Project Management and scheduling

• Objectives of project scheduling

• Network analysis

• Scheduling techniques

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.

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.

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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6 7 8

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PERT/CPMNode

Arrow

Predecessor

SuccessorMerge point

Burst point

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.

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

Example• Activity Predecessor Duration

• A - 2

• B - 6

• C - 4

• D A 3

• E C 5

• F A 4

• G B, D, E 2

Activity on Node Network

StartB6

A2

C4

G2

EndD3

F4

E5

StartB6

A2

C4

G2

EndD3

F4

E5

0 0

0 22 6

2 5

0 6

04 4 9

911

11 11

Forward pass analysis

StartB6

A2

C4

G2

EndD3

F4

E5

0 0

0 22 6

2 5

0 6

04 4 9

9 11

11 11

1111

119

9440

96

64

9300

117

Backward pass analysis

Slack Time in Triangles

StartB6

A2

C4

G2

EndD3

F4

E5

0 0

0 22 6

2 5

0 6

04 4 9

9 11

11 11

1111

119

9440

96

64

9300

117

00

0 0

0

4

5

4

4

Critical path

StartB6

A2

C4

G2

EndD3

F4

E5

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.

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.

Rules for implementation - backward pass

• The latest completion time (LC) of any activity is the smallest of the latest start times of the activity’s immediate successors.

• The latest start time for any activity is the latest completion time minus the activity time.

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

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 are accounted for by using three time estimates for each activity

Variation of Task Completion Time

Task A2464

Task B3454

Average 4 4

PERT Estimates & Formulas

te = a+4m+b6 s2 =

(b-a) 2

36

a = optimistic time estimatem = most likely time estimateb = pessimistic time estimate (a < m < b)te = expected time for the activitys2=variance of the duration of the activity

PERT • Calculate the expected time for each

activity

• 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 project duration by summing up the variances of the activities on the critical path.

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

A PERT Example

• Activity Predecessor 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

What do Te & S2 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)

Probability of finishing the project in 10 days

Te = 11 S2 = V[C] + V[E] + V[G] = 0.25 + 0.25 + 0.1111 = 0.6111

S= 0.7817

P( T<=Td ) = P(T<=10) = P(z<=( 10-Te )

S)

= P(z<=(10-11)

0.7817) = P(z<= -1.2793)

= 0.1003

About 10% probabilty fo finishing the project within 10 days

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<=Td ) = P(T<=10) = P(z<=( 13-Te )

S)

= P(z<=(13-11)

0.7817) = P(z<= 2.5585)

= 0.9948

About 99% probabilty of finishing the project within 13 days

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 be updated periodically.

Gantt Chart

A

B

C

D

E

F

G

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Gantt Chart Variations

• Linked Bars

• Progress - monitoring

• Milestone

• Task - combinations

• Phase-Based

• Multiple-Projects

• Project-Slippage-tracking

Linked Bars Gantt Chart

A

B

C

D

E

F

G

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