Post on 15-Jan-2016
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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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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