period when activities begin at either their earliest start times or latest start times. It also generates periodic reports that evaluate the cost performance of the individual activities, including identifying those where cost overruns are occurring. 

PERT/CPM does have some important deficiencies

These include questionable approximations made when estimating the mean and variance of activity durations as well as when estimating the probability that the project will be completed by the deadline. Another deficiency is that it does not allow an activity to begin until all its immediate predecessors are completely finished, even though some overlap is sometimes possible. In addition, PERT/CPM does not address the important issue of how to allocate limited resources to the various activities. Nevertheless, PERT/CPM has stood the test of time in providing project managers with most of the help they want. Furthermore, much progress is being made in developing improvements and extensions to PERT/CPM (such as the precedence diagramming method for dealing with overlapping activities) that addresses these deficiencies.

Few important Definitions:

1. Oriented graph: A graph in which all the branches are oriented is called an oriented graph

2. Path: A path joining nodes I and j is a sequence of branches connecting these two nodes. 

The nodes I, j are called the extremity points of the path. Two different paths (chains) joining nodes 1 and 5 may be given as follows.

(i) (1, 2), (2, 3), (3, 6), (6, 4), (4, 5)

(ii) (1, 2), (2, 6), (6, 5)

3. Loop: If the extremity points of the path are one and same node, then the path is called a loop. Thus (1, 2), (2, 4), (4,1), is called a loop.

4. Connected graph: A graph is said to be a connected graph if there is a path (or chain) connecting every pair of nodes of the graph.

5. Tree: A tree is a connected graph which has no loops. In other words, a connected graph is a tree if and only if the path joining any two nodes is unique. A tree always has at least two extreme points.

NETWORK 

A network is a graphical representation of project’s operations.If an oriented graph is a network, the orientation to branch is assumed to be the feasible direction of the flow along the branch. A network need not to be oriented since it may be feasible to have flow either direction along a branch. If there is a limit to the magnitude of the flowing any branch of a network, then a capacity restriction is imposed on that branch. The flow of capacity of a branch in a specified direction is the upper limit to the feasible magnitude of the rate of flow capacity is zero in one direction.

A node /in a network is called a source if every branch which has this node as end point is oriented in such way that the flow in the branch moves away from this node/. Similarly, a node in a network is called sink if every branch which has this node as end point is oriented in such a way that the flow is from other nodes to this node. 

In a network, we assume that the branches are connected only at nodes. 

In this unit we shall discuss the problem of network analysis for the following methods.

1. Critical Path Method (CPM)

2. Project evaluation and Review Technique (PERT)

Difference between CPM and PERT 

CPM and PERT are almost as a single technique and the difference between the two is only of the historical or academic interest. However, the main points of difference between them are as follows:

CPM:

1. CPM is an activity oriented technique, i.e, CPM network emphasis more one on the descriptions associated with activities.

2. CPM is a deterministic model, i.e it does not take into account the uncertainties involved in the estimation of time for execution of a job or an activity. 

3. CPM is commonly used for projects involving activities of repetitive nature. 

4. CPM give dual emphasis to time and cost is suitable to evaluate the trade-off between project cost and project time. With additional resources, it allows the project manager to manipulate and shorten the project time within certain limits at an optimal cost.

PERT:

1. PERT is event oriented, i.e, PERT network emphasis more on the descriptions associated with events.

2. PERT is use for Variable Activites.

3. PERT is a probabilistic model. Here, the expected duration of each activity is 

probabilistic 

4. PERT is generally used for one time projects involving activities of non-repetitive nature.

5. PERT give emphasis to time only. It helps the project managers to schedule and co-ordinate various activities so that the project is completed on prescribed time. 

Terminology used in PERT/CPM Network Analysis (Network Components)

PERT/CPM network consists of two major components. 

1. Activity: An activity is a task (or operation or item of work) to be done that consumes time and resources. In a network, activity is represented by an arrow, the tail of which represents the start and the head represents the finish (or end) of the activity. 

2. Events: The beginning and end points of an activity/activities are called events or nodes. Event is a particular instant in time and does not consume any time or resource. It is generally represented by numbered circle. It may also be represented by a rectangle, square, hexagon, or some other geometric shape. 

For example, an activity (i, j) represented by an arrow extends between two nodes i and j, the tail node (or event), called the preceding event represents the start of the activity and the head node, called the succeeding event represents the completion of the activity. This activity is shown in the following figure.

For an activity, the arrow is always from left to right and i<j, the number of head event is always higher than number of tail event.

The events can be classified by the following three categories:

1. Merge Events: An event which represents the end (or head) of more than one activity is called a merge events.

2. Burst Event: An event which represents the beginning (or tail) of more than one activity is called a burst event.

3. Merge and Burst Event: An event which represents the beginning (or tail) of some activity (or activities) and is also the end (head) of some activity (or activities) is called a merge and burst event.

Construction of the Network Diagram 

The following question will generate the necessary information for the construction of a network diagram. 

1. Which activities (or operation) must be completed immediately before each activity (or operation)? Such activities are called predecessor (or preceding) activities.

2. Which activities (or operation) can be carried out simultaneously?

3. Which activities (or operation) follow other given activities (or operations) such activities are called successor activities?

For the construction of a network diagram the following rules are followed:

Rule 1: Each activity (or operation) is represented by one and only one arrow in the network.

This rule implies that none of the operation can be represented more than once in the network. 

Rule 2: No two activities can be identified by the same end events (nodes).If two activities have the same end events, then we introduce a dummy activity between end events of the activities. It should be noted that a dummy activity does not consume any time or resources.