project management notes

5/27/2018 Project Management Notes

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Project Management and scheduling

Objectives of project scheduling

Network analysis

Scheduling techniques


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Objectives of project scheduling Produce an optimal project schedule in

terms of cost, time, or risk.

Usually, it is difficult to optimize the three

variables at the same time. Thus,

setting an acceptable limit for two of the

three varaibles and optimizing the project in

terms of the third variable.


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Critical Path Method (CPM) Produce the earliest and lastest starting and

finishing times for each task or activity.

Calculate the amount of slack associated

with each activity.

Determine the critical tasks (Critical path).

Forward pass and backward pass

computational procedures.


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Network control Track the progress of a project on the basis

of the network schedule and taking

corrective actions when necessary.

Evaluate the actual performance against

expected performance.


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1 2

3

5

6 7 8

4

PERT/CPM

Node

Arrow

Predecessor

SuccessorMerge point

Burst point


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Two models of PERT/CPM Activity-on-Arrow (AOA): Arrows are used

to represent activities or tasks. Nodes

represent starting and ending points of

activities.

Activity-on-Node (AON): Nodes are used

to represent activities or tasks, while arrows

represent precedence relationships.


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Recap - purpose of CPM Critical path

Earliest starting time ES Earliest completion time EC

Latest starting time LS

Latest completion time LC Activity Capital letter

Duration t


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Example Activity Predecessor Duration A - 2

B - 6 C - 4

D A 3

E C 5

F A 4

G B, D, E 2


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Activity on Node Network

Start B

6

A

2

C

4

G

2

EndD

3

F4

E

5


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Start B

6

A

2

C

4

G

2

EndD

3

F

4

E

5

0 0

0 2

2 6

2 5

0 6

04 4 9

9 11

11 11

Forward pass analysis


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Start B

6

A

2

C

4

G

2

EndD3

F4

E

5

0 0

0 2

2

6

2 5

0 6

04 4 9

9 11

11 11

1111

119

9440

96

64

9

3

00

117

Backward pass analysis


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Slack Time in Triangles

Start B

6

A

2

C

4

G

2

EndD

3

F

4

E

5

0 0

0 2

2 6

2 5

0 6

04 4 9

9 11

11 11

1111

119

9440

96

64

93

00

117

00

0 0

0

4

5

4

4


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Critical path

Start B

6

A

2

C

4

G

2

EndD

3

F4

E

5


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Computational analysis

of network Forward pass: each activity begins at its

earliest time. An activity can begin as soon

as the last of its predecessors is finished.

Backward pass: begins at its latest

completion time and ends at the latest

starting time of the first activity in the

project network.

R l f i l i


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Rules for implementation -

forward pass

The earliest start time (ES) for any node (j)is equal to the maximum of the earliest

completion times (EC) of the immediate

predecessors of the node. The earliest completion time (EC) of any

activity is its earliest start time plus its

estimated time (its duration). The earliest completion time of the project

is equal to the earliest completion time the

very last activity.


16/30

Rules for implementation -

backward pass The latest completion time (LC) of any

activity is the smallest of the latest start

times of the activitys immediate

successors.

The latest start time for any activity is the

latest completion time minus the activity

time.


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Calculate slack time for each

activity Slack time: the difference in time between

the two dates at the beginning of a job or

the two dates at the end of the job. Slack

time represents the flexiblity of the job.

Thus, slack time = LS - ES or LC - EC


18/30

PERT

PERT is an extension of CPM. In reality, activities are usually subjected to

uncertainty which determine the actual

durations of the activities. It incorporates variabilities in activity

duration into project entwork analysis.

The poetntial uncertainties in activity areaccounted for by using three time estimates

for each activity


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Variation of Task Completion TimeTask A

2

4

6

4

Task B

34

5

4Average 4 4


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PERT Estimates & Formulas

te= a+4m+b6 s

2= (b-a)2

36

a = optimistic time estimatem = most likely time estimate

b = pessimistic time estimate (a < m < b)

te= expected time for the activitys2=variance of the duration of the activity


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PERT

Calculate the expected time for eachactivity

Calculate the variance of the duration of

each activity

Follow the same procedure as CPM does to

calculate the project duration, Te

Calculate the variance of the projectduration by summing up the variances of

the activities on the critical path.


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Sources of the Three Estimates Furnished by an experienced person

Extracted from standard time data

Obtained from historical data

Obtained from regression/forecasting

Generated by simulation Dictated by customer requirement


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A PERT Example

ActivityPredecessor a m b te s2

A - 1 2 4 2.17 0.2500

B - 5 6 7 6.00 0.1111 C - 2 4 5 3.83 0.2500

D A 1 3 4 2.83 0.2500

E C 4 5 7 5.17 0.2500

F A 3 4 5 4.00 0.1111

G B, D, E 1 2 3 2.00 0.1111


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What do Te& S

2

tell us? How likely to finish the project in a

specified deadline.

For example, suppose we would like to

know the probability of completing the

project on or before a deadline of 10 time

units (days)


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Probability of finishing the

project in 10 daysTe= 11 S

2= V[C] + V[E] + V[G]

= 0.25 + 0.25 + 0.1111

= 0.6111

S= 0.7817

P( T


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Probability of finishing the

project in 13 days

Te= 11 S2= V[C] + V[E] + V[G]

= 0.25 + 0.25 + 0.1111

= 0.6111

S= 0.7817

P(T


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Gantt Chart Gantt chart is a matrix of rows and columns.

The time scale is indicated along the

horizontal axis. Activities are arranged

along the vertical axis.

Gantt charts are usually used to represent

the project schedule. Gantt charts should beupdated periodically.


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Gantt Chart

A

B

C

D

E

F

G

1 2 3 4 5 6 7 8 9 10 11


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Gantt Chart Variations

Linked Bars

Progress - monitoring

Milestone

Task - combinations

Phase-Based Multiple-Projects

Project-Slippage-tracking


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Linked Bars Gantt Chart

A

B

C

D

E

F

G

1 2 3 4 5 6 7 8 9 10 11

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