Critical Path Analysis

Introduction

Planning, Scheduling and Controlling are three important functions of management. Planning involves the formulation of objectives and goals that are subsequently translated into Specific plans and projects. Scheduling is concerned about the implementation of activities necessary to achieve the laid down plans. The function of control is to institute a mechanism that can trigger a warning signal if actual performance is deviating (in terms of time, cost and some other measures of effectiveness) from the plan.

If such a deviation is unacceptable to the concerned manager, he will be required to take corrective action to bring performance in conformity with the plans. The PERT and CPM models are extremely useful for the purpose of planning, scheduling and controlling the progress and completion of large and complex projects or for carrying out the analysis of these three managerial functions. Before we describe the basic concepts used in the construction and analysis of these models, let us first understand the meaning of a project. What is a project?

A project can be defined as a set of large number of activities or jobs that are performed in a certain sequence determined logically or technologically and it has to be completed within

• a specified time,
• a specified cost and
• meeting the performance standards.

Examples of a project from fairly diverse fields are given below:

1. Introducing a new product in the market.
2. Construction of a new bridge over a river or construction of a 25 storied building,
3. Executing a large and complex order on jobbing production.
4. Sending a spacecraft to the mars.

General Framework of PERT/CPM

A network is a graphical representation of a project, depicting the flow as well as the sequence of well-defined activities and events. Developed during the 1950s, both CPM (Critical Path Method) and PERT (Programme Evaluation and Review Technique) are network techniques/models. The network approach helps project managers in planning, Scheduling and controlling. As a planning tool it helps the manager to estimate the requirements of resources viz. , materials, equipment, manpower, cost and time for each activity or tasks of the project. This approach cannot make decisions by its own.

It only provide additional information to executives to facilitate decision making process. Also it does not provide solution to every management problem. It certainly helps in identification of those activities, jobs or events which control the completion of the project. The working methodology of critical path analysis (CPA) which includes both CPM and PERT, consists of following five steps:

1. Analyse and break down the project in terms of specific activities and/ or events.
2. Determine the interdependence and sequence of specific activities and prepare a net work.
3. Assign estimates of time, cost or both to all the activities of the network.
4. Identify the longest or critical path through the network.
5. Monitor, evaluate and control the progress of the project by replanning, rescheduling and reassignment of resources.

The central task in the control aspect of these models is to identify the longest path through the network. The longest path is the critical path because it equals the minimum time required to complete the project. All other paths other than the critical path (i. e. o critical or slack paths) offer flexibility in scheduling and transferring resources, because they take less time to complete than the critical path.

Advantages of Critical Path Analysis

There are a number of advantages in using critical path analysis. 1. It allows for a comprehensive view of the entire project. Because of the sequential and concurrent relationships, time scheduling becomes very effective. Identifying the critical activities keeps the executive alert and in a state of preparedness, with alternative plans ready in case these are needed.

1. Breaking down the project into smaller components permits better and closer control.
2. Critical path analysis offers economical and effective system of control based on the principle of management by exception i. e. need for corrective action arises only in exceptional situations and in most of other cases, performance is in conformity with the plans.
3. It is a dynamic tool of management which calls for constant review, a reformulation of the network, and finding the current path of relevance and optimum resources allocation.

Fundamentals of a CPA Network

( Activity An activity is any portion of a project which consumes time or resources and has a definable beginning and ending. For example, “laying of pipe” is an activity requiring the use of resource mainly effort. Activity may involve labour, paper work, contractual negotiations, machinery operations, etc. Commonly used terms synonymous with “activity” are “task” and “job”.

The tail of the arrow portraying an activity represents the starting point of the activity and its head represents its completion. The arrow may be straight slanting, or bent but not broken. The arrow is not a vector and need not be drawn to scale. ( Events The beginning and ending points of an activity or a group of activities are called events. Synonyms of an event are “node” and “connectors” An event is often represented graphically by a numbered circle, although any geometric figure such as square, oval, rectangle etc. will serve the purpose.

We shall, however, stick to the most commonly used convention for representing an event viz, the circle. A few examples of events are as follows :

1. Material procured,
2. Design completed,
3. Project started,
4. Bricks laid, etc.

All activities in a network must commence from some event. Such events are called the tail events because they are connected to the tail of an activity. Similarly, all activities in a network must have terminal points called the head event because it is at the head of an activity.

Tail and head events connected by arrows representing activities i. e. it depicts the dual role of an event. Event 14 is the head event for one activity and tail event for another. In a network, symbol “i” is used for the tail event (also called preceding event) and “j” for the head event (or succeeding event) of an activity. The activity, then being I-j. If an event represents the joint completion of more than one activity, it is called a merge event. If an event represents the joint initiation of more than one activity, it is called a burst event.

A network is, then, a graphical representation of a project plan, showing the inter-relationship of the various activities. Networks are also called arrow diagrams. When the results of time estimates and computations have been added to a network, it may be used as a project schedule. Conventions adopted in drawing networks: There are two conventions normally adopted while drawing networks. In the early stages of network drawing, it is suggested that the conventions should be respected until sufficient experience has been gained to justify dropping them.

These conventions are: a) Time flows from left to right. b) Head events always have a number higher than that of the tail events. The above stated conventions allow activities to be referred uniquely by their tail and head event numbers, so that “activity 3-4” means only “the activity which starts from event 3 proceeds to event 4”; it cannot mean “the activity which starts from event 4 and finishes event 3”. Graphical representation of events and activities: Events are represents by numbers within circles. Activities are represented by arrows, the arrow-heads represent the completion of the activities.

The length and orientation of the arrow are of no significance whatsoever (chosen only for the convenience of drawing). The activity of leaving place A and walking to place B can equally well be represented. Fundamental properties governing the representation of events and activities: The representation of events and activities is governed by one simple dependency rule which requires that an activity which depends upon another activity is shown to emerge from the head event of the activity upon which it depends and that only dependent activities are drawn in this way.

Thus, if activity B depends upon activity A, then the two activities.

1. An event cannot occur until all activities leading to it are complete.
2. No activity can start until its tail event in reached.

The above two properties can be combined into a single one, namely that “no activity may start until all previous activity in the same chain are completed. Logical sequencing are connection of activities; A project entails several activities. The arrows are arranged to show the plan of logical sequence in which the activities of the project are to be accomplished.

The sequence is ascertained for each activity by answering the following three quires viz:

1. Which activity or activities must be completed before the start of a particular activity ?
2. Which activity or activities should follow this?
3. Which activities can be accomplished simultaneously?

The activity or activities which immediately come before another activity without any intervening activities are called predecessor activities to that activity. The activities which follow another activity without any intervening activities are called successor activities to that activity.

In a project of laying a pipe line, the three activities involved may be trenching, laying pipe and welding pipe. To decide the logical connection between these three activities necessary that they be carried out in series, the reasoning being that the pipe cannot be laid until trenching has been done and welding cannot be undertaken until the pipe has been laid. This way we decide the logical sequencing between different activities. Errors in logical sequencing: Two types of errors in logic may arise while drawing a network, particularly when it is a complicated one. These are known as looping dangling.

Looping

Normally in a network, the arrow points from left to right. This convention is to be strictly adhered, as this would avoid illogical looping.

Dangling

The situation represented by the following diagram is also at fault, since the activity represented by the dangling arrow 9-11 is undertaken with no result. A To overcome the problem arising due to dangling arrows, following rules may be adopted.

1. All events, except the first and the last, must have at least one activity entering and one activity leaving them,
2. All activities must start and finish with an event.

Duplicate activities

Activities A and B may be called duplicate activities because they have same head event (i. e. 6) and the same tail event (i. e. 7). One remedy for such a situation is the introduction of a dummy activity

Dummy activity

It is a hypothetical activity which consumes no resource and time. It is represented by dotted lines and is inserted in the network to clarify activity pattern under the following situations:

1. It is created to make activities with common starting and finishing events distinguishable.
2. To identify and maintain the proper precedence relationship between activities that are not connected by events.
3. To bring all “loose ends” to a single initial and a single terminal event in each network using dummies, if necessary.

For example, problem of duplicate activities above may be circumvented. Three cases for the following set of dependency relationships: Activity C is dependent upon both A and B.

Activity D is dependent upon A alone. BC AC A DD BA C B AD The first portrayal is clearly wrong since it shows D as dependent upon not only A but also B which is not desired. The other portrayal (ii) is also wrong since A is being shown twice and thus contravenes the fundamental axiom of network that three must be one arrow for each activity. The way out to this dilemma is the representation by means of the dummy activity. C is dependent upon both A and B (via dummy) whereas D is dependent upon just A.

Numbering the events

The event numbers in a network should in some respect reflect their logical sequences. When a complicated network has been drawn then the problem of assigning numbers to the events involved in the network arises. A rule devised by D. R. Fulkerson, involving the following steps may be followed to resolve the problem numbering the events. An “initial” event is one which has arrow/arrows coming out of it and none of the arrow entering it. In a network there will be only one such event. Call it “1”. Delete all arrows coming out from the event This will give us at least one more “initial event”.Number these events as “2, 3…. ” (iv) Delete all emerging arrows from these numbered events which will create new initial events. Then follow step (iii). (v) Continue the above steps till last event is obtained which has no arrows coming out of it. Consider the numbering of events in the following figure.

 Here we proceed from left to right. The event with least x- co-ordinate is assigned the smallest integer, say 1. other events are assigned progressively higher integers with regard to x-co-ordinate.

If two or more events (4 and 5 above) have the same x-co-ordinate, the one towards arrow should have higher number. Further, it is not necessary, and in fact also not desirable to number the events consecutively. It would be a better scheme to number the events as 10, 20, 30, 40, 50, 60, 70 in the above diagram instead of 1, 2, 3, 4, 5, 6, 7. This affords insertion of more activities and events omitted by oversight or having become necessary in view of certain logic revisions. It was mentioned earlier that it is desirable that all the activity arrows point from left to right. If the arrow is vertical it may point downwards or upwards.

For the sake of preventability it is to be recommended that activities emanating from one event or converging to another may make as great angles between themselves as possible. A few more conventions are given below:

1. Keep the arrow to the extreme right.
2.  As far as possible avoid drawing arrows that cross each other. Usually by suitable ‘stretching’ the network diagram it is possible to avoid this.
3. Where, however, crossing is unavoidable, bridging may be done.

This applies to dummies as well. Draw boldly a big network. Smaller ones are confusing. Use of pencil and rubber is recommended.