Critical Path Method in Project Management

                             WELCOME

                             WELCOME

TO

TO

                              LECTURE 6

                              LECTURE 6

SELESTIAN AUGUSTINO

SELESTIAN AUGUSTINO

Try this question now:  Draw a network diagram

    3.1.11 Critical Path Method ES, EF, LS, LF, FLOATS

    3.1.11 Critical Path Method ES, EF, LS, LF, FLOATS

Early Start-ES

Early Start

 or 

ES

 is the earliest time that activity can start. An activity

near the end of path or much later will only start if all the previous

activities in the path also started early. If any one of the previous

activities slips then it will push this activity out.

Early

 Finish-EF

Early Finish

 or 

EF

 is the earliest time that activity can finish. It is the

date that an activity can finish if all previous activities started early and

none of the activities slipped.

If project manager and team knows about early start and early finish

dates of all the activities(tasks) then they will know how much freedom

they have to move the start dates without causing any problem to the

project.

Tips for calculation of ES, EF during forward pass

Forward pass is the direction from left to right as you traverse on network

diagram.

➨

 ES of first activity = 1

➨

 ES of all other activities = EF(of previous activity) + 1

➨

 If two activities say A and B converge (i.e. merge) to one activity, say C

in forward pass, then ES of activity C = (greater EF from activity A and B)

+ 1

➨

 EF = ES + duration -1

                          Sample diagram

Late Start-LS

Late Start

 or 

LS

 is the latest time an activity can start. If an activity is

on the path which is much shorter compare to critical path, then it can

start much late without any delay to the project.

Late Finish-LF

Late Finish

 or 

LF

 is the latest time that an activity can finish.

If an activity is on a shorter path and all of the other activities on same

path start as well as finish early, then it can finish very late without

causing project to be late.

Knowing late start and late finish will help you see how much it can

be played around in the schedule. If an activity has large LS and LF

means there are more options available.

Tips for calculation of LS, LF during reverse pass

Reverse/Backward pass is the direction from right to left as you

traverse on network diagram.

➨

 LF of last activity = EF of the same last activity

➨

 For all other activities except the convergence mentioned in the next

line, LF = LS(of previous activity) -1

➨

 If two activities say A and B converge (i.e. merge) to one activity in

the reverse pass say C then, LF(of activity C) = (Lesser LS from

activity A and B) -1

➨

 LS = LF - duration +1

                         Sample diagram

Problem 3: 

The following data are available for construction project. a)

Construct a network diagram  b) Calculate the project completion time  c)

Find the critical path and critical activities  d) Determine the ES, EF, LS,

LF and TF of each activity

Floats

Float

 / 

Slack

 is the amount of time an activity or project can be delayed from the

early start without changing the completion date of the project.

Types of float

Types of float

                              1.Total Float (TF)

The amount of time that an activity can be delayed or extended from its early start

date without delaying the 

project finish date

 or 

violating a schedule constraint

.



Mathematically: Late Finish – Early Finish = Total Float

Mathematically: Late Finish – Early Finish = Total Float

                             2. Free Float (FF)

The amount of time that an activity can be delayed without delaying the 

early start

date of any successor

 or 

violating a schedule constraint

.



Mathematically: Earliest Successors’ Early Start – Activity’s Early Finish = Free

Mathematically: Earliest Successors’ Early Start – Activity’s Early Finish = Free

Float

Float

                                  Floats

                   3.  Interfering Float (INTF)

The amount of time that an activity can be delayed or extended from its early start

date without delaying the 

project finish date

, but delaying an activity into interfering

float will delay the start of one or more following non-critical activities. If an

activity is delayed for the amount of the Free and Interfering Float, its successor

activities are critical.



Mathematically: Total Float – Free Float = Interfering Float

Mathematically: Total Float – Free Float = Interfering Float

                   4.  Independent Float (INDF)

The maximum amount of time an activity can be delayed without delaying the 

early

start of the succeeding activities

 and 

without being affected by the allowable delay

of any predecessor activity.



Mathematically: Predecessors’ Late Finish – Activity’s duration = Independent

Mathematically: Predecessors’ Late Finish – Activity’s duration = Independent

Float

Float

Remark

: when the result is a negative value, we set the value to zero.

Advantages of CPM



The CPM makes it easier for the project managers to build a team and create

human network for efficient handling of a multi-tasked project.



The Critical Path Method binds the entire team together and motivates the human

resources in timely completion of the tasks in a project.



 The CPM takes into consideration the requirements well in advance to complete a

project in the most efficient way possible.



With help of the Critical Path Method the project managers can determine the

duration and estimate exact time and cost of the project. It helps to monitor human

resources, and the direct and indirect costs associated with the project.



The CPM assists the project managers in planning schedules, monitoring tasks,

and helps control the project expenses.



The Critical Path Method also makes it convenient for the project managers to

calculate the time required to complete the tasks of the project. That helps them to

predict completion date of every phase, anticipate problems along the way, if any,

and react accordingly.

Disadvantages of CPM



In a big project, a CPM can become extremely complicated and difficult to fathom

for the new recruits to the project team.



If the project is far too bulky and lengthy, the Critical Path Method requires

software to monitor the plan.



CPM can become ineffective and difficult to manage if it is not well-defined and

stable.



It cannot effectively handle sudden changes in the implementation of the plan on

ground. It is very difficult to redraw the entire CPM chart if the plan of the project

suddenly changes midway.



The Critical Path Method cannot form and control the schedules of the persons

involved in the project.



The allocation of resources cannot be properly monitored.



The critical path of the CPM of a big project is not always clear. The project

managers have to spend a lot of time to calculate it carefully.



The Critical Path Method takes longer to identity and to monitor the critical path

when the project is of big dimension

.



Using CPM, identifying and determining a critical path is difficult when

there are many other similar duration paths in the project.



At times, to design a CPM is time consuming. It is also difficult to estimate

the activity completion time in a multidimensional project.

                     Self study

                     Self study

1.  Enumerate the concrete significance of CPM (At least 4 points).

3.1.12 Time Estimation in PERT (With Calculation)

There are three different estimates of activity duration in PERT:

1. Optimistic time 2. Pessimistic time 3. Most Likely time

1. Optimistic time 2. Pessimistic time 3. Most Likely time

1. Optimistic time

1. Optimistic time

, expressed as ‘

t

o

‘, represents estimate of minimum

possible time by which an activity can be completed assuming that

everything is in order according to the plan and there can be only

minimum amount of difficulty.

2. Pessimistic time

2. Pessimistic time

, expressed as ‘

t

p

’ represents estimate of maximum

possible time by which an activity can be completed assuming that

things may not be in accordance with the plan and there can be

incidence of difficulties in carrying out the activity.

3. Most Likely time

3. Most Likely time

, expressed as ‘

t

m

‘, represents estimate of time for

completion of an activity, which is neither optimistic nor pessimistic,

assuming that things should go in a normal way, and if the activity is

repeated several times, in most of the cases, it will be completed in

time represented by 

t

.

From the above three different time estimates, PERT suggests to work out the

following;



The expected time, expressed as (

The expected time, expressed as (

t

t

e

e

) which is the average of  

) which is the average of  

t

t

o

o

 , t

 , t

p

p

 and

 and

t

t

m

m

 calculated as,

 calculated as,

                               t

                               t

e

e

= (t

= (t

o

o

 + 4t

 + 4t

m

m

 + t

 + t

p

p

) / 6

) / 6



The variance expressed as (Var.) , calculated as,

The variance expressed as (Var.) , calculated as,

                             Var.= ((

                             Var.= ((

t

t

p

p

 -

 -

t

t

o

o

)/6)²

)/6)²



The standard deviation expressed as 

The standard deviation expressed as 

σ 

σ 

,which is the square root of

,which is the square root of

variance (Var.) calculated as,

variance (Var.) calculated as,

σ

σ

 = √(Var.) = √((

 = √(Var.) = √((

t

t

p

p

 -

 -

t

t

o

o

)/6)²= (

)/6)²= (

t

t

p

p

 -

 -

t

t

o

o

)/6

)/6

Problem 4: 

Using the tabulated schedules below,

a)

Draw the PERT network diagram

b)

Calculate the expected time, variance and  standard

deviation of each activity

c)

Draw the CPM network diagram

d)

Calculate the project completion time

e)

Find the critical path

f)

Identify the critical activities

Table 1

Table 2

                             Difference between PERT and CPM

Self study

Self study

1.

What are the advantages and disadvantages of PERT?

What are the advantages and disadvantages of PERT?

(At least 5 points @)

(At least 5 points @)

      3.2.0 Resource Management

      3.2.0 Resource Management

Resource

 is a stock or supply of money, materials, staff, and other assets that can be

drawn on by a person or organization in order to function effectively.

Resource management 

is the process of planning, scheduling, and allocating

resources in the best possible way.

The ultimate aim is to maximize the resources’

efficiency. This means, it ensures that internal and external resources are used

effectively on time and to budget.

OR

OR

Resource management 

is the process of planning the resources necessary to meet the

objectives of the project, and to satisfy the client’s requirements.

OR

OR

Resource management

 is the efficient and effective development of an

organization's resources when they are needed.

Example: Financial resources, inventory, human skills, production resources, or

information technology (IT) and natural resources.

OR

OR

Resource management

 is acquiring, allocating and managing the resources, such as

individuals and their skills, finances, technology, materials, machinery and

natural resources required for a project.

       3.2.1 Need for resource management

Resource management is needed because:



It provides the overview of everyone and everything involved in the

project



It enables utilization planning



It makes the planning and management process more transparent



It help you to see problems before they start



It gives control over the project

Techniques used in resource management are:

                                1.   Resource Levelling

                                1.   Resource Levelling

                                2.   Resource Allocation

                                3.   Resource Forecasting

 3.2.2 Basic important types of resources in

construction projects

                                   1.    Human resource

                                   2.    Financial resource

                                   3.    Material resource

                                   4.    Machinery resource

1. Human resource

1. Human resource



No matter the size and complexity of the project, in order for the project

tasks to be performed effectively, human resources are essential.



Human resources are considered to have the most complex requirements

than the other two types of project resources. Therefore, project managers

should plan in advance and identify potential people to become part of the

project team by making sure they are available and skilled for the project in

question.



Normally a project team is a group of people that is managed by a project

manager. The team management part is often the hardest part of the project,

especially if the manager hasn’t had to lead a team in the past.



Managing the project team’s time and workload can be tricky too, as,

usually, most of the project team members don’t work solely on one project.

They often have day jobs and may be involved in other projects at the same

time.

                                    1. 

                                    1. 

Human resource

Human resource



If you, as a project manager, know what individuals you need for your

project it could be a lot easier to do your resource planning, which

should help you balance those peaks and troughs of availability in the

team. Spend some time thinking through the different skill sets that you

need and the kind of tasks that are required for the project, regardless of

the project complexity and type.



Even at this early stage, you can still get a good idea of who needs to be

involved. You’ll have to work out who is needed on the project at what

times, based on your project schedule. You’ll need to bring in different

types of subject matter experts at different times, and each one will

have to know enough about the project’s objectives to get their part

done successfully.

2. Financial resource (Capital or Cost Resource)

2. Financial resource (Capital or Cost Resource)



The second essential resource for successful project completion is – capital.

As you know, all projects, regardless of their type, scale or complexity,

need money.



The cost resources are used for many things related to the project, including

project team members’ salaries, cost of tools and equipment that you and

your team will be using during the project execution.



Generally, managing a budget for a particular project is one of the core

skills that all project managers must have. As a project manager you need to

be confident handling finances and costs so that every phase of the project

goes smoothly.



One important aspect of this type of resource is for the project manager to

talk to its project sponsors about their expectations for the money that are

planned to be spent. It’s important that project sponsors have a realistic idea

about how much the project will cost, and as a project manager you can

help them do that once you have undertaken some of the planning.

 2.  Financial resource (Capital or Cost Resource)

 2.  Financial resource (Capital or Cost Resource)



If you don’t have enough finances for your project then you won’t be

able to get everything done. It’s that simple: the budget funds the

work and when it runs out the work has to stop. If they want the

project to be completed successfully then it needs to be adequately

funded.



You’ll need to know how much money you are spending because it

helps you establish whether you are on track or not.

 3.  

Material resources

Material resources



Projects also use up material resources that include different materials,

supplies and/or items that are part of the project. Assets, or goods, vary from

project to project but it’s highly likely that your project will need some kind of

tangible resource. It’s normally what you use the project budget to buy.



Equipment or machinery (which you might hire for the life of the project or

buy).



Property (again, it might be something you hire for the project such as a

temporary cabin on a building site).



Project managers can also make use of assets that the company already has

although they may have to budget for borrowing them or schedule in the right

time to use them so that they don’t clash with another project. An example

might be a testing lab that is used for multiple projects and that you will need

to book in advance in order not to coincide with other project teams using the

resource. This type of resource is particularly important to be planned in

advance because otherwise you can encounter huge problems for your project.

 3.2.3  Resource planning

 3.2.3  Resource planning

   1. What is resource planning?

   1. What is resource planning?



Resource planning is a specific area in project management that

deals with gathering and making use of all the necessary resources

required to deliver a project. In this respect, anything can be viewed

as a resource: people, equipment, materials and facilities.



Resource planning is also about managing available talent. It allows

project managers to make sure that one person will be working on

one thing, at one time, for a specific project. Managing resources is

also about matching skill level to task difficulty level. This way,

team members get to do challenging work and stay motivated.

2. 

2. 

Why is resource planning important in project management?

Why is resource planning important in project management?



Resources can make or break your project. Without the right resources, they

won’t turn into reality. Strategic use of resources allow project managers to

ship on time, respecting deadlines and costs. To this end, resource planning

is an essential step.



 Priorities can change on the fly. In order to accommodate changes, project

managers need to keep an eye on resource availability and utilization so

they can shift resources when needed.



It keeps an eye on utilization rates. This is very important if you charge

clients according to the number of hours.



It can help project managers to create balance and a good mood inside their

team. Matching tasks and skill set will keep team members happy and

engaged. Also, by constantly managing individual availability, project

managers make sure that work is divided equally and that no one gets

overworked.

      3.2.4  Resource levelling

      3.2.4  Resource levelling



Resource levelling 

is a technique in project management that overlooks

resource allocation and resolves possible conflict arising from over-

allocation. When project managers undertake a project, they need to

plan their resources accordingly. This will benefit the organization

without having to face conflicts and not being able to deliver on time.

Resource levelling is considered one of the key elements to resource

management in the organization.

                                         OR



Resource levelling 

is a project management technique in which the

demand for limited resources is accommodated by adjusting the project

program. In construction, resource levelling can be used to analyse the

variations in resource usage that can occur over time, and which can be

inefficient and costly.

       3.2.4  Resource levelling

       3.2.4  Resource levelling

                                           OR



Resource levelling

 is a technique in which start and finish dates are

adjusted based on 

resource

 constraints with the goal of balancing

demand for 

resources

 with the available supply.

                                          OR



Resource levelling

 is a PM technique’s which is begins and ends dates

is adjusted depends on 

resource

 restraints to the 

objectives

 of balance

the requirements for 

resources

 with presented supply.

                                          OR



Resource levelling

 is a technique in project management that overlooks

resource allocation and resolves possible conflict arising from over-

allocation. When project managers undertake a project, they need to

plan their resources accordingly

       3.2.5  Objectives of resource levelling

       3.2.5  Objectives of resource levelling



To allocate resource efficiently, so that the project can

be completed in the given time period



To overcome staff level constraints



To maximize the utilisation of resources between project

      3.2.6  Project crashing

      3.2.6  Project crashing



Project crashing 

is the process by which duration of project is reduced

by 

increasing

 the amount of 

resources

 allocated.

It can be used in the

management of construction works when the program is running behind

schedule. It is important to note that crashing is done only to 

critical

activities. This can be achieved by any one of the following approaches:

1)  Addressing productivity issues of the current resources and making

them more efficient. This can be done by taking better care of resources

available and cutting cost and time wherever possible.

2)  Bringing in new additional resources to speed up the processes.

3)  By evaluating alternatives available and analysing them in order to

find which one will help in compressing the duration with lowest cost.

3.2.6  Project crashing

3.2.6  Project crashing

Risks of Project Crashing in Project Management (PM) 

Risks of Project Crashing in Project Management (PM) 

1)  Various external and internal factors may lead project manager to go

for crashing but it usually affects the quality of work as the time taken

(besides cost) is the major issue on his mind.

2)  Using additional resources does not always guarantee better results.

Example if an organisation decides to hire more employees or outsource

them, one can't be sure that they are trained enough to deliver as per

expected standards which one will help in compressing the duration with

lowest cost.

3.2.7

3.2.7

Need for crashing

Need for crashing

   Project crashing can be necessary when:



The program planning has been inaccurate



When there have been unforeseen events which have caused delays,

such as defects being discovered.



Or if the client has requested that the projects, or a section of the

project, is completed earlier than previously specified, for example if

there has been an extension of time, but the client still wishes to

achieve the original completion date (this is generally referred to as

acceleration).

The aim of crashing is to achieve the maximum decrease in schedule for

minimum additional cost. This can be done by:



Addressing productivity issues being experienced by the current

resources and trying to find ways of increasing their efficiency.

3.2.7

3.2.7

Need for crashing

Need for crashing



Increasing the assignment of resources on critical path activities.

These could be internal resources or subcontracted resources.



Working longer hours.



Additional supervision.



Changes to design or specification (for example standardisation

replacing bespoke solutions)



Reduction in scope (for example transferring work to a separate

post-contract agreement for occupational work).



Early procurement of items.

           3.2.8  Tips for project crashing

           3.2.8  Tips for project crashing



Create project network



Identify the critical path



Identify the cost of reducing each activity on path



Reduce the most cost effective activity



Look for critical path changes i.e. if there is a multiple of critical

paths



 Crash next activity

          3.2.9  Principal Methods of crashing

          3.2.9  Principal Methods of crashing



Improving existing resources’ productivity



Changing work methods



Compromise quality/ reduce project scope



Work overtime



Increasing the quantity of resources



Scenarios to use crashing

Scenarios to use crashing

1.

 Imagine you are the Project Manager for XYZ project. You realize that

the project cannot be completed within 5 months. You decide to get

management's approval to add more resources to complete the project on

time, without changing the scope of the project. The technique used is?

Answer:

Crashing

Crashing

2.

 The Critical path of the project is 23 weeks. If the management wishes

to finish the project within 18 weeks. What is the impact on the term of the

critical path?

Answer

: If the management wishes to complete the project within 18

: If the management wishes to complete the project within 18

weeks, then the project slack will be- 18-23 = -5 weeks. The project slack

weeks, then the project slack will be- 18-23 = -5 weeks. The project slack

compares the critical path with an imposed date by the management, if

compares the critical path with an imposed date by the management, if

the project slack is negative, then you have an option to either perform

the project slack is negative, then you have an option to either perform

crashing or fast-track to ensure that the project is completed on time as

crashing or fast-track to ensure that the project is completed on time as

desired by the management. So, there will not be any changes in the

desired by the management. So, there will not be any changes in the

critical path.

critical path.



Scenarios to use crashing

Scenarios to use crashing

3.

 Crashing helps to bring the project back on schedule if it is delayed.

What should you do?

Answer:

Crashing should be done on the activities of the critical path

Crashing should be done on the activities of the critical path

of the project if you want to reduce the duration of the project.

of the project if you want to reduce the duration of the project.

4.

 The customer has given you a project to construct a building. The

project is delayed due to some unforeseen incidents and the customer has

demanded that you pay a penalty of 2,500,000Tshs, if you are not able to

complete the project on time. To avoid the penalty, you planned to work

overtime, add more human resources and rent physical resources to

complete the project on time. This is an example of:

Answer:

Crashing, as you have brought some extra resources to bring

Crashing, as you have brought some extra resources to bring

the project on track.

the project on track.



Scenarios to use crashing

Scenarios to use crashing

5.

 You are behind schedule by 3 months and you are under-budget

by  700,000Tshs. What is your best course of action?

Answer:

Since the project is delayed and I am under budget, I have

Since the project is delayed and I am under budget, I have

enough funds; and so, I can crash the project to make up for the

enough funds; and so, I can crash the project to make up for the

delay in the project schedule.

delay in the project schedule.



Scenarios to use crashing

Scenarios to use crashing

6.

 The project schedule network diagram for your project is as shown

in the figure below (duration is in days):



Scenarios to use crashing

Scenarios to use crashing

If Customer wants to complete this project within 14 days, what would

be the project float?

Answer:



Start→ Task 1→ Task 2→ Task 6→ End: 1+6+3+4=14 Days



Start→ Task 3→ Task 4→ Task 8→ End: 3+2+5+6=16 Days



Start→ Task 5→ Task 7→ Task 8 → End: 4+3+5+6=18 Days ->

This has Critical Path.



The duration on the critical path for the project is 18 days. If the

project has to be completed within 14 days, the project float is - 4

days; i.e., 14 - 18. So, Project Manager may either have the option to

perform crashing on the project schedule or otherwise, if the project

has a negative project float; i.e., -4 days).

     3.2.10  Time-Cost Trade-Off

     3.2.10  Time-Cost Trade-Off

The objective of the time-cost trade-off analysis is to reduce the

original project duration, determined from the critical path analysis,

to meet a specific deadline, with the least cost. In addition to that it

might be necessary to finish the project in a specific time to:



Finish the project in a predefined deadline date



Recover early delays



Avoid liquidated damages



Avoid adverse weather conditions that might affect productivity



Receive an early completion-bonus



Improve project cash flow

       3.2.10  Time-Cost Trade-Off

       3.2.10  Time-Cost Trade-Off

The activity duration can be reduced by one of the following actions:



Applying multiple-shifts work



Working extended hours (over time)



Offering incentive payments to increase the productivity



Working on week ends and holidays



Using additional resources



Using materials with faster installation methods



Using alternate construction methods or sequence

3.2.11  Project Costs

3.2.11  Project Costs

There are two types of costs associated with a project as here under:

(i) Direct costs

It represents the expenditure which can be allocated to different activi­

ties in a project, like manpower, material etc.

(ii) Indirect costs

It represents the expenditure on those items which are shared by more

than one activity and cannot be directly allocated to individual activity

of a project. Otherwise, one may say, indirect costs of a project are those

expenditures which cannot be apportioned or clearly allocated to the

individual activity. These include the expenditure related to the

administration and establishment charges, overhead, supervision, loss of

revenue etc.

                      1.  

Cost Slope and its significance in crashing

Cost Slope and its significance in crashing



In actual practice, we assume the time-cost curve to be linear between crash

point and nor­mal point. The curve in the figure below shows that, there is a

change in cost for change in time. The term ‘cost-slope’ is defined as the

“

in­crease in the cost of the activity per unit decrease in the time

”

.

        Mathematically, we can say,

        Cost slope = (Crash cost – Normal cost)/(Normal time – Crash time)



In simple words, we can say that 

cost slope of an activity is the increase in

cost of an activity by reducing the duration by one unit

.

                1. Cost Slope and its significance in crashing

                1. Cost Slope and its significance in crashing



Conducting a crash programme usually result in an increase in cost

of those activities that are constructed under the crash programme. In

order to keep the total increase in cost to a minimum, it is necessary

to crash those activities which permit reduction in construction time

at the least total increase in cost. The reduction in time for a project

can be achieved by reducing the duration of one or more activities

lying on the critical path.



The cost slope concept helps in finding lowest cost solution by

sequential compressing the activities having lowest cost slope, i.e.,

having lowest incremental cost, on critical path.

                      2.  Cost vs Time optimization curve

                      2.  Cost vs Time optimization curve

EXERCISE  3

EXERCISE  3

2 Marks questions

2 Marks questions

1.

What do you mean by scheduling in project management?

2.

 What are the uses of project schedule?

3.

Name the three project scheduling techniques.

4.

What do you understand by job layout?

5.

What do you know about WBC?

6.

What is a network diagram in project management?

7.

Name the two main types of network diagrams in project management.

8.

(i) What is an event?

     (ii) Mention two types of events

9.   What is an activity?

10.

 Define the slack.

11.

 What is resource management?

12.

 Mention the techniques used in resource management.

13.

 What are basic important types of resources in construction projects?

14.

What is resource planning?

15.

 Brief about resource levelling.

16.

 What do you know about project crashing?

17.

 For what purpose project crashing is needed?

18.

 State the general objective of time-cost trade-off analysis.

19.

 Name the two types of project costs.

20.  Define cost-slope and write it’s mathematical equation.

21.  Draw the cost-time optimization curve, label all the important features.

4 Marks questions

4 Marks questions

1.

Briefly explain the common steps in scheduling preparation.

2.

Classify project schedule.

3.

Discuss a Gantt chart with simple relevant diagram.

4.

Name and explain the principal preparation of job layout.

5.

What are the factors affecting job layout?

6.

Briefly explain any four (4) benefits of WBC.

7.

Explain the PDM.

8.

Using simple diagram, explain four (4) types of activities.

9.

Differentiate activity from event (at least 4 points).

10.

State the Fulkerson’s rule for numbering the events.

11.

Explain three time estimates of activity duration in PERT.

12.

Why do we need resource management?

15.

Explain in short about Critical Path, Earliest Start times, Earliest

Finish times, Latest Start times and Latest Finish times.

16.

Why is resource planning important in project management?

17. 

When is the project crashing necessary to be undertaken?

12 Marks questions

12 Marks questions

1.

Discuss in detail the temporary facilities needed to be constructed on

site.

2.

Enumerate the basic assumptions in creating a network diagram.

3.

Highlight and discuss the rules for drawing a network diagram.

4.

Differentiate PERT from CPM.

5.

What are the advantages and disadvantages of PERT?

6.

 Use the two tables below to: (a) Draw the PERT network diagram

(b) Calculate the expected time, variance and  standard deviation of

each activity (c) Draw the CPM network diagram (d) Calculate the

project completion time (e) Find the critical path (f) Identify the critical

activities.

                            END OF LECTURE 6

                            END OF LECTURE 6

                                   THANK YOU

                                   THANK YOU

SELESTIAN AUGUSTINO

SELESTIAN AUGUSTINO