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    Project Management Unit 5

    Sikkim Manipal University Page No. 105

    Unit 5 PERT and CPM

    Structure:

    5.1 Introduction 

    Objectives 

    5.2 Development of Project Network

    5.3 Time Estimation

    5.4 Determination of the Critical Path

    Calculate the Earliest Occurrence Time (EOT) for each event 

    Calculate the Latest Occurrence Time (LOT) for ach event  

    Calculate the slack for each event 

    Obtain the critical and slack paths 

    Compute the activity floats 

    5.5 PERT Model 

    Measures of variability 

    Probability of completion by a specified date 

    5.6 CPM Model 

     Assumptions 

    Procedure 

    5.7 Network Cost System 

    5.8 Summary 

    5.9 Glossary 

    5.10 Terminal Questions 

    5.11 Answers 

    5.12 Case Study

    5.1 Introduction

    In the previous unit, we dealt with the concept of organisational structure,

    the roles and responsibilities of a project leader, the relationship between

    project manager and line manager, leadership styles for project managers,

    the concept of conflict resolution, the concepts of team management and

    diversity management, and the concept of change management. In this unit,

    we will deal with the development of project network, time estimation,

    determination of the critical path, PERT model, CPM model, and network

    cost system.

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    Once a project gets selected, the entire focus will be on its implementation.

    This involves the completion of numerous activities (project components) byemploying various resources  – men, materials, machine, money, and timeso that a project blueprint gets translated into concrete reality.

    The project activities have inter-relationships occurring from physical,

    technical, and other considerations. For suitable planning, scheduling, and

    control of the activities of a project, given their inter-relationships and

    constraints regarding the availability of resources, network techniques are

    found very useful. Note that financial institutions and the Government of

    India insist that a network plan must accompany feasibility reports.

    The two fundamental network techniques are: PERT and CPM. PERT, an

    acronym for Programme Evaluation Review Technique was originallydeveloped to facilitate the planning and scheduling of the Polaris Fleet

    Ballistic Missile Project of the US government. Designed to handle risk and

    uncertainty, PERT is quite suitable for research and development

    programmes, aerospace projects, and other projects relating to new

    technology. In such projects, there exists variability in the time requirement

    for completing different jobs or activities. Therefore, the orientation of PERT

    is 'probabilistic'.

    CPM, a short form for Critical Path Method, is similar to PERT. It was

    developed in US by the DuPont Company in 1956-57 for solving industries

    scheduling problems. CPM is principally concerned with the matter involving

    cost and time. Its application is mainly to projects that use a fairly stable

    technology and are quite risk free. Therefore, its orientation is 'deterministic'.

    Extensively diverse projects are open to analysis by PERT and CPM, for

    example launching a spaceship, research and development programme,

    construction of a plant, building a river valley project, overhaul of an

    organisation, training of manpower, starting a new venture, and adult

    literacy programme. This unit discusses the basics of PERT, CPM, and

    network cost system.

    Objectives: After studying this unit, you should be able to:

      identify the network technique for project management

      explain the characteristics of network technique

      describe the time estimation

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      identify the Critical Path

      describe the term PERT and CPM model  explain the network cost system

    5.2 Development of Project Network

    The network diagram is basic to PERT and CPM. The network diagram,

    also known as project graph, depicts the project activities and events and

    their logical relationships. Figure 5.1 depicts a simplified network diagram

    for a dinner project.

    Send Invitation

    Prepare Dinner 

    Receive Guests

    Take Dinner   

    Fig. 5.1: Development of Project Network

     Activities and events are used to construct network diagram An activity is a

    specific task, job, or function to be carried out in a project. For example,

    'prepare dinner' (see Figure 5.1) is an activity. An activity is symbolised by

    an arrow. The head of the arrow depicts the completion of the activity and

    the tail of the arrow depicts its beginning. (There is no significance of length

    and 'compass' direction of the arrow.) The event is a specific point in time

    representing the beginning or end of one or more activities. It stands for a

    milestone and does not consume time or resources.

    It is essential to detail all the activities of the project because activities are

    the basic building blocks of a network diagram. For this reason, it is useful to

    break the project into some steps. The number of steps in a project depends

    upon its magnitude and complexity. For industrial projects, usually, a two-step procedure is sufficient. In the primary step, there is identification of

    major parts of the project and in the next step the activities of each major

    part are defined. Activities must be so defined that they are distinct, logically

    uniform tasks for which time and resource requirement can be estimated.

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     After specification of activities, it is essential to define for each activity, the

    activities which precede it, the activities which succeed it, and the activitieswhich can take place simultaneously. After getting this information, the

    network diagram is developed through forward method or backward method,

    showing the logical relationship among activities and events.

    The forward method starts with the initial event, showing the beginning of

    the project, and proceeds forward till the end event is accomplished. The

    backward method starts with the end event and works backwards till the

    beginning event is reached.

    Rules for network construction

    The rules to be observed in constructing the network diagram are discussed

    below:

    Every activity must have a preceding and a succeeding event. An activity is

    numerically represented by the pair of preceding and succeeding events. In

    the dinner project, for instance, the activity ‘send invitations’ is designatedas (1-2).

    1. Each event must have a distinct number. The number specified to an

    event can be chosen in any way, provided this condition is fulfilled. In

    practice, yet, events are numbered in the manner that the number at the

    head of the arrow is greater than that at its tail.

    1

    23

     

    Fig. 5.2: A Network Diagram

    2. There must not be any loops in the project network; a situation similar tothe one shown in Figure 5.2 is not permissible.

    3. The preceding and succeeding events are not same for more than one

    activity. This signifies that every activity is represented by a uniquely

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    numbered arrow and a situation depicted in Figure 5.3 is not

    permissible.Figure 5.3 depicts a loop.

    1 2

     

    Fig. 5.3: A Loop

    To make sure that each activity is uniquely numbered, at times it isnecessary to introduce dummy activities. A dummy activity is an imaginary

    activity that can be completed in zero time and it does not consume

    resources. It is symbolised by a dashed arrow. Figure 5.4 shows a variant of

    Figure 5.3 with a dummy activity (3-2) introduced to conform to the rules of

    network construction.

    Fig. 5.4: A Dummy Activity

     A dummy activity is also be used for representing a constraint, obligatory to

    show proper relationship between activities. Figure 5.5 shows part of a

    network diagram having a dummy activity (dotted arrow line).

    In Figure 5.5, X, represented as (7-6), is a dummy activity showing a certainlogical relationship. According to this figure, activities P (4-6) and Q (5-7)

    must be completed before activity R (6-8) can start.

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    Fig. 5.5: A Dummy Activity

    Illustration

     A building project consists of the following activities:

     A = Lay foundation

    B = Erect framework

    C= Install millwork

    D = Install wiring

    E = Install plumbing

    F = Plaster walls

    G = Install siding

    H= Decorate the interior

    I = Finish the exterior

    The interrelationship among these activities is as follows:

     A should precede B.

    B should precede C, D, E, F, and G.

    C, D, E, and F should precede H.

    G should precede I

    4 6 8

    5 7 9

    P

    S Q

    R

    X

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    Figure 5.6 depicts the network diagram for the project.

    Fig. 5.6: Network Diagram for the Project

    Given the above interrelationship the network diagram for the project is

    developed in several steps using the forward method as shown in figure 5.6.

    Self Assessment Questions

    1. The ________________, also referred to as the project graph, shows

    the activities and events of the project and their logical relationships.

    2. __________ must be so defined that they are distinct, logically uniform

    tasks for which time and resource requirement can be estimated.

    Erect FrameLay Foundation

    1 2

    1 2 3

    Install Mill WorkInstall Wiring

    Lay FoundationErect Frame Install plumbing

    Plaster Walls

    Install Siding

    F

    E

    D

    BA

    A B

    1 23

    6

    8

    9

    Finish the

    Exterior

    Decorate the interiorInstall Wiring

    Install plumbing

    Plaster walls

    Install siding

    Erect frameLay Foundation

    C

    D H

    EF

    G

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    3. The ____________ begins with the initial event, marking the beginning

    of the project, and proceeds forward till the end event is reached.4. The _____________ begins with the end event and works backwards

    till the beginning event is reached. 

    5.3 Time Estimation

     After establishing the logic and detail of the network, time estimates must be

    assigned to each activity. Usually, three time values are obtained for each

    activity:

      Optimistic time (to)

      Most likely time (tm)

      Pessimistic time (tp)

    If no hurdles or complications happen, the time required is known as

    optimistic time (to). The time in which the activity is most likely to be

    completed is called most likely time (tm). The most likely time considers

    normal circumstances and makes allowance for some foreseen delays. The

    time required in case abnormal complications and, or unforeseen difficulties

    arise is known as pessimistic time (tp ). We shall use figure 5.7 that depicts a

    network design to explain the aspects of PERT.

    Fig. 5.7: Network Design

    Obtaining time estimates

    The PERT planner must obtain time estimates from the persons who are

    accountable for estimation. The following points must be kept in mind while

    obtaining time estimates:

      Time estimates must be obtained by skipping around the network

    instead of following a specific path. In case, estimates are obtained by

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    following one path, there is a chance for the person giving the estimates

    to add them mentally and compare them with a pre- conceived notion ofthe time of the total path.

      The estimates of to, tm, and tp  must be defined independently of each

    other for each activity (1-2, 1-3, 2-4, 3-4, 2-5, 4-5)

      The time available for completing the project must not pressure the

    estimates of to, tm and tp.

      It must be considered that to, tm and tp are estimates and not schedule

    commitments.

      The estimates of to, tm and tp must comprise allowances for occurrences

    which are usually considered as random variables (weather conditions,

    administrative delays, etc.) but not for occurrences which are notconsidered usually as random variables (flood, wars, etc.)

      The expected time is calculated using the formula:

    6

    ptmt4otet

     

    These expected times are then depicted in the network diagram, for

    example., as shown in fig. 5.7.

    Self Assessment Questions

    5. The pessimistic time, to, is the time required if no hurdles or

    complications arise. (True/False)6. The optimistic time, tp, is the time required if unusual complications

    and, or unforeseen difficulties arise. (True/False)

    7. Time estimates should be obtained by the PERT planner from persons

    who are responsible for estimation. (True/False)

    5.4 Determination of the Critical Path

    Once the network diagram with single time estimates has been developed,

    the following computational procedure may be employed for determining the

    critical path/s, event slacks, and activity floats.

    5.4.1 Calculate the Earliest Occurrence Time (EOT) for each event

     After completion of all leading activities, an event occurs. In the network

    diagram shown in Figure 5.8, for example, event 4 occurs when activities

    (2-4) and (3-4) are completed. Clearly activity (2-4) cannot begin unless

    event 2 occurs, which sequentially requires the completion of activity (1-2).

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    Similarly, activity (3-4) cannot start unless event 3 occurs which sequentially

    requires the completion of activity (1-3). Therefore, we establish that event4 occurs when activities (1-2), (2-4), (1-3), and (3-4) are completed.

     Alternatively we can say that, event 4 occurs when paths (1-2-4) and (1-3-4)

    are completed.

    The time when the event can be completed at the earliest is known as EOT

    (earliest occurrence time). Looking at event 4, we locate that as the paths

    leading to it, viz. (1-2-4) and (1-3-4) take 15 weeks and 20 weeks,

    respectively, the EOT of event 4 is 20 weeks. In common terms, the EOT of

    an event is the duration of the longest path (from the beginning event whose

    EOT is set at 0) leading to that event. The EOTs of different events in our

    illustrative project are shown in Figure 5.8. It is to be considered that inFigure 5.8 and subsequent figures an event is depicted by a circle. The

    upper half of the circle represents the event number, the left quarter in the

    lower half represents the EOT, and the right quarter in the lower half

    represents the Latest Occurrence Time (LOT).

    Fig. 5.8: EOT

    The EOT of the end event depicts the minimum time required for project

    completion. For getting, the EOT of various events we begin from the start

    event and move forward towards the finish event. This procedure of

    computation is known as the forward pass. For computation, we assume

    that each activity starts instantly on the occurrence of the event earlier to it.

    1 5

    3

    2

    4

    1315

    2

    12

    8

    2

    13

    0 28

    2012

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    Therefore, the starting and finishing time for different activities obtained from

    the computation are called Earliest Starting Time (EST) and EarliestFinishing Time (EFT).

    5.4.2 Calculate the Latest Occurrence Time (LOT) for each event

    The LOT for an event depicts the latest allowable time by which the event

    can occur, given the time that is allowed for the completion of the project

    (occurrence of end event). Normally, the time allowed for the completion of

    the project is set equal to the EOT of the end event. (In other words, the

    project is supposed to be completed at the earliest possible time.) This

    means that for the end event the LOT and EOT are set equal. The LOT for

    various events is obtained by working backward from the end event. This

    procedure is known as the backward pass. The LOT for event 4 in ourillustrative project, for instance, is equal to the LOT for event 5, the end

    event, minus the duration of the activity (4-5) which connects event 4 with 5.

     As the LOT for event 5 is 28 weeks and the duration of activity (4-5) is 2

    weeks the LOT for event 4 is 26 weeks (28-2). This depicts the latest time

    by which event 4 should occur to enable the project to be completed in 28

    weeks. Similarly, the LOT for other events can be calculated by moving

    backward. Figure 5.9 depicts the LOT for various events (in the right quarter

    of the lower half of event nodes).

    Fig. 5.9: LOT

    5.4.3 Calculate the slack for each event

    1 5

    2

    43

    13

    82

    2

    15

    13

    280

    18 26

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    The difference between the LOT and EOT of an event is known as slack.

    The slacks for different events of our illustrative project are shown inTable 5.1.

    Table 5.1: Event Slack

    Event LOT EOT (In weeks)

    Slack

    = LOT

    = EOT

    5 28 28 0

    4 26 20 6

    3 18 12 6

    2 13 13 0

    1 0 0 0

    5.4.4 Obtain the critical and slack paths

    The critical path starts with the starting event, terminates with the last event,

    and is marked by events which have a zero slack. This is the path on which

    there is no slack, no cushion. Other paths are slack paths with some

    cushion. The critical path is (1-2-5) for our illustrative project. It is specified

    by doubled arrows in Figure 5.10.

    The critical path is the longest path from the start event to the end event.

    The project is completed, only when this longest path is crossed, Critical

    path duration is the minimum time required for completing the project. The

    duration on the critical path of the project is 28 weeks; this is the least time

    required for completing the project. (It is previously indicated by the EOT of

    event 5, the end event.)

    Activity

    The following table gives the activities of a construction project and

    duration:

    Activity 1 –2 1 –3 2 –3 2 –4 3 –4 4 –5

    Duration

    (days)

    20 25 10 12 6 10

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    (i) Draw the network for the project.

    (ii) Find the critical path.

    5.4.5 Compute the activity floats

     Activity floats are calculated from the estimates of activity time and event

    slacks. The three measures of float are: (i) total float; (ii) free float; and (iii)

    independent float. For illustrating these measures, let us consider activity

    (2-4) of our illustrative project. Activity (2-4) is shown in Figure 5.10.

    Fig. 5.10: Computing the Activity Floats

    Total float of an activity is the additional time available to finish the activity if

    the activity is started as early as possible without postponing the completion

    of the project and is given by

    TF(i,j)= LOT(j) – EOT(i) – d(i,j)Where d is duration of the activity i-j

    Therefore the total float for activity (2-4) is

    TF(2,4)= LOT(4)-EOT(2)- d(2,4)

    1

    2

    43

    5

    13 15

    2

    122

    13 13

    0 0

    12 18 20 26

    2828

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    = 26-13-2

    =11 weeks

    Free float of an activity is the additional time available to finish the activity

    when the activity is started at the EOT of its preceding event and completed

    by the EOT of the succeeding event.

    FF(i,j)= EOT(j) – EOT(i) – d(i,j)

    Therefore the free float for activity (2-4) is

    FF(2,4)= EOT(4)-EOT(2)- d(2,4)

    =20-13-2

    = 5 weeks

    Independent float of an activity is the additional time available to finish the

    activity when the activity is started at the LOT of its preceding event and

    completed by the EOT of the succeeding event

    IF(i,j)= EOT(j) – LOT(i) – d(i,j)

    Therefore the independent float for activity (2-4) is

    IF(2,4)= EOT(4)-LOT(2)- d(2,4)

    = 20-13-2

    = 5 weeks

    Total float denotes the float under most positive conditions whereas

    independent float denotes the float under most adverse conditions.

    Self Assessment Questions

    8. The _____________ of an event refers to the time when the event can

    be completed at the earliest.

    9. The ___________ for various events is obtained by working backward

    from the end event. This procedure is known as the backward pass.

    10. The ________ for an event is the difference between its LOT and EOT.

    5.5 PERT Model

    So far, the analysis was focused on the determination of the critical path,

    event slacks, and activity floats. For this purpose, we used single time

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    estimates of activity duration though initially three time estimates were

    developed for each activity. Now we consider the variability of projectduration.

    5.5.1 Measures of variability

    Variability in PERT analysis is measured by variance or its square root, i.e.

    standard deviation. Variance of a set of numbers is the average squared

    difference of the numbers in the set from their arithmetic average. A simple

    example may be given to illustrate the calculation of variance. Let us take a

    series that consist of numbers 4, 6, and 8. The average of this series is 6.

    The differences of various numbers in the series from this average are -2, 0,

    and 2. Squaring them we get 4, 0, and 4. Hence, the variance  – the average

    of squared difference – is 8/3 and standard deviation is √8/3. 

    The steps involved in calculating the standard deviation of the duration of

    critical path are as follows:

    Step 1:  Determine the standard deviation of the duration of each activity on

    the critical path.

    Step 2:  Determine the standard deviation of the total duration of the critical

    path on the basis of information obtained in step 1.

    In order to determine the standard deviation of the duration of an activity, we

    require the complete probability distribution of the activity distribution. We,

    though, have just three values from this distribution: tp, tm, and to. In PERT

    analysis, a simplification is used for calculating standard deviation. It is

    calculated by the formula:

    Standard deviation = (tp - to)/6

    Where, tp = pessimistic time

    to = optimistic time

    Variance is obtained by squaring standard deviation.

    The standard deviation and variance of the activities on the critical path of

    our illustrative project are shown in the following table 5.2:Table 5.2: Standard deviation and variance of the activities

    Activity tp  to  O=(tp-to)/6 Variance=O2 

    (1-2) 21 9 2 5.00

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    (2.5) 24 10 2.33 5.43

     Assuming that the probability distribution of various activities on the critical

    path is independent, the variance of the critical path duration is obtained by

    adding the variance of activities on the critical path.

    In real life projects which have a large number of activities on the critical

    path, we can sensibly presume that the critical path duration is around

    normally distributed, with mean and standard deviation attained.

     A normal distribution looks like a bell shaped curve as shown in Figure 5.11.

    It is symmetric and single peaked and is fully described by its mean and

    standard deviation. The probability of values lying within certain ranges is as

    follows:

    Range Probability

    Mean ± One standard deviation 0.682

    Mean ± Two standard deviations 0.954

    Mean ± Three standard deviations 0.998

    Standard Normal Distribution

    Mean =0, Std Dev=1

    -4 -3 -2 -1 0 1 2 3 4

    Fig. 5.11: Normal Distribution

    Figure 5.11 depicts a normal distribution curve.

    5.5.2 Probability of completion by a specified date Armed with information about mean (T) and standard deviation (a) for critical

    path duration, which is normally distributed, we can compute the probability

    of completion by a specified date (D) as follows:

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      Find Z = (D – T) / S.D, where Z is known as standard normal variate with

    mean and variance  Obtain cumulative probability up to Z by looking at the probability

    distribution of the standard normal variate.

    Table 5.3 depicts the cumulative probability up to Z for standard normal

    distribution.

    Table 5.3: Cumulative Probability up to Z for Standard Normal Distribution

    z Cumulative probability

     – 3.0 0.001

     – 2.8 0.003 – 2.6 0.005

     – 2.4 0.008

     – 2.2 0.014

     – 2.0 0.023

     – 1.8 0.036

     – 1.6 0.055

     – 1.4 0.081

     – 1.2 0.115

     – 1.0 0.159

     – 0.8 0.212

     – 0.6 0.274

     – 0.4 0.345

     – 0.2 0.421

    0.0 0.500

    0.2 0.579

    0.4 0.655

    0.6 0.726

    0.8 0.788

    1.0 0.841

    1.2 0.885

    1.4 0.919

    1.6 0.945

    1.8 0.964

    2.0 0.977

    2.2 0.986

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    2.4 0.992

    2.6 0.9952.8 0.997

    3.0 0.999

    The above procedure may be illustrated for our project which has T = 28

    and SD = 3.07. Table 5.4 depicts the probability of completing this project by

    certain specified dates.

    Table 5.4: Probability of Completing the Project

    Specified ZProbability of

    completion by D

    20

    20 282.6

    3.07

      0.005

    2525 28

    1.03.07

     0.159

    3030 28

    0.63.07

     0.726

    Self Assessment Questions

    11. Variability in PERT analysis is measured by variance or its square root

    and standard deviation. (True/False)

    12. Standard deviation is obtained by squaring variance. (True/False) 

    5.6 CPM Model

    For projects considered uncertain, the PERT model was developed and for

    projects which are comparatively risk-free the CPM model was developed.

    Both the approaches start with the development of the network and a focal

    point on the critical path. Tthe PERT approach is 'probabilistic' while the

    CPM approach is 'deterministic'. This does not, however, mean that in CPM

    analysis we work with single time estimates. Actually the main focus of CPM

    analysis is on variations in activity times as a consequence of changes in

    resource assignments. These variations are planned plus related to

    resource assignments as well as are not caused by random factors outside

    the control of management as in the case of PERT analysis. The major

    focus of CPM analysis is on time cost relationships and it seeks a project

    schedule that minimises total cost.

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    5.6.1 Assumptions

    The usual assumptions underlying CPM analysis are:1. The costs associated with a project can be divided into two components:

    direct costs and indirect costs. Direct costs are incurred on direct

    material and direct labour. Indirect costs consist of overhead items like

    indirect supplies, rent, insurance, managerial services, etc.

    2. Activities of the project can be expedited by crashing which involves

    employing more resources.

    3. Crashing reduces time but enhances direct costs because of factors like

    overtime payments, extra payments, and wastage. The relationship

    between time and direct activity cost can be reasonably approximated

    by a downward sloping straight line. Figure 5.12 depicts a typical cost

    time line.

    Normal TimeCrash Time  Duration

     

    Directcost of

     Activity 

     Activity  

    Fig. 5.12: A Typical Cost Time Line

    4. Indirect costs associated with the project increase linearly with project

    duration. Figure 5.13 depicts a typical line for indirect costs.

    Indirect cost

    of project

    Procedure Duration

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    Fig. 5.13: Indirect Costs

    5.6.2 Procedure

    Given the above assumptions, CPM analysis seeks to examine the

    consequences of crashing on total cost (direct cost plus indirect cost). Since

    the behaviour of indirect project cost is well defined, the bulk of CPM

    analysis is concerned with the relationship between total direct cost and

    project duration. The procedure used in this respect is generally as follows:

    Step 1:  Obtain the critical path in the normal network. Determine the project

    duration and direct cost.Step 2:   Examine the cost time slope of activities on the critical path

    obtained and crash the activity which has the least slope.

    Step 3:   Construct the new critical path after crashing as per step 2.

    Determine project duration and cost.

    Step 4:  Repeat steps 2 and 3 till activities on the critical path (which may

    change every time) are crashed.

    Example:   The above procedure may be illustrated with an example.

    Table 5.4 depicts the activities, durations, and direct activity costs of a

    project. The indirect cost is Rs. 2,000 per week.

    Table 5.4: Normal and Crash Time and Cost

    Activity Time in Weeks

    Normal Crash

    Cost

    Normal Crash

    Cost to Expedite

    per Weeks

    1-2

    1-3

    2-4

    3-5

    2-5

    4-6

    5-6

    6-7

    8 4

    5 3

    9 6

    7 5

    5 1

    3 21/2

     

    6 2

    10 7

    3,000 6,000

    4,000 8,000

    4,000 5,500

    2,000 3,200

    8,000 12,000

    10,000 11,200

    4,000 6,800

    6,000 8,700

    450

    2,000

    500

    600

    1,000

    2,400

    700

    900

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    5-7 9 5 4,200 9,000

    45,200 70,400

    1,200

    Figure 5.14 depicts the project network with normal duration.

    Fig. 5.14: Project Network (1)

    The critical path in the all normal network is (1-2-4-6-7). The project duration

    is 30 weeks and the total direct cost is Rs. 45,200.

    Examining the time cost slope of activities on the critical path, we find that

    activity (2-4) has the lowest slope; in other words, the cost to expedite per

    week is the lowest for activity (2-4). Hence, activity (2-4) is crashed. Figure5.15 depicts the project network after such a crashing.

    Fig. 5.15: Project Network (2)

    2 4 6

    1

    3 5

    7

    8 5

    57

    9

    10

    39

    6

    24 6

    1

    3 5

    7

    7

    5

    8

    6 3

    10

    6

    9

    5

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     As per Figure 5.15 the critical path is (1-2-5-6-7), with a length of 29 weeks,

    and the total direct cost is Rs. 46,700.Looking at the time cost slope of the activities on the new critical path (1-2-

    5-6-7), we find that the activity (5-6) has the lowest slope. Hence, this

    activity is crashed. Figure 5.16 depicts the project network after such

    crashing, the critical path is (1-2-4-6-7) with a length of 27 weeks and the

    total direct cost is Rs. 49,500.

    Fig. 5.16: Project Network (3)

    Comparing the time cost slope of the non-crashed activities on the new

    critical path (1-2-4-6-7), we find that the activity which costs the least to

    crash is (1-2). Hence, this is crashed. Figure 5.17 depicts the projectnetwork after such a crashing. As per Figure 5.17, the critical path is (1-3-5-

    6-7) with a length of 24 weeks and the total direct cost is Rs. 52,500.

    Fig. 5.17: Project Network (4)

    2 4 6

    1 7

    3 5

    5

    85

    6 3

    10

    2

    9

    7

    2 4 6

    1 7

    3 57

    5

    4

    5

    6 3

    10

    9

    2

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    Looking at the time cost slope of the non-crashed activities on the new

    critical path, (1-3-6-7), we find that activity (6-7) has the lowest slope.Hence, it is crashed. Figure 5.18 depicts the project network after such a

    crashing. As per Figure 5.18, there are two critical paths (1-3-5-6-7) and

    (1-3-5-7), both with a length of 21 weeks, and the total direct cost is Rs.

    55,200.

    Fig. 5.18: Project Network (5)

    Considering the time cost slope of non crashed activities on critical paths

    (1-3-5-6-7) and (1-3-5-7), we find that activity (3-5) which is common to both

    the critical paths is the least costly to crash. Hence, it is crashed. Figure

    5.19 depicts the project network after this crashing. As per Figure 5.19, the

    critical path is (1-2-4-6-7) with a duration of 201/4 weeks and the total direct

    cost is Rs. 56,400.

    9

    2 4 6

    1 7

    3 5

    7

    2

    75

    4

    5

    6 3

    2 4 6

    1 7

    3 5

    45 2

    9

    7

    36

    5

    5

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    Fig. 5.19: Project Network (6)

    Looking at the new critical path (1-2-4-6-7), we find that the only non-crashed activity is (4-6). Figure 5.20 depicts the project network given by

    crashing this. As per Figure 5.20, the critical path again is (1-2-4-6-7) with a

    duration of 191/2 weeks and the total direct cost is Rs. 57,600.

    Fig. 5.20: Project Network (7)

    Since all the activities on the critical path (1-2-4-6-7) are crashed, there is no

    possibility of further time reduction. Hence, let us now look at the time-cost

    relationship. This is shown in Figure 5.20.

    From table 5.5, we find that the total cost is minimised for the projectschedule represented by the activities crashed are (1-2), (2-4), (3-5), (5-6),

    (6-7). The information provided in table 5.5 is useful for decision-making.

    Table 5.5 depicts the project duration and total cost.

    Table 5.5: Project Duration and Total Cost

    FigureNo.

    Activities Crashed ProjectDuration in

    Weeks

    TotalDirectCost

    TotalIndirect

    Cost

    TotalCost

    5.14 None 30 45,200 60,000 105,200

    5.15 (2-4) 29 46,700 58,000 104,700

    5.16 (2-4 and (5-6) 27 49,500 54,000 103,500

    5.17 (1-2), (2-4) and(5-6)

    24 52,500 48,000 100,500

    5.18 (1-2), (2-4), (5-6),and (6-7)

    21 55,500 42,000 97,200

    5.19 (1-2), (2-4), (3-5),(5-6), and (6-7)

    20 56,400 40,000 96,400

    2 4 6

    17

    3 5

    55

    9

    2

    7

    26

    45

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    5.20 (1-2), (2-4), (3-5),(5-6), (4-6), and

    (6-7)

    191/2

      57,600 39,000 96,600

    If the objective is to minimise the total cost of the project, the pattern of

    crashing suggested by Figure 5.19 is optimal. If the objective is to minimise

    the project duration, then the pattern of crashing suggested by Figure 5.20

    is optimal. In real life situations, however, both the factors may be important.

    In addition, factors like strain on resources and degree of manageability are

    also important. The final decision would involve a careful weighing and

    balancing of these diverse factors, some quantitative and some qualitative.

    Self Assessment Questions

    13. CPM analysis is on variations in activity times as a result of changes in

     ________________ .

    14. _____________seeks to examine the consequences of crashing on

    total cost (direct cost plus indirect cost). 

    5.7 Network Cost System

    The techniques of PERT and CPM discussed above are essentially time

    oriented. They seek to answer questions like:

      What is the most desirable time schedule of activities?

      How much time would it take, on an average, to complete the project?  What is the probability of completing the project in a specified time?

    Such analysis largely overlooks the cost aspect which is usually as

    important as the time aspect and sometimes even more. To provide a

    vehicle for cost planning and control of projects, the network cost system

    was developed. This represents a very useful supplement to the traditional

    time-oriented network analysis. Let us look at cost projection and cost

    analysis and control under the network cost system.

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    Activity

    The managing director of M/s Raj Kumari Manufacturing Company had

    an opportunity to deal with a project. The project x is required to be

    completed within 8 months at a cost of `1,00,000. The president received

    a letter of intent in November. The managing director called production

    manager Shri L.N. Gupta and the finance manager Shri. Srinivas Gupta

    in the 1st  week of December to finalise the appropriate time and cost

    based on past jobs and new technology acquired in the organisation.

    President needs positively the answer in the 3 rd  week of December, so

    that project can be started, if profitable, from 1st  January. Therefore,

    production manager and finance manager have been requested to

    determine profitability of the project on a 8 month basis. The time and

    cost under normal conditions and crashing conditions has been

    calculated as follows:

    Activity Normal Crashing

    Time Cost Time Cost

    1 – 21 – 31 – 42 – 32 – 42 – 5

    3 – 54 – 5

    2

    3

    6

    4

    2

    7

    4

    3

    8,000

    7,000

    11,000

    6,000

    9,000

    8,500

    10,500

    5,000

    1

    1

    5

    3

    1

    6

    3

    2

    13,000

    19,000

    13,500

    10,000

    10,000

    11,500

    16,000

    7,000

    Main issues involved are:

    1. What suggestions should be given to managing director forundertaking the project?

    2. After having long discussions with the general manager, who is the

    second in command in the organisation, the management some how

    feels that during implementation of the project, it will not be possible

    to crash the activity 2  –  4 from its normal time. If so, how will the

    production manager and finance manager respond?Projected costs or budgeted costs assists in analysing variances while

    balancing actual costs incurred on the project from time to time and keeps a

    proper check on the overall budget. Budgeted costs also happen to be an

    indicator of the extent the project can be crashed in case of emergency. For

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    instance Common wealth games project for Delhi crossed the budgeted

    costs by more than 40 % to meet the project deadlines in time. When workon the project began in 2006 the mega budget was Rs. 22,000 crore. Four

    years later the budget is Rs. 30,000 crore. It swell by nearly 40 per cent

    forcing the Delhi government to increase taxes and roll back crucial

    subsidies. The budget for 11 stadia was Rs. 1200 crore in 2004 and it rose

    to Rs. 5000 crore . Also, construction was way behind the deadline. All

    projects were delayed, including the Commonwealth Village sub-project,

    which had a budget of Rs. 465 crore in 2004 and got completed with

    Rs. 1400 crore. All this happened because of the lack of knowledge on

    fundamentals of networking times and costs factors .

    Self Assessment Questions

    15. To provide a vehicle for ______________ and control of projects, the

    network cost system was developed.

    16. PERT and CPM analysis largely overlooks the _____________ which

    is usually as important as the time aspect and sometimes even more.

    5.8 Summary

    Let us recapitulate the important concepts discussed in this unit:

      In order to properly plan, schedule, and control of the activities of a

    project, given their interrelationships and constraints on the availability ofresources, network techniques are found reasonably helpful.

      The two fundamental network techniques are PERT and CPM.

      PERT is applied mainly to projects containing uncertainty; its orientation

    is probabilistic.

      CPM is useful to projects which are comparatively risk-free; its

    orientation is deterministic. Extensively varied projects are open to

    analysed by PERT and CPM.

      The construction of network diagram is in terms of activities and events.

    The activity in a project is defined as a definite task, job or function to be

    performed.   A definite point of time indicating the beginning or end of one or more

    activities is known as event. To make sure that each activity is uniquely

    numbered it is required to introduce dummy activities.

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       A dummy activity is imaginary activities that can be completed in zero

    time and does not consume resources. A dummy activity is utilised todepict a constraint needed to show the correct relationship among

    activities.

    5.9 Glossary

    CPM:  Critical Path Method

    EFT:  Earliest Finishing Time

    EST:  Earliest Starting Time

    LOT:  Latest Occurrence Time

    PERT:  Programme Evaluation Review Technique

    5.10 Terminal Questions

    1. Define activity, event, and path as used in network development. What

    is a dummy activity?

    2. Discuss the time estimation.

    3. What do you mean by determination of the critical path?

    4. Define PERT model.

    5. Describe the CPM model. Briefly explain.

    6. Explain network cost system.

    5.11 Answers

    Self Assessment Questions

    1. Network diagram

    2. Activities

    3. Forward method

    4. Backward method

    5. False6. False

    7. True

    8. EOT

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    9. LOT

    10. Slack11. True

    12. False

    13. Resource assignments

    14. CPM analysis

    15. Cost planning

    16. Cost aspect

    Terminal Questions

    1. Basic to PERT as well as CPM is the network diagram. The network

    diagram, also referred to as the project graph, shows the activities and

    events of the project and their logical relationships. Refer to 5.2.

    2. Once the logic and detail of the network have been established, time

    estimates must be assigned to each activity. Refer to 5.3.

    3. Once the network diagram with single time estimates has been

    developed, the following computational procedure may be employed for

    determining the critical path/s, event slacks, and activity floats. Refer

    to 5.4.

    4. For this purpose, we used single time estimates of activity duration

    though initially three time estimates were developed for each activity.Variability in PERT analysis is measured by variance or its square root,

    standard deviation. Refer to 5.5.

    5. The CPM model was developed for projects which are relatively risk-

    free. Refer to 5.6.

    6. To provide a vehicle for cost planning and control of projects, the

    network cost system was developed. Refer to 5.7.

    5.12 Case Study

    Unconventional Fibres

     A project for identifying the use of unconventional fibres for the manufacture

    of fabric was sponsored by a known Indian organisation and a leading

    research institute in North India was entrusted with the task. The research

    institute decided to explore the scope for extracting fibre from pineapple leaf

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    and also the machinery for spinning the fibre into yarn. The machinery

    designed for the extraction of fibre from leaf performed well and came outsuccessful. 

    But, the discouraging factor was that the recovery rate of fibre from the leaf

    was only around 2% to 3%. Moreover, in view of the very low fibre recovery

    rate, the cost of pineapple leaf fibre was found to vary between 1.60 to 1.75

    times the costs of cotton fibre. Since cotton, though a conventional fibre was

    cheaper than pineapple leaf fibre and as cotton had all favourable qualities

    for making a fabric suited for man, pineapple leaf fibre was not found

    competitive and was found incapable of replacing cotton.

    In order to improve the financial viability of the project, the research institute

    explored the possibility of using the wastage recovered from the fibre

    extraction machine for producing some other by-product. This was

    considered essential since the waste material constituted about 97% to 98%

    of the total raw material (i.e., pineapple leaf). Further research into the

    above aspect yielded encouraging results. The pineapple leaf waste was

    made useful for the manufacture of paper boards.

    The paper board manufactured using pineapple waste was found to

    possess the required physical properties. Since the leaf waste was used for

    producing a by-product, the financial viability of the composite project

    showed improvement. However, even after assuming that the boardsmanufactured using pineapple leaf waste could be sold at a price on par

    with the boards manufactured using other raw materials (like waste paper,

    waste cloth, etc), the composite project was found to break-even only if the

    pineapple leaf fibre could be sold at a price about 20% more than that of

    cotton fibre. Hence, the research institute concluded that the fabric

    produced out of pineapple leaf fibre could not replace cotton fabric as it

    would not be price competitive, even if a composite project is opted for. The

    institute hopes that the fabric produced using pineapple leaf fibre could be

    exported to high-end markets by propagating it as a novel, eco-friendly, and

    natural product.The institute has also received enquiries from abroad for the procurement of

    pineapple leaf fibre at a price that is nearly 40 times the price of cotton fibre,

    These are, however, initial phases and full exploitation of commercial

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    potential is yet to be ascertained. The technology is available with the

    research institute.1. Analyse the case. Can a promising entrepreneur opt for the composite

    project? If so, what are his or her prospects and problems?

    Hint:  A leading research institute in North India explore the scope for

    extracting fibre from pineapple leaf and also the machinery for spinning

    the fibre into yarn. The cost of pineapple leaf fibre was found to vary

    between 1.60 to 1.75 times the costs of cotton fibre. The research

    institute explored the possibility of using the wastage recovered from the

    fibre extraction machine for producing some other by-product (paper

    boards.).

    Source:  Mishra Rajendra (2012), Project Management: Excel Books,New Delhi

    References:

      Clements/Gido, Effective Project Management , Publication: Thomson.

      Gray, C. F. and Larson, E. W. Project Management , Publication: Tata

    McGraw Hill.

      Lock, D, Project Management , Ninth Edition, Publication: Gower

      Nagarajan, K. Project Management , Third Edition, Publication: New Age

    International.

      Chandra, P, Projects-Planning , Selection, Financing, Implementation,

    and Review , Sixth Edition, Publication: Tata McGraw Hill.

      Rao, P.C.K. Project Management and Control , Publication: Sultan

    Chand & Sons.

      Desai, V, Project Management , Second Revised Edition, Publication:

    Himalaya Publishing House.

    E-References:

      www.projectsmart.co.uk. retrieved on 21/01/2012

      www.projectmanagement.com. retrieved on 22/01/2012

      www.pmearth.com. retrieved on 23/01/2012