CRITICAL PATH METHOD & PERT

1. Meaning of Critical Path

A network consists of chains of activities called paths of network. Addition of durations of activities on any path gives the duration of that path. the comparison of durations of the paths identifies a path whose duration is the longest. It is this path, the path with the longest duration which sets the overall duration of the project is called critical path. And the activities on the critical path are known as critical activities.

2. Characteristic Of Critical Path

Identifying critical path is of great importance as it determines duration of the project. if any activity on this path is delayed, then the entire project will be delayed

Some important characteristics of critical path are:.

  1. Every network has a critical path
  2. It is possible to have more than one critical paths
  3. A critical path is one of the connecting links between the first & the last event.
  4. A critical path may have lesser number of activities compared to non-critical paths.
  5. A critical path may run through a dummy activity.

3. Benefits Of Critical Path

Major benefits of identifying the critical path are

  1. Critical path helps to identify a set of activities and events which are critical and as such must be carefully monitored and controlled.
  1. Mere allocation of additional resources does not help to reduce duration of the project. To shorten the time of a project, some of activities on the critical path must be shortened.
  2. Certain resources (men, machines and money) are generally common to different activities. Critical path identifies the activities to be given preference in allocation of resources.
  3. Each and every activity of the project need not be controlled. If critical activities are started and completed on time, the project automatically gets completed on schedule. Since critical activities are few in number identification of critical path helps to exercise control by exception.

4. How To Identify Critical Path ?

Critical path in a small network can be identified by performing the following four steps:

  • Enumerate all the paths in the network
  • List down the activities on each of the above paths
  • Sum up the times of the activities along each path.
  • Compare the duration of the paths to identify a path (s) whose duration is the longest. It is this path which is called critical path.
  • Showing critical path in the network
    Critical path is shown in the network by either red line or by double line or by thick line.

5. Non Critical Paths And Float Times

All activity chains which do not lie on the critical path are called non-critical pathsand the activities along these paths are called non-critical activities. Logically itwould not affect the project completion time if such activities take little longer time than planned.

Although non-critical activities can safely be allowed to take longer thanplanned, yet it is important that the extended time should not result in total chain time of activities to exceed lime along the parallel critical path. It is, therefore, necessary to know the spare time available along a non-critical path. The spare time which is called float or slack can be obtained by subtracting the “non-critical path time from the “parallel critical path / time”.

6. Critical Path In A Big Network

In a small network, it is a simple process to identify the critical path by tracing and comparing all the paths in the network.
As the number of activities increases, it becomes very difficult and lime consuming to find the critical path by complete enumeration or inspection. Therefore, for larger networks, a more systematic procedure is needed to determine the critical path.

The most commonly used method employs two sets of calculations: forward pass computation and backward pass computation.

The forward pass computation begins from start event moves towards the end event of the project network. It determines the earliest expected time for each event, called earliest starting (event) time (TE).

The backward pass computation begins from the end event and move backward to the start event of the pro network. It determines the latest all time for each event, called latest Completion (event ) time (TL). Earliest event time (TE) represents earliest possible occurrence time of the activity emanating from event. Latest event time represents latest allowable occurrence time of activities terminating into the event.

7. Analysis Of Activity Durations Based On Computations

Mere computation of event time is not sufficient. Equally important is the task of establishing the date at which each activity should start and end to maintain

1. Earliest Start time (ES). The network logic indicates that an activity can not commence until its preceding event is completed. This implies that the earliest start time of an activity equals earliest event time (TE)of the tail event.

2. Earliest finish time (EF) equals the earliest start time of the activity plus duration of the activity emanating from the tail event.
3. Latest finish time (LF) is the latest time of the head event.

4. Latest start time (LS) is the latest finish time of the activity minus duration of the activity converging on the head event.

Identifying Critical Path Based On Computations

Once activity durations have been worked out, the critical path can be identified by comparing the “earliest finish times” and “latest finish times’ of the activities. Clearly activities whose earliest finish times and latest finish times are equal will constitute the critical path.

8. Activity Cost Slope

Activity Cost Slope is the rate of increase in the cost activity per unit with a decrease in time. A necessary measure for the analysis is the calculation of the cost slope for each activity. The cost slope indicates the additional cost incurred per unit of time saved in reducing duration of art activity. It can be understood more clearly by considering following diagram:

D

Cost Slope

C

O B A

Let OA represent the normal time duration for completing a job and OC the normal cost involved to complete the job. Assume that the management wishes to reduce time of completing the job to OB from normal time OA. Therefore, under such a situation the cost of the project increases and it goes up to say OD (Crash Cost). This only amounts to saying that by reducing the time period by AB the cost has increased by the an CD. The rate of increase in the cost of activity per unit with a decrease in time is known as activity cost slope and is described as below:

Since the project duration is determined by the length of the critical path, it can be shortened by reducing the time of critical activities. As the objective of the management is to reduce the project duration at the lowest possible cost, the critical activity with the lowest cost slope is selected for crashing.

The amount of time by which an individual activity can be reduced is limited by its crash time. However, during such a crashing other factors must be taken into account. For example, the next longest route may also become critical. There will be then two critical paths and any further reduction in project time must occur on both the paths for overall project time to be reduced. The process is continued in this manner and the sum of direct and indirect costs i.e. the total for each completion time are tabulated. The optimum schedule corresponds to minimum total cost.

9. Activity Float Analysis

Float of an activity represents the excess of available time over its duration. Float is an important concept in project planning. It allows planners to

  1. Decide priorities in allocation of resources.
  2. Transfer resources from less pressing areas to more pressing areas.
  3. Minimize requirements of a resource.
  4. Prevent peaks and valleys in requirements of a resource.

10.Types of floats

Float is mainly of Three types: Total float, Free float & Independent float.

All activities lying on the non-critical paths have total float and some of them may also free floats. Total float and free float have following significance.

1. Total Float

It signifies the maximum delay that can be permitted in the completion of the activity without affecting the project completion Total float can be interpreted in two ways:
(I) The maximum time available to delay the commencement of an activity.
(ii) The maximum expansion of the duration of the activity.

(iii)Some combination of decisions (i) and (ii)

If total float is used up an activity, that activity and subsequent activities in the chain become critical.

Total float may be viewed as the maximum leeway available to an activity when all preceding activities occur at the earliest start time and all succeeding activities occur at the latest start time. Total float of an activity thus can be obtained as under:

Total float = Latest occurrence time of the succeeding event minus Earliest occurrence time of the preceding event minus Duration of the activity.

2. Free Float

Free float is the amount of time an activity can be delayed without affecting the commencement of a succeeding activity at its earliest start time but may affect the float of previous activity. Free float results when all preceding activities occur at the earliest event times and all succeeding activities also occur at the earliest event times.

Free float = Earliest occurrence time of the succeeding event minus Earliest occurrence time of the preceding event minus Duration of the activity
3. Independent Float

Sometimes, it may be desirable to know what spare time is present in an activity if it is started as late as possible and finished as early as possible. This characteristic is known as independent float.

Independent float therefore, is the amount of time an activity can be delayed when all preceding activities are completed as late as possible and all succeeding activities are completed as early as possible. Independent float thus neither affects the float of preceding activities nor that of succeeding activities.
Independent float = Earliest occurrence time of the succeeding event minus Latest occurrence time of the preceding event minus Duration of the activity

11. Node Labeling

The Fulkerson’s Rule

The Fulkerson’s rule consists of following four steps:

Once the network is drawn, it is a good practice to label the events systematically. As a general rule, the numbering system must ensure that
a) the event numbers as far as possible reflect logical relationships of the activities.

b) for a given activity, the number of its tail event is higher than that of its head event.

A very simple and logical approach suggested by D.R. Fulkerson called Fulkerson’s rule is the commonly accepted technique for numbering.

  1. Identify an initial event and number it as “1’’. (An initial event is one which has arrows originating from it and none entering it).
  2. Delete the arrows emerging from event “1’’ so as to create one or more initial events.
  3. Number these new initial events as 2, 3
  4. Repeat steps (ii) and (iii) until last event is obtained which has no arrows emerging out of it,

12. PERT Concept Of Multiple Times

One major difference between PERT and CPM is the formers adaptability for the projects where high degree of uncertainty prevail and activity times during performance are expected to vary considerably for certain activities.

The concept of multiple times (three time estimates) was evolved in PERT to reduce the incidence of uncertainty in project planning. The three time estimates are

a) Optimistic time (a)

This indicates the minimum time that an activity can take if everything goes smoothly The chances that such a time could i be shorter would be one in hundred or less. The optimistic time is represented by ‘a’.

b) Pessimistic time (b)

It indicates the maximum time an activity can take under adverse conditions. The chances that time could even be longer would be one in hundred or less. The pessimistic time is denoted by ‘b’.

c) Most likely time (m)

This indicates the time an activity can take most often if it is repeated again & again under the same conditions Most likely is denoted by “m’.

Three time estimates are not directly entered into the network. They are transformed into an expected time using the statistical relation given as Te = a + 4m + b / 6

13. Differences Between CPM & PERT

  1. PERT is event oriented while CPM is activity oriented
  2. PERT provides for an allowance for uncertainty while CPM does not(PERT makes three time estimates for each activity, while CPM makes only one time estimate)
  3. Activity times in CPM technique are related to costs while it is not so in PERT since it is event oriented
  4. PERT is applied generally to the projects of non-repetitive nature whereas the CPM is applied where the projects are of repetitive time where time estimates can be made on the basis of experience.

14. Crashing

Crashing is employed when we want to shorten the project completion time by spending extra resources i.e., ultimately money. In real life, it is always possible to employ more resources or book a lightening call. Therefore we have to estimate the crashing limit for each activity as also extra money for crashing each activity. Once these estimates are available, any analysis can be made to determine the time cost trade off curve i.e., what (cost) it takes to crash the project to a given duration.

In many situations, there may be compelling reasons to complete the project earlier than the originally estimated duration of the critical path on the basis of normal activity times or in many cases, the execution of project gets delayed due to certain reasons. We have to reduce the duration of future activities so that the project is completed earlier/or as per schedule.

Under these circumstances, additional resources can be used to expedite certain activities resulting in earlier completion of the project. This shortening of activity times, which usually can be achieved by adding resources such as manpower of overtime is referred to as crashing the activity time However, Since the additional resource associated with crashing activity times usually result in added costs, the management would want to identify the least cost activities to crash and the amount of duration by which activities may be crashed to meet the desired project completion date.

In order to determine just where and how much to crash activity times, management
would need following information:

15. Objectives Of Project Crashing

  1. To complete the project in the least possible time
  2. To effect cost of economy (to reduce the project cost below its normal cost).
  3. To expedite one or more unfinished activities when earlier critical activities have taken more than estimated time and thereby prevent lateness penalties and cost overruns.
  4. To reduce idle time of the facilities in the non-critical paths and achieve uniformity in requirement of resources
  5. To release the facilities more quickly for transfer to other profitable projects
  6. To enhance reputation of the firm and thereby improve its competitive position

A major advantage of CPM is its ability to evolve a relationship between time and cost of the activity and it is this concept which is exploited in project crashing.

16. UP-dating of the Project:

A network designed during planning may not adhere to the schedule when put to work because situations sometimes keep on changing & during execution they are different than those assumed at the stage of planning.

In spite of best efforts, some activities need more time than originally planned or some new activities crop-up. To ensure that schedule time is maintained, it is necessary to review the progress of the project & redrafting the network according to latest requirements. If it is not possible to delay the project, then activities on new critical path are accelerated by allocating extra resources in order to adhere to committed date. Hence the process of up to date the network diagram of the project by incorporating in it the changes which has occurred due to re-planning & rescheduling is called updating.

There is no rule about the time to go for updating. The frequency of updating may be more when the project duration is small because few slippages in detecting the progress will affect the project as a whole, as the time for absorbing such slippages is less. However to add dynamism to the nature & progress of work, updating may be carried out as frequently as possible & viable.

CONCEPTS

  1. Activity. It is a time consuming job or task that is a key sub-part of the total project. It is a clear definable portion of a project that requires for its completion, the consumption of resources, and time in particular.
  1. Activity Cost Slope(AC / AT) is the additional cost to be incurred to reduce the duration of an activity by one unit of time. ( Activity cost slope of an activity = Crash cost - Normal cost / Normal time - Crash time )
  2. Activity Time. Physical time required to complete an activity.
  1. Activity Duration. In CPM, the best estimate of the time to complete an activity. In PERT, the expected time or average time to complete an activity.
  1. Activity List. A list of the jobs in a project with their immediate predecessors, expected times and resources required.
  1. Backward Pass. A procedure that moves from the end of the network to the beginning of the network. It is used in determining the latest finish and start times.
  1. Crashing. It is the process of reducing the total time that it takes to complete a project by expending additional funds. A term in the CPM method describing the process of reducing the time required to complete an activity.
  1. Crash Time : In CPM, the minimum possible time for completion of an activity, corresponding to maximal resource concentration.
  1. Crash cost of an activity represents the lowest possible direct cost required to complete an activity within its crashed time.
  1. Crash duration of the project refers to the irreducible minimum duration of the project and it occurs when all activities on the critical path have been crashed. Crash time of the project, therefore, is sum of crashed times of the activities on the critical path
  1. Critical Activity. An activity becomes critical if delay in its estimated time duration delays the whole project to that extent.
  1. Critical Path. The series of activities that have a zero slack. It is the longest time path through the network. A delay for an activity that is on the critical path will delay the completion of the entire project.
  1. Critical Path Analysis. An analysis that determines! the total project completion time, the critical path for project, and the slack, ES, EF, LS, and LF for every activity.
  1. CPM.An acronym for Critical Path Method, a method for scheduling and controlling projects
  1. Dummy activity. In most projects many activities can be performed concurrently or simultaneously. It is possible that two activities could be drawn by the same beginning and end events. In situations where two or more activities can be performed concurrently, the concept of dummy activity is introduced to resolve this problem. Therefore there will be only one activity between two events.

As a result of using the dummy activity, other activities can be identified by unique end events. Dummy activities consume no time or resources. By convention, dummy activities are represented by a dashed arrows on the project network and are Inserted in the network to clarify activity pattern in the following situations