1. Project Management Chapter Topics
The Elements of Project Management
The Project Network
Probabilistic Activity Times
Project Crashing and Time-Cost Trade-Off
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2. Project Management Overview
Uses networks for project analysis.
Networks show how projects are organized and are used to determine time duration for completion.
Network techniques used are
- CPM (Critical Path Method)
- PERT (Project Evaluation and Review Technique)
Developed during late 1950s.
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3. The Elements of Project Management
Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity.
Project Management is concerned with control of an activity for a relatively short period of time after which management effort ends
Primary elements of Project Management to be discussed:
- Project team
- Project planning
- Project Control.
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4. The Elements of Project Management The Project team
Project team typically consists of a group of individuals from various areas in an organization and often includes outside consultants.
Members of engineering staff often assigned to project work.
Most important member of project team is the project manager.
Project manager is often under great pressure because of uncertainty inherent in project activities and possibility of failure.
Project manager must be able to coordinate various skills of team members into a single focused effort.
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5. QP5013 - PROJECT MANAGEMENT
The Project Network
A branch reflects an activity of a project.
A node represents the beginning and end of activities, referred to as events.
Branches in the network indicate precedence relationships.
When an activity is completed at a node, it has been realized.
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6. The Project Network Planning and Scheduling
- Network aids in planning and scheduling.
- Time duration of activities shown on branches:
Network for building a house with activity times
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7. The Project Network Concurrent Activities
- Activities can occur at the same time (concurrently)
- A dummy activity shows a precedence relationship but reflects no passage of time.
- Two or more activities cannot share the same start and end nodes.
Expanded network for building a house showing
concurrent activities.
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8. The Project Network Paths Through the Network
Expanded network for building a house showing
concurrent activities.
Paths Through the
House-Building Network
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9. The Project Network The Critical Path
The critical path is the longest path through the network; the minimum time the network can be completed.
path A: 12  3  4  6  7, = 9 months path B: 1  2  3  4  5  6  7, = 8 months path C: 1  2  4  6  7, = 8 months path D: 1  2  4  5  6  7, = 7 months
Alternative paths in the
network
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10. The Project Network Activity Scheduling- Earliest Times
- ES is the earliest time an activity can start. ESij = Maximum (EFi)
- EF is the earliest start time plus the activity time. EFij = ESij + tij
Earliest activity start and finish times
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11. The Project Network Activity Scheduling - Latest Times
- LS is the latest time an activity can start without delaying critical path time. LSij = LFij - tij
- LF is the latest finish time LFij = Minimum (LSj)
Latest activity start and finish times
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12. The Project Network Activity Slack
Slack is the amount of time an activity can be delayed without delaying the project.
Slack time exists for those activities not on the critical path for which the earliest and latest start times are not equal.
Shared slack is slack available for a sequence of activities.
Earliest activity start and finish times
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13. The Project Network Calculating Activity Slack Time
- Slack, Sij, computed as follows: Sij = LSij - ESij or Sij = LFij - EFij
Activity Slack
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14. Probabilistic Activity Times
Activity time estimates usually can not be made with certainty.
PERT used for probabilistic activity times.
In PERT, three time estimates are used: most likely time (m), the optimistic time (a) , and the pessimistic time (b).
These provide an estimate of the mean and variance of a beta distribution:
mean (expected time):
variance:
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15. Probabilistic Activity Times Example
Network with mean activity times and variances
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16. Earliest and latest activity times QP5013 - PROJECT MANAGEMENT
Probabilistic Activity Times Earliest and Latest Activity Times and Slack
Earliest and latest activity times
Activity Earliest and Latest Times and Slack
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17. Probabilistic Activity Times Expected Project Time and Variance
The expected project time is the sum of the expected times of the critical path activities.
The project variance is the sum of the variances of the critical path activities.
The expected project time is assumed to be normally distributed (based on central limit theorem).
In example, expected project time (tp) and variance (vp) interpreted as the mean () and variance (2) of a normal distribution:
 = 25 weeks
2 = 6.9 weeks
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18. Probability Analysis of the Project Network
- Using normal distribution, probabilities are determined by computing number of standard deviations (Z) a value is from the mean.
- Value is used to find corresponding probability in Table A.1, App. A.
Normal distribution of network duration
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19. Probability Analysis of the Project Network Example 1
2 =  = 2.63
Z = (x-)/  = (30 -25)/2.63 = 1.90
- Z value of 1.90 corresponds to probability of in Table A.1, appendix A. Probability of completing project in 30 weeks or less : ( ) =
Probability the network will be completed in 30 weeks or less
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20. Probability Analysis of the Project Network Example 2
Z = ( )/2.63 = -1.14
Z value of 1.14 (ignore negative) corresponds to probability of in Table A.1, appendix A.
Probability that customer will be retained is .1271
Probability the network will be completed in 22 weeks or less
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21. QP5013 - PROJECT MANAGEMENT
Probability Analysis of the Project Network CPM/PERT Analysis with QM for Windows
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22. Project Crashing and Time-Cost Trade-Off Definition
Project duration can be reduced by assigning more resources to project activities.
Doing this however increases project cost.
Decision is based on analysis of trade-off between time and cost.
Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time.
Crashing achieved by devoting more resources to crashed activities.
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23. Project Crashing and Time-Cost Trade-Off Example Problem (1 of 3)
Network for constructing a house
Time–cost relationship for crashing activity 1 : 2
Crash cost and crash time have linear relationship: total crash cost/total crash time = $2000/5 = $400/wk
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24. Project Crashing and Time-Cost Trade-Off Example Problem (2 of 3)
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25. Project Crashing and Time-Cost Trade-Off Example Problem (3 of 3)
Network with normal activity times and weekly activity crashing costs
- As activities are crashed, the critical path may change and several paths may become critical.
The revised network with activity 1 : 2 crashed
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26. QP5013 - PROJECT MANAGEMENT
Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows
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27. QP5013 - PROJECT MANAGEMENT
Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost
Project crashing costs and indirect costs have an inverse relationship.
Crashing costs are highest when the project is shortened.
Indirect costs increase as the project duration increases.
Optimal project time is at minimum point on the total cost curve.
The time–cost trade-off
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28. PERT Project Management Example Problem Problem Statement and Data
- Given the following data determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less.
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29. PERT Project Management Example Problem Solution (1 of 3)
Step 1 : Compute the Expected Activity Times and Variances
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30. PERT Project Management Example Problem Solution (2 of 3)
Step 2: Determine the Earliest and Latest Times at each Node
Step 3: Identify the Critical Path and Compute Expected Completion Time and Variance
Critical path (activities with no slack): 1  2  3  4  5
Expected project completion time (tp): 24 days
Variance: v = 4 + 4/9 + 4/9 + 1/9 = 5 days
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31. PERT Project Management Example Problem Solution (3 of 3)
Step 4: Determine the Probability That the Project Will be Completed in 28 days or less.
Z = (x - )/ = (28 -24)/5 = 1.79
Corresponding probability from Table A.1, appendix A, is and P(x  28) =
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32. QP5013 - PROJECT MANAGEMENT
Additional Exercises
No 10, 12, 16, 18, 24, 25 & 26; page 342 – 351, Chapter 8, Taylor.
Please try these questions & we will discuss it during our class.
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