Estimation Of Project Duration

Basics in Building Construction 4(2+2)

Lesson 31 and 32 : Construction Project Management

Estimation Of Project Duration

After the network for a project is developed based on the methods stipulated above next step is to estimate the completion time of the project, based on the time required to perform different activities comprising the project. To assess the project duration, following four steps have to be followed in their sequential order.

  1. Estimation of activity duration time (te)
  2. Estimation of earliest expected event time (TE)
  3. Estimation of latest allowable event time (TL)
  4. Calculation of event slack.

These steps are elaborated below.

  1. Estimation of activity duration time (te): Activity duration time is a time that is required to perform an activity. This is designated by a symbol (te). On the network diagram the value of (te) is recorded below the relevant activity arrow. The unit of time may be in days, weeks or months etc. In case of dummy activity value of ‘te’ is zero. The activity duration time can be assessed based on two methods.

    1. Single time estimate: In case of projects involving repetitive nature of activities, where adequate knowledge and experience of their completion time is available, the time allotted for each activity is based on single time estimate. Thus in case of single time estimate, the activity duration time is judiciously arrived at taking into consideration the available resources in terms of men, material, money, machines etc. and the local working conditions. Since activity duration time forms the basis for working out the total duration of the project, it is necessary that time for each and every activity is arrived at by experienced people who have complete knowledge for performing similar type of activities.

    2. In other words the single time estimate represents a definite time allotted to an activity based on past experience.

    3. Three time estimate: In case of projects involving research and development or projects involving activities never handled before, it is not possible to allocate single time estimate to the activities for want of adequate information or knowledge. In such cases, the activity time estimate could be highly uncertain. To deal with such projects, three time estimates are made initially and the value of te is thereafter worked out by an empirical formula.
    4. The three time estimates to be considered in such a case are:

      1. Optimistic time: Time required to complete the activity assuming every thing goes alright. This is designated by a symbol "to"

      2. Passimistic time: Time required to complete the activity assuming that everything goes wrong. This is designated by a symbol "tp"

      3. Most likely time: Time required completing the activity assuming such things go wrong which are normally expected to be wrong. This is represented by a symbol "m"
      4. The three time estimates are then converted into a single time estimates or ‘te’ for each activity by the following formula:

        111

        The working of three times estimates is based on the theory of probability.

        The main difference between the Critical Path Method (CPM) and the PERT is that in case of CPM the values of ‘te’ are based on single time estimates and in case of PERT values ‘te’ are based on three time estimates.

  2. Estimation of earliest expected event time (TE): After writing down the values of ‘te’ for all activities on the network, next step is to calculate the minimum time required for the accomplishment of all the events in the network. The earliest possible time at which an event can occur assuming that preceding activities take at the time estimated for them is known as earliest event time. All activities shown terminating at the event must be completed before the event occurs. The earliest expected time for each event is designated by symbol (TE).

  3. Thus the earliest expected event time (TE) for any given event is obtained by adding the activity time (te) for all preceding activities along the longest path from the beginning to the given event.

  4. Estimation of latest allowable event time (TL): The latest allowable event time is the latest time by which an event must takes place if the total project time is not to be exceeded. The latest allowable time for each event is designated by symbol TL.

  5. After fixing TL value for the end event, the next step to work out TL in respect of all the events in the network. The aim of calculating TL is just reverse of that of calculating TE substracting the duration of succeeding activities along the path starting at the final event.

  6. Calculation of Event slack: Having calculated the TE and TL value of all events in a network, next strep is to calculate the event slack in respect of all the events. Event slack is the free time available up to which occurrence of an event can be delayed without causing any delay in the completion date of the project. Event slack is the difference between the latest allowable time (TL) and the earliest expected time (TE ) of and event. The value of slack can be positive zero or minus.

  7. Zero slack occurring in any event will indicate that the event is on schedule. Any delay caused in the occurrence of events having zero slack will result in corresponding delay in the completion of the project.

    Positive slack occurring at any event will indicate that the event ahead of schedule. Thus, in case there is delay in occurrence to the extent of the positive slack available; it will not cause the overall completion of the project. This information can enable the management to temporarily divert the resources (men, money and machines etc.) to other activities while rescheduling,>p/

    Negative slack occurring at the event shows that the event is negative. Negative slack thus indicates that there will be delay in the completion of the project to the extent of the negative slack of the end event . The information allows the management to take advance action to speed up the concerned activities to minimize chances of delay.

Identification of the critical path:

From the review of the network diagram it can be seen that there are a number of alternative paths along the network from start of the project to its completion. The critical path is path along the network which requires the longest time for the project from start to its completion and thus, decides the time of completion of the project as a whole. In most cases the critical path passes through all events whose TE and TL values are the same.

Any event on critical path is known as critical event. Similarly any activity on critical path is known as critical activity. There can be more than one critical paths in a network. Any delay in the accomplishment of events on the critical path, would necessarily result in corresponding delay in the completion of the project.

Identification of critical path has the following main advantages.

  1. The project management need not spend time and efforts in reviewing all the activities in a project and instead concentrate only on the critical activities for ensuring timely completion of project.
  2. In case the management decides to shorten the time of the completion of the project, attention can be concentrated on speeding up only critical activities.

Compressing the critical path:

Critical path governs both the project duration as well as the minimum time required to complete a project.9 Very often the project duration worked out based on network analysis has to be reduced to meet the directive from top management to complete project in shorter time. Thus ‘TE’ of the end events becomes greater than TL (the directed time of completion of project) and there is negative slack along the critical path. In such situations it becomes necessary to compress the critical path, to avoid negative slack.
Compressing of critical path can be achieved by following one or more steps given below:

  1. By closer examination of the activity duration time (te) for different activities along critical path and reducing them wherever feasible.
  2. By re planning the network by introducing number of parallel or concurrent activities on critical path.
  3. By transfer of resources (men, materials, money and machines etc.) from the non- critical activities to the critical activities within permissible limits to reduce activity duration time along the critical path.
  4. By adding more resources to the critical activity to effect reduction in activity duration.
  5. By reducing the scope of work or by changing or lowering performance requirements of some activities, which are relatively few as compared to numerous activities in the project.

The network for a certain project is shown in figure below. Determine the expected time for each of the path. Which path is critical?
In the network, event 1 is the starting event while event 8 is the end event. There are following four paths from the starting event to the end event:

Path A : 1-2-7-8
Path B: 1-2-6-8
Path C: 1-3-6-8
Path D: 1-4-5-6-8

In PERT analysis, the expected time tE is taken as the basis for finding the critical path. The expected time tE for each activity can be found from the equation

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The expected time (tE) for any path is equal to tE of all activities. The computations are shown in Table below, from which we find that path D is critical since ?tE for this path is maximum.

Path

Activity

t0

tL

tP

tG

? tE

A

1-2
2-7
7-8

6
8
5

8
10
8

11
12
12

8.17
10.00
8.17

26.34

B

1-2
2-6
6-8

6
4
7

8
8
10

11
14
15

8.17
8.33
10.33

26.83

C

1-3
3-6
6-8

3
8
7

7
10
10

9
12
15

6.77
10.00
10.33

27.00

D

1-4
4-5
5-6
6-8

5
4
3
7

7
6
5
10

10
8
6
15

7.17
6.00
4.83
10.33

28.23

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Last modified: Monday, 2 July 2012, 10:23 AM