Network Analysis

NETWORK ANALYSIS

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What exactly is a project?

PM 1 – I’m in charge of the construction of a retail development in the centre of a large town. There are 26 retail units and a super market in the complex. My main responsibilities are to co-ordinate the work of the various contractors to ensure that the project is completed to specification, within budget and on time.

PM 2 – I am directing a team of research scientists. We are running trials on a new analgesic drug on behalf of a pharmaceutical company. It is my responsibility to design the experiments and make sure that proper scientific and legal procedures are followed, so that our results can be subjected to independent statistical analysis.

PM 3- The international aid agency which employs me is sending me to New Delhi to organize the introduction of multimedia resources at a teachers’ training college. My role is quite complex. I have to make sure that appropriate resources are purchased- and in some cases developed within the college. I also have to encourage the acceptance of these resources by lecturers and students within the college.

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PM 2 – I am directing a team of research scientists. We are running trials on a new analgesic drug on behalf of a pharmaceutical company. It is my responsibility to design the experiments and make sure that proper scientific and legal procedures are followed, so that our results can be subjected to independent statistical analysis.

A new drug

PM 3- The international aid agency which employs me is sending me to New Delhi to organize the introduction of multimedia resources at a teachers’ training college. My role is quite complex. I have to make sure that appropriate resources are purchased- and in some cases developed within the college. I also have to encourage the acceptance of these resources by lecturers and students within the college.

A new method of teaching students

PM 1 – I’m in charge of the construction of a retail development in the centre of a large town. There are 26 retail units and a super market in the complex. My main responsibilities are to co-ordinate the work of the various contractors to ensure that the project is completed to specification, within budget and on time.A shopping complex

Project is not defined by the type of outcome it is set up to achieve

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Characteristic of a project

A project is a temporary endeavour involving a connected sequence of activities and a range of resources, which is designed to achieve a specific and unique outcome and which operates within time, cost and quality constraints and which is often used to introduce change.

1. A project has identifiable beginning and end point; it is an entity by itself.2. It is not a permanent entity; it is usually a non-repetitive task.3. It can be broken down into identifiable activities which require time and resources for their execution.4. It is schedule to be completed by a target date.5. The objectives are clear and output or end product definite.6. It is usually large and complex with time horizon of 2 to 3 years. However some projects have taken more than 10 years while others have lasted for less than 6 months.7. It usually involves heavy investment.8. Execution of project activities and hence completion of the project is always subject to some uncertainties and risks

9.Need leadership

Project

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Examples– constructing houses, factories, shopping malls,

athletic stadiums or arenas– developing military weapons systems, aircrafts,

new ships– launching satellite systems– constructing oil pipelines– developing and implementing new computer

systems– planning concert, football games, or basketball

tournaments– introducing new products into market

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What is project management

• The application of a collection of tools and techniques to direct the use of diverse resources towards the accomplishment of a unique, complex, one time task within time, cost and quality constraints.

• Its origins lie in World War II, when the military authorities used the techniques of operational research to plan the optimum use of resources.

• One of these techniques was the use of networks to represent a system of related activities

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Project Management Process

• Each project, whether big or small has three basic requirements:

• It should be completed without any delay.• It should use available man power and other

resources as small as possible.• It should involve as small investment as

possible.

The project management helps to fulfill the above requirements.

The project management involves the following three

phases

(i) Project planning

(ii) Project scheduling

(iii) Project controlling

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BASIC TOOLS AND TECHNIQUES OF PROJECT MANAGEMENT

The various tools and techniques of project management are grouped into the following two

trades:- 1.Bar charts, milestone chart and velocity

diagrams.2. Network techniques.

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Work breakdown structure

• A method of breaking down a project into individual elements ( components, subcomponents, activities and tasks) in a hierarchical structure which can be scheduled and cost

• It defines tasks that can be completed independently of other tasks, facilitating resource allocation, assignment of responsibilities and measurement and control of the project

• It is foundation of project planning• It is developed before identification of dependencies and

estimation of activity durations• It can be used to identity the tasks in the CPM and PERT

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Project Planning

• Resource Availability and/or Limits– Due date, late penalties, early completion

incentives– Budget

• Activity Information– Identify all required activities– Estimate the resources required (time) to complete

each activity– Immediate predecessor(s) to each activity needed

to create interrelationships

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Project Scheduling and Control Techniques

Gantt Chart

Critical Path Method (CPM)

Program Evaluation and Review Technique (PERT)

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History of CPM/PERT

• Critical Path Method (CPM)– E I Du Pont de Nemours & Co. (1957) for construction of new

chemical plant and maintenance shut-down– Deterministic task times– Activity-on-node network construction– Repetitive nature of jobs

• Project Evaluation and Review Technique (PERT)– U S Navy (1958) for the POLARIS missile program– Multiple task time estimates (probabilistic nature)– Activity-on-arrow network construction– Non-repetitive jobs (R & D work)

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Project Network• Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects• Use of nodes and arrows Arrows An arrow leads from tail to head directionally

– Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work.

Nodes A node is represented by a circle- Indicate EVENT, a point in time where one or more activities start and/or

finish.• Activity

– A task or a certain amount of work required in the project– Requires time to complete– Represented by an arrow

• Dummy Activity– Indicates only precedence relationships– Does not require any time of effort

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• Event– Signals the beginning or ending of an activity– Designates a point in time– Represented by a circle (node)

• Network– Shows the sequential relationships among activities using nodes

and arrows

Activity-on-node (AON)

nodes represent activities, and arrows show precedence relationshipsActivity-on-arrow (AOA)

arrows represent activities and nodes are events for points in time

Project Network

• One of the most challenging jobs that any manager can take on is the management of a large-scale project that requires coordinating numerous activities throughout the organization. A myriad of details must be considered in planning how to coordinate all these activities, in developing a realistic schedule, and then in monitoring the progress of the project.

Fortunately, two closely related operations research techniques,

• PERT (program evaluation and review technique)

• CPM (critical path method)

• In 1957 the Critical Path Method (CPM) was developed as a network model for project management. CPM is a deterministic method that uses a fixed time estimate for each activity. While CPM is easy to understand and use, it does not consider the time variations that can have a great impact on the completion time of a complex project.

• The Program Evaluation and Review Technique (PERT) is a network model that allows for randomness in activity completion times. PERT was developed in the late 1950's for the U.S. Navy's Polaris project having thousands of contractors. It has the potential to reduce both the time and cost required to complete a project.

PERT and CPM have been used for a variety of projects, including the following types:

• Construction of a new plant • Research and development of a new product• NASA space exploration projects • Movie productions • Building a ship • Government-sponsored projects for developing a new weapons system • Relocation of a major facility • Maintenance of a nuclear reactor • Installation of a management information system• Conducting an advertising campaign

STEPS IN THE PERT PLANNING PROCESS

PERT planning involves the following steps:• Identify the specific activities and milestones.• Determine the proper sequence of the

activities.• Construct a network diagram.• Estimate the time required for each activity.• Determine the critical path.(ES,EF,LS,LF)• Update the PERT chart as the project

progresses.

BENEFITS OF PERT

• PERT is useful because it provides the following information:

• Expected project completion time.• Probability of completion before a specified date.• The critical path activities that directly impact the

completion time.• The activities that have slack time and that can

lend resources to critical path activities.• Activity start and end dates.

LIMITATIONS

• The activity time estimates are somewhat subjective and depend on judgment.

• Even if the activity times are well-estimated, PERT assumes a beta distribution for these time estimates, but the actual distribution may be different.

• Even if the beta distribution assumption holds, PERT assumes that the probability distribution of the project completion time is the same as the that of the critical path. Because other paths can become the critical path if their associated activities are delayed, PERT consistently underestimates the expected project completion time.

A PROTOTYPE EXAMPLETHE RELIABLE CONSTRUCTION CO. PROJECT

• The RELIABLE CONSTRUCTION COMPANY has just made the winning bid of $5.4 million to construct a new plant for a major manufacturer. The manufacturer needs the plant to go into operation within a year. Therefore, the contract incudes the following provisions:

• A penalty of $300,000 if Reliable has not completed construction by the deadline 47 weeks from now.

• To provide additional incentive for speedy construction, a bonus of $150,000 will be paid to Reliable if the plant is completed within 40 weeks.

• Reliable is assigning its best construction manager, David Perty, to this project to help ensure that it stays on schedule. He looks forward to the challenge of bringing the project in on schedule, and perhaps even finishing early. However, since he is doubtful that it will be feasible to finish within 40 weeks without incurring excessive costs, he has decided to focus his initial planning on meeting the deadline of 47 weeks.

The PERT Three-Estimate Approach

• Most likely estimate (m) = estimate of the most likely value of the duration,

• Optimistic estimate (o) = estimate of the duration under the most favorable conditions,

• Pessimistic estimate (p) = estimate of the duration under the most unfavorable conditions.

FORMULAS

SOME EXAMPLE OF PERT CHART

CPM - Critical Path Method

In 1957, DuPont developed a project management method

designed to address the challenge of shutting down chemical plants for maintenance and then restarting the plants once the maintenance had been completed.

Given the complexity of the process, they developed the Critical Path Method (CPM) for managing such projects.

• On July 20, 1969, just eight years after Kennedy's speech, Apollo 11 landed two men on the moon.

• This achievement was possible only with careful planning that included the critical path method.

• NASA used the critical path method to help determine an efficient schedule for the tasks that led to the moon landing.

Benefits

•Provides a graphical view of the project.•Predicts the time required to complete the

project. •Shows which activities are critical to

maintaining the schedule and which are not

CPM Diagram

Events are depicted as nodes/circle on the network and activities that signify the beginning or ending of events are depicted as arcs or arrow lines between the activity. The following is an example of a CPM network diagram:

Why the CPM?

• The CPM formally identifies tasks which must be completed on time for the whole project to be completed on time.

• Identifies which tasks can be delayed for a while if resource needs

to be reallocated to catch up on missed tasks. • It helps you to identify the minimum length of time needed to

complete a project. • The CPM determines both the early start and the late start date

for each activity in the schedule.

CPM calculation

PathA connected sequence of activities leading from the starting event to the ending event

Critical PathThe longest path (time); determines the project duration

Critical ActivitiesAll of the activities that make up the critical path

CPM steps

• Draw the CPM network• Analyze the paths through the network• Determine the float for each activity

– Float is the maximum amount of time in which activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project

• Find the critical path i.e,the sequence of activities and events where there is no “slack” i.e.. Zero slack– Longest path through a network

ACTIVITY 1-2 1-3 2-3 2-5 3-4 3-6 4-5 4-6 5-6 6-7

DURATION 15 15 3 5 8 12 1 14 3 14

5

15 1 3

3 14 14 15 8 12

2 5

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Forward Pass:

Earliest Start Time-earliest time an activity can start Forward calculation from left to right.For any arrow max. value by addition should be taken..Events are converging in.

E=15 5 E=27

15 1 3 E=40 E=54

E=0 3 E=26 14 14

15 8 12 E=18

2 5

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Backward pass

Latest finish time- latest time an activity can be completed without

delaying critical path time.Backward calculation from right to left.For any arrow minimum value by subtraction should be

taken..Events are diverging out.

E=15:L=15 5 E=27:L=37

15 1 3 E=40: L=40 E=54:L=54

E=0 3 E=26 14 14 14 L=26 L=0 15 8 12 E=18:L=18

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TAIL EVENT START HEAD EVENT FINISH FLOATACTIVITY

DURATION

EARLIEST

LATEST EARLIEST

LATEST TOTAL FREE INDEPENDENT

1-2 15

1-3 15

2-3 3

2-5 5

3-4 8

3-6 12

4-5 1

4-6 14

5-6 3

6-7 14


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0

1-3 15 0

2-3 3 15

2-5 5 15

3-4 8 18

3-6 12 18

4-5 1 26

4-6 14 26

5-6 3 27

6-7 14 40


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 15

1-3 15 0 18

2-3 3 15 18

2-5 5 15 37

3-4 8 18 26

3-6 12 18 40

4-5 1 26 37

4-6 14 26 40

5-6 3 27 40

6-7 14 40 54

Earliest finish time (EST):

Latest time by which an activity can be finished.

Mathematically,

EFT= EST + duration of activity


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 15 15

1-3 15 0 15 18

2-3 3 15 18 18

2-5 5 15 20 37

3-4 8 18 26 26

3-6 12 18 30 40

4-5 1 26 27 37

4-6 14 26 40 40

5-6 3 27 30 40

6-7 14 40 54 54

Latest Start Time (LST)Latest time by which an activity can be started.

Mathematically,

LST= LFT – duration of activity


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 0 15 15

1-3 15 0 3 15 18

2-3 3 15 15 18 18

2-5 5 15 32 20 37

3-4 8 18 18 26 26

3-6 12 18 28 30 40

4-5 1 26 36 27 37

4-6 14 26 26 40 40

5-6 3 27 37 30 40

6-7 14 40 40 54 54

Float

Total float: Total float is an extra surplus time allocated to an

activity. Total float can be: 1.Positive 2.Negative

3.Zero Mathematically,Total float=LFT-EST-Duration of activity


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 0 15 15 0

1-3 15 0 3 15 18 3

2-3 3 15 15 18 18 0

2-5 5 15 32 20 37 17

3-4 8 18 18 26 26 0

3-6 12 18 28 30 40 10

4-5 1 26 36 27 37 10

4-6 14 26 26 40 40 0

5-6 3 27 37 30 40 10

6-7 14 40 40 54 54 0

Free float: It is that fraction of total float which can be used for

re-scheduling the activity without affecting the succeding activity.

Mathematically, Free float=Total float - slack of head event


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 0 15 15 0 0

1-3 15 0 3 15 18 3 3

2-3 3 15 15 18 18 0 0

2-5 5 15 32 20 37 17 7

3-4 8 18 18 26 26 0 0

3-6 12 18 28 30 40 10 10

4-5 1 26 36 27 37 10 0

4-6 14 26 26 40 40 0 0

5-6 3 27 37 30 40 10 10

6-7 14 40 40 54 54 0 0

Independent float: It is that fraction of free float which can be used for re-

scheduling the activity without affecting the preceding and succeding activity.

Mathematically, independent float=Free float – slack of tail event


DURATION

EARLIEST

LATEST EARLIEST


1-2 15 0 0 15 15 0 0 0

1-3 15 0 3 15 18 3 3 3

2-3 3 15 15 18 18 0 0 0

2-5 5 15 32 20 37 17 7 7

3-4 8 18 18 26 26 0 0 0

3-6 12 18 28 30 40 10 10 10

4-5 1 26 36 27 37 10 0 0

4-6 14 26 26 40 40 0 0 0

5-6 3 27 37 30 40 10 10 0

6-7 14 40 40 54 54 0 0 0

PERT planning involves • 1. Identify the specific activities

and milestones. • 2. Determine the proper

sequence of the activities. • 3. Construct a network diagram. • 4. Estimate the time required

for each activity.

CPM planning involves• 1. Specify the individual

activities. • 2. Determine the sequence of

those activities. • 3. Draw a network diagram. • 4. Estimate the completion time

for each activity.

DIFFERENCE BETWEEN PERT AND CPM

• 5. Determine the critical path.

• 6. Update the PERT chart as the project progresses.

• 7. It has the potential to reduce both the time and cost required to complete a project.

• 5. Identify the critical path (longest path through the network)

• 6. Update the CPM diagram as the project progresses.

• 7. usable for projects with activities having single time estimates

ADVANTAGES OF PERT/CPM

• Simple to understand and use• Show whether the project is on schedule; or

behind/ ahead of the schedule• Identify the activities that need closer

attention (critical)• Determine the flexibility available with

activities

• Show potential risk with activities (PERT)• Provide good documentation of the project

activities• Help to set priorities among activities and

resource allocation as per priority

LIMITATIONS OF PERT/CPM

• Demand clearly defined and stable activities• Precedence relationship should be known in

advance• Overemphasis on Critical path• Activity time estimates are subjective• Activity times in PERT may not follow Beta PD

in reality

• Cost of crashing an activity may not be linearSome Computer Software Available for Network

Analysis• Microsoft Project (Microsoft Corp.)• Power Project (ASTA Development Inc.)• Primavera Project Planner (Primavera)

TIME COST TRADE COST OFFASPECT IN PERT/CPM

Project cost• Each activity of the project consumes some

resources and hence has cost associated with it.• Almost in all the cases cost of an activity varies to

some extent with the amount of time consumed by the activity.

• The cost of the project will also depend upon the duration time of project.

• Thus increasing the costs the project duration can be cut down to some extent.

• To obtain an optimum project schedule- Maintain a balance between the costs and time.

• An optimum project schedule implies- lowest possible cost and minimum possible time.

• The total cost = consists of the direct and indirect costs

Direct cost• Cost of material, equipment and labor required to

perform the activity.• Cost is directly dependent upon- amount of

resources involved in the individual activity. • Direct cost-time relationship activity can varied by

varying the cost i.e., if the duration of any activity is further increased that will decreases in cost.

• Normal point- The cost of the activity decreases in significantly if the duration is further increased.

• Crash point- The minimum activity duration to which an activity can be compressed by increasing the resources and hence by increasing the direct cost.

Crash cost – Normal costCost slope = Normal Time – crash Time

Indirect costIT IS OF TWO TYPE

FIXED INDIRECT COST

general and administrative exp

license fee , insurance cost ,

tax etc.

VARIABLE INDIRECT COST

duration of project and consist of

overhead expenditure

supervision , depreciation etc.

It is with assumption that the indirect cost increases linearly with time as shown in the figure give below:

MINIMUM COST

• The sum of direct and indirect cost gives the total project cost.

• When the direct cost decrease with time and indirect cost increase with time, the total project cost curve will have a point where the total cost will be minimum.

Crashing the networkThe crashing of network following terminology is used

a) Activity costb) Crash timec) Crash costd) Normal coste) Normal timef) Cost slopeg) Total Project cost

The process of shortening a project, i.e., crashing involves following steps:

• Step 1: Prepare the network diagram find the normal critical path and determine the critical activities.

• Step 2: In this step cost slope is calculated for different activities with the help of following formula-

Crash cost – Normal cost Cost slope = Normal time – Crash time

• Step 3: This step is to identify those activities along the critical path which can be crashed. Crash the least expensive activity, i.e., the activity with the least slope.

• Step 4: By crashing the critical activity of critical path if other paths also become critical, we obtain a situation of parallel critical paths which implies that the duration of project can further be reduced through simultaneous crashing of the activities in the parallel critical paths.

• Step 5: This step involves the computation of total cost. After following the step, 3rd and 4th point is obtained beyond which further crashing in project duration is not possible. Total cost is obtain by adding corresponding fixed cost to the direct cost and direct cost will refer to the sum of cumulative crashing cost and normal cost.

General rules for crashing:a) Crash only critical activities on the critical path

which are with zero slack. (Slack time = latest time – earliest time)b) Do not crash non-critical activities as it will not

reduce the duration of project.c) First the activities with the lowest crashing cost per

unit of time should crash and this process should be repeated until the desired duration of project is achieved.

d) In the case of parallel critical path, each of the parallel must compressed.

e) The minimum duration of the project with minimum cost network can be obtain.

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UER

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Network Analysis

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