Project Scheduling

Project Scheduling

Project Scheduling refers to the process of laying out all the activities of a project in the time order in which they are to be performed, keeping in view the logical sequence of the activities.

The logical sequence of the activities of a project (shopping mall) is:

  • Digging of foundation
  • Pouring foundation concrete
  • Construction

A project consists of many activities, which are interrelated to each other. All activities consume resources of three kinds viz. time, men, materials (money). The project scheduling techniques are concerned with the resources ‘time’. Scheduling techniques are used to optimize the project time.

Project Scheduling Project Scheduling

Project Scheduling Techniques

Bar Chart

  1. Bar Chart: it is a pictorial representation showing the various activities of a project.

For example if the project is construction a shopping mall, the various activities which are involved are

Project Scheduling

Advantages of Bar chart

  • Easy to construct and understand
  • Not effective for large and complex projects as it does not show the impact of delay of one activity on another.

Project Scheduling Project Scheduling

Network based Scheduling

Network Based Scheduling technique is used for bigger and complex projects involving large number of activities. In this technique network diagrams are constructed.

Network Diagram: it is a graphical flow plan of activities arranged in a logical sequence that must be accomplished for completing a project. There are two popular network scheduling techniques:

  1. Critical Path Method (CPM)
  2. Programme Evaluation and Review Technique (PERT)

Advantage of Network Technique

  • Precedence relationships
  • large projects
  • more efficient

Project Scheduling Project Scheduling

Difference Between PERT And CPM

PERT

CPM

PERT is probabilistic

CPM is deterministic

This technique is developed in 1950 by US Navy

This is developed in 1957 by Du Pont

PERT is event oriented

CPM is activity oriented

PERT is generally used for those projects where time required to complete various activities is not known with certainty.

CPM is used for those projects which are repetitive in nature and where one has experience of handling similar projects.

PERT analysis does not usually consider costs

It deals with the cost of the project schedule and their minimization. The concept of crashing is applied mainly to CPM model.

PERT is used in Research & Development Projects

CPM is used in plant maintenance and construction work

PERT can be used as an important control device as it assists manager to review those activities which may cause a delay in project completion date

It is difficult to use CPM as a controlling device.

Project Scheduling Project Scheduling

How to construct Network Diagram

Activity: All projects are composed of various operations or tasks, which require time and resources to complete. These tasks and operations are called an activity. For example in the previous illustration digging of foundation, pouring foundation concrete and construction of walls are the activities of a project constructing a shopping mall.

An activity is represented by an arrow 

  1. The length of the arrow does not signify anything.
  2. Each activity has a significant beginning and a definite end.
  3. Each activity consumes resources (time, manpower and material).
  4. The head of the arrow shows the flow of activity.
  5. The circle placed at the beginning of the arrow represents the starting point of the activity, while the circle placed at the end of the arrow represents the finishing point of the activity.
network based scheduling

Predecessor Activities: Activities that must be completed immediately before the start of another activity are called predecessor activities of it.

network based scheduling 

Activity A is the predecessor of Activity B

Successor Activities: Activities that must follow immediately after completion of a given activity are called successor activities of it.

network based scheduling

Activity B is the successor of activity A.

Concurrent Activities: Activities that can be completed at the same time are called Concurrent Activities.

network based scheduling

A and B are concurrent activities.

Dummy Activity: A dummy activity is an imaginary activity added in a network to maintain the logical sequence only. Since it is not a real activity, it does not consume any resources (time, manpower and materials). It is represented by a dashed arrow.

network based scheduling

Example 1: Draw the network diagram for the following project::

  1. Activity A and activity B are concurrent activities.
  2. Activity C follows activity A.
  3. Activity D succeeds activities A and B
  4. Activities C and D are last activities.
network based scheduling

Event: An event is the beginning and end of an activity. An event represents a specific point in time. It does not consume time, manpower or material resources. In the network diagram an event is represented by a circle.

network based scheduling

Network Rules:

  1. Each activity is represented by one and only one arrow in the network. Therefore no single activity can be represented twice in the network.
  2. No two activities can be identified by the same beginning and end events. In such cases a dummy activity is introduced to resolve the problem.

3. Before an activity can be undertaken, all activities preceding it must be completed.

4. The arrows depicting various activities are indicative of the logical precedence only. The length of the arrow has no significance.

5. The flow of diagram should be from left to right.

6. Arrows should not be crossed.

7. Arrows should be kept straight and not curved/bent.

8.The general rule for numbering the event is that no event can be numbered until all preceding events have been numbered. The number at the head of an arrow is always larger than at its tail.

  1. Identify the initial event and assign it number 1.
  2. Delete all the emerging arrows from the initial event (event 1). This will create one or more ‘new initial events’, number these initial events as 2, 3, 4……….etc.
network based scheduling

3. Delete all the emerging arrows from the initial events which will create a new set of initial events. Assign numbers to these initial events starting from the number next to the number that has so far been assigned.

Example 2: Number the events in the following network:

network based scheduling

network based scheduling network based scheduling 

Interdependency

  • If activity A is the predecessor of activity B, it means activity B can not start until activity A is completed.
network based scheduling
  • If activity A is the predecessor of activities B and C both, it means activities B and C can not start until activity A is completed.
network based scheduling
  • If activities A and B are the predecessors of activity C, it means that activities A and B can occur concurrently but both must be completed before C can begin.
network based scheduling
  • Activities A and B both must be completed before activities C and D can begin independently.
network based scheduling
  • Activities A and B can occur concurrently but both must be completed before activity C can begin. However only activity B must be completed before activity E can begin. Activity C is a dummy activity which shows a precedence relationship but has zero time duration.
network based scheduling
network based scheduling
network based scheduling
network based scheduling

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Critical Path Method (CPM)

Critical Path Method technique was developed by Du Pont in 1950 and was first used in missile defense construction projects.

Critical Path: In project management, a critical path is the sequence of project network activities which add up to the longest overall duration, regardless if that longest duration has float or not. This determines the earliest possible time to complete the project. The activities that lie on the critical path are known as critical activities. These are those activities which do not have any cushion time to either postpone or prepone its starting time from its original starting time. Each non-critical activity will have some cushion time so it can be postponed or preponed its starting time from its original time. If the activity of the critical path is delayed, the project completion time will also be delayed.

 Steps to find out critical path:

  1. Break down the project into various activities and arrange all activities in logical sequence.
  2. Number all the events and activities.
  3. Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each event.
    1. Earliest start time for activity (Es): it is the time at which the activity can start without affecting the total project time.
    2. Earliest finish time for activity (Ef):
    3. Latest start time for activity (Ls):
    4. Latest finish time for activity (Lf): it is the latest time by which an activity must get completed without delaying the project completion.
    5. Total Float: the total float of an activity represents the amount of time by which an activity can be delayed without delay in the project completion date. In other words, it refers to the amount of the free time associated with an activity which can be used before, during or after the performance of this activity.

Total Float TF = Lf – Ef or Ls – Es

  1. Free Float: the free float indicates the value by which an activity can be delayed without causing any delay in its immediate successor activities.

Free Float FF =

  1. Independent Float: it is the time by which an activity can be delayed for start without affecting floats of the preceding activities.

Independent Float IF =

Difference between Float and Slack: Slack is event related whereas float is related to activities.

  1. Determine the slack for each activity by taking difference between earliest and latest time.
  2. Identify the critical activities (with zero slack) and connect them by double arrow. This shows the critical path.
  3. Calculate the total project duration.
Critical Path Method

A – D – G – K            10+12+20+6 = 48 days

A – D – H – L            10+12+3+18 = 43 days

A – E – I – L              10+4+9+18 = 41 days

B – I – L                    9+9+8 = 36 days

C – J – N                     12+13+9 = 34 days

C – F – I – L              12+8+9+18 = 47 days

C – J – M – L            12+13+7+18 = 50 days*

C – J – M – L  is the critical path and the project duration is 50 days.

Critical Path Method

Example 1: Construct the network and find out the critical path.

Critical Path Method
Critical Path Method

Example 2: Draw the network and find out the critical path and total float using Critical Path Method (CPM)

Critical Path Method
Critical Path Method

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Programme Evaluation and Review Technique (PERT)

In most of the projects the activity times are not known with certainty and they may be assumed as random variable. In such cases where activity times are not known with certainty PERT can be used for planning, scheduling and controlling the project. It was developed in 1950 by US Navy to control large defense projects.

The PERT makes the following assumptions:

  1. Activity times are statistically independent and usually associated with beta distribution.
  2. There are enough activities involved in the network that sum of activity times based on their means and variance will be normally distributed.
  3. In PERT, for each activity three time estimates can be obtained.
    1. Optimistic time estimate (to): it is the minimum time in which an activity can be completed under favourable conditions.
    2. Most Likely time estimate (tm): it is the time required to complete an activity under normal conditions or it is the time required to complete an activity most often if it is repeated number of times.
    3. Pessimistic time estimate (tp): it is the maximum time in which an activity can be completed under unfavourable conditions.

After determining three time estimates of an activity its expected time can be computed on the basis of beta distribution.

Expected (Mean) time = (t+ 4 t+ tp) / 6

Where t= optimistic time estimate

               tm = Most Likely time estimate

                tp = Pessimistic time estimate

              t= expected time

Standard Deviation s2 = (tp – to/6)2

 Steps to apply PERT

  1. Identify the activities to complete the project and their predecessor requirement.
  2. Calculate the expected time and standard variation for each activity.
  3. Construct the network and find out the critical path considering the expected time as the activity time.
  4. Find out the expected time for project completion.

Example: A small project consists of nine activities, the details of which are given below:

Programme Evaluation and Review Technique
  1. Draw the network diagram, number the nodes.
  2. Find out the critical path and the expected project completion time.
  3. What is the probability of completing the project within 36 days?
  4. What is the probability of completing the project within 31 days?
  5. What project duration will have 95% confidence of completion?
Programme Evaluation and Review Technique
Programme Evaluation and Review Technique
  • Alternative Paths: 

    1-2-4-8  = 24 days

    1-3-6-8 = 32 days

    • = 34 days
    1. Critical path is 1-3-5-7-8 = 34 days

    Variance of critical path = 4+16+4+1 = 25 days

    • Probability of completing the project in 31 days

     Z = (due date – expected date of completion)/√variance of critical path

     = 36 – 34/ √25   = 2/5   = 0.40

    Probability = .5+.1554 (area under normal distribution table for z=.1554)

                        = .6554 = 65.54%

    • Probability of completing the project in 31 days

     Z = (due date – expected date of completion)/√variance of critical path

     = 31 – 34/ √25   =  -3/5   = -0.6

    = .5 – .2257 (area under normal distribution table for z=.2257)

    = .2743 = 27.43%

    For 95% confidence level, the value of z = 95% – 50% = 45% or 0.45

    Z = (due date – expected date of completion)/√variance of critical path

    1.65 (z value from the table equivalent to 0.45) = due date – 34 / 5

    Due date = 34+1.65*5 = 42.25 days

Example: A small project consisting of eight activities has the following characteristics:

Programme Evaluation and Review Technique
  1. Draw the PERT network.
  2. Determine the critical path and project duration.
  3. If a 30 weeks deadline is imposed, what is the probability that the project will be finished within the time limit?
  4. If the project manager wants to be 99% sure that the project is completed on the schedule date, how many weeks before that date should he start the project work?
Programme Evaluation and Review Technique
Programme Evaluation and Review Technique

Alternative Paths are

1-2-4-5-6

1-2-3-5-6

1-3-5-6

The critical path of the project is 1-2-4-5-6 and project duration is

Example: A small project consisting of eight activities has the following characteristics:

Programme Evaluation and Review Technique
Programme Evaluation and Review Technique

Alternative Paths

Critical Path B-E-G-H

Expected duration of project is 19 days.

The variance of the critical path is  = 1+4+4+0.108 = 9.108

                                                       Std deviation = 3.02

Z= due date – expected date of completion/ √variance of critical path

Z = due date – 19 / 3.02 ( for 95% confidence level z = 1.65 from normal distribution table)

1.65 =  due date – 19 / 3.02

Due date = 24 days

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Project Time Cost Trade-off

The cost of a project comprises of two components – direct cost and indirect cost.

Direct costs include the cost of materials, labour and equipments etc. direct cost of a project is the sum total of direct costs of all the activities contained in the project. It is inversely proportional to the project duration means the direct cost of any project reduces with the duration of the project.

Indirect costs are the cost associated with sustaining a project. Indirect costs include the cost of supervision, overheads, facilities, penalty cost and lost incentive payments. Project indirect cost is dependent upon the length of the project duration. A project having longer duration will have higher indirect cost.

Project Time Cost Trade-off 
 

The normal and crash times and direct costs for the activities are shown below:

Project Time Cost Trade-off 
  • Draw the network diagram.
  • Determine the critical path.
  • Find the minimum cost project schedule if the indirect cost is Rs. 150 per day.

Step I Calculate the slope using the formula slope = Crash Cost – Normal Cost/ (Normal time – Crash time)

Project Time Cost Trade-off 

Step II Construct the network and find out the critical path.

Critical path (longest normal duration) is 1-3-5-6. Project duration is 16 days. It can be crashed to 11 days (Maximum in crash time).

It is the critical path which decides the duration of the project so we will crash the activities of critical path only. So the eligible activities for crashing are

Activities

Slope

1-3

100

3-5

100

5-6

200

As Activities 1-3 and 3-5 have the least cost slope, we can select any of the activity for crashing.

Step I: Crash activity 1-3 by 1 day. The project duration is 15 days.

Total cost = Normal cost + crash cost of activity 1-3

                = 10,600 + 100 = Rs.  10, 700

After crashing the project by 1 day, the length of each path is checked to find out the critical path. It is observed that the same path 1-3-5-6 is still the longest duration path and the same activities are eligible for crashing.

Step II: Crash activity 1-3 by 1 day. The project duration is 14 days.

Total cost = Normal cost + crash cost of activity 1-3

                = 10,700 + 100 = Rs.  10, 800

After crashing the project by 1 day, the length of each path is checked to find out the critical path. It is observed that the same path 1-3-5-6 is still the longest duration path. The activity 1-3 is completely crashed and it can not be reduced further. The eligible activities for crashing are 3-5 / 5-6.

Activities

Slope

3-5

100

5-6

200

 Step III: Crash activity 3-5 by 1 day. The project duration is 13 days.

Total cost = Normal cost + crash cost of activity 3-5

                = 10,800 + 100 = Rs.  10, 900

After crashing the project by 1 day, the length of each path is checked to find out the critical path. Now there are two critical paths – 1-3-5-6 and 1-2-4-6. Now we have to crash both the paths together. We can one common activity in both the path or combination of two activities be selecting one from each path. We can compare the cost of the alternative options for crashing.

Activities

Slope

1-2, 3-5

300

1-2, 5-6

400

2-4, 3-5

300

2-4, 5-6

400

4-6, 3-5

600

4-6, 5-6

700

Step IV: Crash activities (1-2) and (3-5) by 1 day. The project duration is 12 days.

Total cost = Normal cost + crash cost of activities 1-2 and 3-5

                = 10,900 + 300 = Rs.  11, 200

Activity 3-5 and 1-2 are completely crashed now. After crashing the project to 12 days, again we check the duration of different alternative paths. It is observed now that all three paths are critical, that’s why needs to be crashed together.

Step V: Crash activities 4-6 (which is common in two paths) and 5-6 by 1 day. Project duration is 11 days.

Total cost = Normal cost + crash cost of activities 4-6 and 5-6

              = 11,200 + 700 = 11,900 Rs.

Project Time Cost Trade-off 

Answer:

The minimum time for project completion is 11 days and associated cost is Rs. 13550.

The minimum cost for project completion is 12850 and associated time is 13 days.

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By Hassham

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