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Project Planning and Scheduling
Faculty of Science and Technology
SBS5224 Engineering Management
http://ibse.hk/SBS5224/
1
Intended Learning Outcomes
• By the end of this lecture, you will be able to…
• Define project planning and project scheduling
• Describe the use of a Work Breakdown Structure (WBS)
• Discuss the objectives of project planning
• Explain the principles of planning and scheduling
• Identify the roles of the parties in project planning
• Apply the various techniques for planning and scheduling.
2
Definition
• Project planning
• The process of identifying all the activities necessary to successfully
complete the project.
• Project scheduling
• The process of determining the sequential order of the planned activities,
assigning realistic durations to each activity, and determining the start and
finish dates for each activity.
 Thus, project planning is a prerequisite to project scheduling because
there is no way to determine the sequence or start and finish dates of
activities until they are identified.
3
Definition
• “Project planning” and “project scheduling” are often used synonymously because
planning and scheduling are performed interactively.
4
A specific list of activities
may be planned and
scheduled for a project.
The schedule is
reviewed.
Additional activities may
be added or some activities
may be rearranged in order
to obtain the best schedule
of events for the project.
• Planning is more difficult to accomplish than scheduling because it demands
the ability of the project planner/scheduler to identify all the work required to
complete the project.
• The process of developing a well-defined work breakdown structure (WBS)
results in a list of activities that must be performed to complete a project.
Work Breakdown Structure (WBS)
• For any size project, large or small, it is necessary to develop a well-defined
Work Breakdown Structure (WBS) that divides the project into identifiable parts
that can be managed.
• The concept of the WBS is simple;
• In order to manage a whole project, one must manage and control each of its parts.
• It is the cornerstone of the project work plan.
• It defines the work to be performed, identifies the needed expertise, assists in selection
of the project team, and establishes a base for project scheduling and control.
• It is a graphical display of the project that shows the division of work in a multi-level
system.
• The number of levels in a WBS varies depending upon the size and complexity of the
project.
• The smallest unit in the WBS is a work package, which must be defined in sufficient
detail so the work can be measured, budgeted, scheduled, and controlled.
5
Work Breakdown Structure (WBS)
6
WBS
• The development of the WBS is
a continuing process that starts
when the project is first assigned
to the project manager and
continues until all work
packages have been defined.
• After the activities are identified,
it is relatively easy for a good
planner to determine the
schedule for a project.
7
Project Planning
• Project planning
• The heart of good project management because it provides the central
communication that coordinates the work of all parties.
• Establishes the benchmark for the project control system to track the quantity,
cost, and timing of work required to successfully complete the project.
• Should include a clear description of the required work before the work is
started.
• (It must be recognized that changes are a necessary part of project work, especially
in the early development phases. If changes in the work are expected, or probable,
then project planning should include provisions for a reasonable allowance of the
anticipated changes.)
8
Desired Results of Planning
• Desired results of project planning and scheduling
1. Finish the project on time
2. Continuous (uninterrupted) flow of work (no delays)
3. Reduced amount of rework (least amount of changes)
4. Minimize confusion and misunderstandings
5. Increased knowledge of status of project by everyone
6. Meaningful and timely reports to management
7. You run the project instead of the project running you
8. Knowledge of scheduled times of key parts of the project
9. Knowledge of distribution of costs of the project
10. Accountability of people, defined responsibility/authority
11. Clear understanding of who does what, when, and how much
12. Integration of all work to ensure a quality project for the owner
9
Principles of Planning and Scheduling
• There must be an explicit operational plan to guide the entire project.
• The plan must include and link the three components of the project:
a. Scope
b. Budget
c. Schedule
1. To develop an integrated total project plan, the project must be broken into
well-defined units of work that can be measured and managed, starting with
the WBS.
2. Once this is completed, the project team members who have the expertise to
perform the work can be selected.
3. Team members have the ability to
• Clearly define the magnitude of detail work that is required
• Define the time and cost that will be required to produce the work.
10
Principles of Planning and Scheduling
• The project plan and schedule must clearly define (i) individual
responsibilities, (ii) schedules, (iii) budgets, and (iv) anticipated problems.
• Key principles for planning and scheduling:
1. Begin planning before starting work, rather than after starting work
2. Involve people who will actually do the work in the planning and scheduling
process
3. Include all aspects of the project: scope, budget, schedule, and quality
4. Build flexibility into the plan, include allowance for changes and time for
reviews and approvals
5. Remember the schedule is the plan for doing the work, and it will never be
precisely correct
6. Keep the plan simple, eliminate irrelevant details that prevent the plan from
being readable
7. Communicate the plan to all parties; any plan is worthless unless it is known.
11
Responsibilities of Parties
• The principal parties of owner, designer, and contractor all have a
responsible role in project planning and scheduling.
1. Owner
• Establishes the project completion date, which governs the scheduling of
work for both the designer and contractor
• Sets priorities for the components that make up the project, so as to
• assist the designer in the process of organizing his/her work and developing the
design schedule to produce drawings that are most important to the owner
• assist in the development of the specifications and contract documents that
communicate priorities to the construction contractor.
12
Responsibilities of Parties
2. Designer (Design Organization)
• Develops a design schedule that meets the owner’s schedule
(The schedule should include a prioritization of work in accordance with the owner’s
needs and should be developed with extensive input of all designers who will have
principal roles in the design process.)
3. Contractor (Construction Contractor)
• Develops a schedule for all construction activities in accordance with the
contract documents
• Includes procurement and delivery of materials to the job, coordination of
labour and equipment on the job, and interface the work of all subcontractors
(The construction schedule aims to effectively manage the work to produce the best-
quality project for the owner, but not to settle disputes related to project work.)
13
Project Scheduling
• Purposes of project scheduling
1. To show the relationship of each activity to others & to the whole project
2. To identify the precedence relationships among activities
3. To encourage the setting of realistic time & cost estimates for each activity
4. To help make better use of people, money, & material resources by
identifying critical bottlenecks in the project
• Outcomes of project scheduling
1. Identified precedence relationships
2. Sequenced activities
3. Estimated material and worker requirements
4. Determined activity times and costs
5. Determined critical activities
14
Techniques for Planning & Scheduling
• The technique used for project scheduling varies depending upon the
project’s
a. Size
b. Complexity
c. Duration
d. Personnel
e. Owner’s requirements
• Methods of scheduling
1. Gantt chart
2. Network Analysis Systems (NAS)
a. Critical Path Method (CPM) – deterministic approach to scheduling
b. Program Evaluation and Review Technique (PERT)
– probabilistic approach to scheduling
15
Gantt Chart
• A programme chart, a bar chart, a graphical time-scale of the schedule,
developed by Henry L. Gantt.
• Characteristics:
• Simple, easy to use/interpret, does not require extensive interrelationships of activities
• Difficult and require significant time to update, does not show interdependences of
activities, does not integrate costs or resources with the schedule
• An effective technique for overall project scheduling, but has limited application for
detailed contraction work.
16
• The activities involved in a project
and the time taken for each activity
is displayed in this chart.
Gantt Chart
17
Network Analysis Method (NAS)
• Provides a comprehensive method for project planning, scheduling, and controlling.
• A general title for the technique of defining and coordinating work by a graphical
diagram that shows work activities and the interdependences of activities.
• Steps of CPM/PERT:
1. Define the project and all of its significant activities or tasks
2. Develop relationships among the activities
(Decide which activities must precede and which must follow others)
3. Draw the network connecting all of the activities
4. Assign time and cost estimates to each activity
5. Compute the longest time path through the network – the critical path
6. Use the network to help plan, schedule, monitor, and control the project
18
Critical Path Method (CPM)
• Developed in 1956, now commonly used in engineering and construction industry.
• The most commonly used NAS for project management.
• Characteristics:
• Simple concept, computations only require basic arithmetic, a large number of
computer programs are available to automate the work required of CPM scheduling.
• The most difficult task is identifying and interfacing the numerous activities that are
required to complete a project, i.e. development of the CPM network diagram.
• If a well-defined WBS is developed first, the task of developing a CPM diagram is
greatly simplified.
19
(Activity-on-node/AON network) (Activity-on-arrow/AOA network)
20
Method 1: Activity-On-Node (AON)
21
Method 2: Activity-On-Arrow (AOA)
22
Method 2: Activity-On-Arrow (AOA)
• Use of dummy activity – it consumes neither time nor resource!
23
Dummy Activity
• Only in Arrow Diagram
24
Example
25
Node
• Determine the activity information
• Earliest Start time (ES) & Earliest Finish time (EF)
• Latest Start time (LS) & Latest Finish time (LF)
• For an activity, the times can be presented as shown:
• Total Float is the allowable delay of an activity.
• Identify the critical path
• Longest path in network
• Shortest time project can be completed
• Any delay on critical path activities delays project
• Critical path activities have zero slack
26
Computation
a. Forward Pass Computation
• Involves the computation of the Earliest Start time (ES) of each activity.
• When two activities merge, the later of the Earliest Finish time (EF)
becomes the ES of the successor activity.
• The Earliest Finish time (EF) of the last node is the overall duration of the
project.
b. Backward Pass Computation
• Provides the Latest Finish time (LF) by which an activity must be
completed if there is to be no delay in the project.
27
Forward Pass Procedure
• Determine ES & EF times for each activity,
1. EFi = ESi + Di
2. ESi = Maximum EFj of predecessor(s)
28
Forward Pass Procedure
• Determine ES & EF times for each activity,
1. EFi = ESi + Di
2. ESi = Maximum EFj of predecessor(s)
29
+2
+6
+4
Forward Pass Procedure
• Determine ES & EF times for each activity,
1. EFi = ESi + Di
2. ESi = Maximum EFj of predecessor(s)
30
+5
+3
+4
Forward Pass Procedure
• Determine ES & EF times for each activity,
1. EFi = ESi + Di
2. ESi = Maximum EFj of predecessor(s)
31
+2
Backward Pass Procedure
• Determine LS & LF times for each activity,
1. LSi = LFi – Di
2. LFi = Minimum LSj of successor(s)
32
Backward Pass Procedure
• Determine LS & LF times for each activity,
1. LSi = LFi – Di
2. LFi = Minimum LSj of successor(s)
33
-2
-4
Backward Pass Procedure
• Determine LS & LF times for each activity,
1. LSi = LFi – Di
2. LFi = Minimum LSj of successor(s)
34
-5
-3
-6
Backward Pass Procedure
• Determine LS & LF times for each activity,
1. LSi = LFi – Di
2. LFi = Minimum LSj of successor(s)
35
-4
-2
Critical Path Analysis
• Float = LS – ES or LF – EF
36
Gantt Chart Method
• Earliest Start time (ES)
• Critical Path
Start  C  E  G  End
37
Gantt Chart Method
• Latest Start time (LS)
• Critical Path
Start  C  E  G  End
38
Gantt Chart Method
• Earliest Start time with Float
39
Cost Distribution
• The distribution of costs with respect to time
40
Cost Distribution
• S-Curve
41
Cost Distribution
• Some of the S-curves are calculated based on the Start times (ES &
LS) instead of the Finish times (EF & LF).
• Each activity may have its expenses distributed either evenly or in a
certain pattern:
• e.g. Activity A costs $20,000 for 2-day work
i.e. each day costs = $20,000/2 days
average = $10,000/day
Or Day 1 = $15,000 and Day 2 = $5,000
• The target schedule is the midpoint between Earliest Start (ES) and
Latest Start (LS):
• e.g. for Activity D, ES = Day 2, LS = Day 6
Target schedule = Day 4
42
Cost Distribution
• Illustrative S-Curve for cumulative cost curve on Early Start and Late Start,
and Target Schedule
43
PERT
• Program Evaluation and Review Technique (PERT)
• The application of the critical path method (CPM) to calculate project
duration with uncertainty.
• It uses three quantities in estimating the duration of a single activity:
1. The optimistic time
2. The pessimistic time
3. The most likely time
44
• Similarity with CPM
• Both make use of a network
diagram and use critical path
analysis to represent and
analyze a project.
• Difference from CPM
• CPM uses only a single time estimate for
an activity.
• PERT is usually applied to projects which
are carried out under considerable
uncertainty and is used to predict the
probability of completion of a certain
project within a certain period of time.
PERT
• Probability concept
• The optimistic time (a) , i.e. the shortest duration which could be
anticipated for an activity
• The pessimistic time (b), i.e. the duration of the activity when everything
takes a long time to complete
• The most likely time (m)
45
• It is empirical that when an activity is
repeating many times, the activity durations
recorded will follow a β-distribution.
• The optimistic and pessimistic times could
only occur once when under hundred times.
• Hence, the two vertical lines (i.e. a and b)
divide the area under the β-curve into the
ratio of 1:99.
PERT
• Probability concept
• The activity duration time (te) of an activity is given by the expected time
or mean time required to complete the activity:
46
• The vertical line through te in the β-curve
divides the area under the curve into two
equal halves.
• The standard deviation (s) and the variance
( ) of the β-distribution are given by:
te =
a + 4m + b
6
s
b a
6
s
b a
6
PERT
• Although the duration of an individual activity follows a β-distribution,
the completion time for a series of activities in a chain takes the form of
a normal distribution (this is also empirical).
47
• Normal distribution for the project completion time, where Te is the
expected project completion time.
PERT Analysis
• Example (based on the same example for CPM)
48
Given Calculated
PERT Network
• A PERT network is constructed based on te (instead of using m).
• Forward pass and backward pass procedures similar to those used in
the CPM are performed.
• The total duration is found to be 11.83 days.
49
Comparison
• CPM • PERT
50
Uncertainty Analysis
• When the times of individual activity are uncertain, the total project
completion time becomes uncertain.
• It is assumed that the variance in the total project completion time (V) can be
computed by adding the variances along the critical path,
V = S2 = ∑ s2 for all activities on the critical path
• In the example,
V = S2 = sC
2 + sE
2 + sG
2
= 1.000 + 0.250 + 0.444
= 1.694
S = V = 1.694 = 1.302
51
Uncertainty Analysis
• It is also assumed that the distribution of project completion time is normal
based on central limit theorem.
52
Normal distribution
μ = mean
σ = standard deviation
Probability density function = f x =
1
σ 2π
exp
1
2
x μ
σ
Boundaries Area under normal curve
μ ± σ 0.683
μ ± 2σ 0.954
μ ± 3σ 0.997
Uncertainty
Analysis
• Knowing the mean and
standard deviation of a
normal distribution, the
probability of completing
the project by a particular
target time can be
computed.
53
Uncertainty Analysis
• Example 1
• Probability of completing the project on or before 13 days,
P(T ≤ 13) = 0.5 + P(Z ≤ (13 – 11.83)/1.302)
= 0.5 + P(Z ≤ 0.90)
= 0.5 + 0.3159
= 0.8159
• Example 2
• Probability of completing the project on or before 11 days,
P(T ≤ 11) = 0.5 + P(Z ≤ (11 – 11.83)/1.302)
= 0.5 + P(Z ≤ –0.64)
= 0.5 – P(Z ≤ 0.64)
= 0.5 – 0.2389
= 0.2611
54
Checklist
• Can you
1. Differentiate between project planning and project scheduling?
2. Suggest the advantages of using a well-defined WBS?
3. Describe the expected outcomes of planning and scheduling?
4. Identify the responsibilities of the various parties in planning?
5. Plot a Gantt Chart?
6. Determine the critical path of a project?
7. Determine the overall duration of a project?
8. Determine the cost distribution of a project?
9. Determine the probability that a project will
complete on or before a certain numbers of days?
55
Reference
• Oberlender G.D. (2014)
“Project Management for
Engineering and
Construction”. New York:
McGraw Hill Education.
56
• Tang S.L et al. (2003)
“Modern Construction
Project Management”.
HK: HKU Press.

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Project_Planning_and_Scheduling_1742364195.pdf

  • 1. Project Planning and Scheduling Faculty of Science and Technology SBS5224 Engineering Management http://ibse.hk/SBS5224/ 1
  • 2. Intended Learning Outcomes • By the end of this lecture, you will be able to… • Define project planning and project scheduling • Describe the use of a Work Breakdown Structure (WBS) • Discuss the objectives of project planning • Explain the principles of planning and scheduling • Identify the roles of the parties in project planning • Apply the various techniques for planning and scheduling. 2
  • 3. Definition • Project planning • The process of identifying all the activities necessary to successfully complete the project. • Project scheduling • The process of determining the sequential order of the planned activities, assigning realistic durations to each activity, and determining the start and finish dates for each activity.  Thus, project planning is a prerequisite to project scheduling because there is no way to determine the sequence or start and finish dates of activities until they are identified. 3
  • 4. Definition • “Project planning” and “project scheduling” are often used synonymously because planning and scheduling are performed interactively. 4 A specific list of activities may be planned and scheduled for a project. The schedule is reviewed. Additional activities may be added or some activities may be rearranged in order to obtain the best schedule of events for the project. • Planning is more difficult to accomplish than scheduling because it demands the ability of the project planner/scheduler to identify all the work required to complete the project. • The process of developing a well-defined work breakdown structure (WBS) results in a list of activities that must be performed to complete a project.
  • 5. Work Breakdown Structure (WBS) • For any size project, large or small, it is necessary to develop a well-defined Work Breakdown Structure (WBS) that divides the project into identifiable parts that can be managed. • The concept of the WBS is simple; • In order to manage a whole project, one must manage and control each of its parts. • It is the cornerstone of the project work plan. • It defines the work to be performed, identifies the needed expertise, assists in selection of the project team, and establishes a base for project scheduling and control. • It is a graphical display of the project that shows the division of work in a multi-level system. • The number of levels in a WBS varies depending upon the size and complexity of the project. • The smallest unit in the WBS is a work package, which must be defined in sufficient detail so the work can be measured, budgeted, scheduled, and controlled. 5
  • 7. WBS • The development of the WBS is a continuing process that starts when the project is first assigned to the project manager and continues until all work packages have been defined. • After the activities are identified, it is relatively easy for a good planner to determine the schedule for a project. 7
  • 8. Project Planning • Project planning • The heart of good project management because it provides the central communication that coordinates the work of all parties. • Establishes the benchmark for the project control system to track the quantity, cost, and timing of work required to successfully complete the project. • Should include a clear description of the required work before the work is started. • (It must be recognized that changes are a necessary part of project work, especially in the early development phases. If changes in the work are expected, or probable, then project planning should include provisions for a reasonable allowance of the anticipated changes.) 8
  • 9. Desired Results of Planning • Desired results of project planning and scheduling 1. Finish the project on time 2. Continuous (uninterrupted) flow of work (no delays) 3. Reduced amount of rework (least amount of changes) 4. Minimize confusion and misunderstandings 5. Increased knowledge of status of project by everyone 6. Meaningful and timely reports to management 7. You run the project instead of the project running you 8. Knowledge of scheduled times of key parts of the project 9. Knowledge of distribution of costs of the project 10. Accountability of people, defined responsibility/authority 11. Clear understanding of who does what, when, and how much 12. Integration of all work to ensure a quality project for the owner 9
  • 10. Principles of Planning and Scheduling • There must be an explicit operational plan to guide the entire project. • The plan must include and link the three components of the project: a. Scope b. Budget c. Schedule 1. To develop an integrated total project plan, the project must be broken into well-defined units of work that can be measured and managed, starting with the WBS. 2. Once this is completed, the project team members who have the expertise to perform the work can be selected. 3. Team members have the ability to • Clearly define the magnitude of detail work that is required • Define the time and cost that will be required to produce the work. 10
  • 11. Principles of Planning and Scheduling • The project plan and schedule must clearly define (i) individual responsibilities, (ii) schedules, (iii) budgets, and (iv) anticipated problems. • Key principles for planning and scheduling: 1. Begin planning before starting work, rather than after starting work 2. Involve people who will actually do the work in the planning and scheduling process 3. Include all aspects of the project: scope, budget, schedule, and quality 4. Build flexibility into the plan, include allowance for changes and time for reviews and approvals 5. Remember the schedule is the plan for doing the work, and it will never be precisely correct 6. Keep the plan simple, eliminate irrelevant details that prevent the plan from being readable 7. Communicate the plan to all parties; any plan is worthless unless it is known. 11
  • 12. Responsibilities of Parties • The principal parties of owner, designer, and contractor all have a responsible role in project planning and scheduling. 1. Owner • Establishes the project completion date, which governs the scheduling of work for both the designer and contractor • Sets priorities for the components that make up the project, so as to • assist the designer in the process of organizing his/her work and developing the design schedule to produce drawings that are most important to the owner • assist in the development of the specifications and contract documents that communicate priorities to the construction contractor. 12
  • 13. Responsibilities of Parties 2. Designer (Design Organization) • Develops a design schedule that meets the owner’s schedule (The schedule should include a prioritization of work in accordance with the owner’s needs and should be developed with extensive input of all designers who will have principal roles in the design process.) 3. Contractor (Construction Contractor) • Develops a schedule for all construction activities in accordance with the contract documents • Includes procurement and delivery of materials to the job, coordination of labour and equipment on the job, and interface the work of all subcontractors (The construction schedule aims to effectively manage the work to produce the best- quality project for the owner, but not to settle disputes related to project work.) 13
  • 14. Project Scheduling • Purposes of project scheduling 1. To show the relationship of each activity to others & to the whole project 2. To identify the precedence relationships among activities 3. To encourage the setting of realistic time & cost estimates for each activity 4. To help make better use of people, money, & material resources by identifying critical bottlenecks in the project • Outcomes of project scheduling 1. Identified precedence relationships 2. Sequenced activities 3. Estimated material and worker requirements 4. Determined activity times and costs 5. Determined critical activities 14
  • 15. Techniques for Planning & Scheduling • The technique used for project scheduling varies depending upon the project’s a. Size b. Complexity c. Duration d. Personnel e. Owner’s requirements • Methods of scheduling 1. Gantt chart 2. Network Analysis Systems (NAS) a. Critical Path Method (CPM) – deterministic approach to scheduling b. Program Evaluation and Review Technique (PERT) – probabilistic approach to scheduling 15
  • 16. Gantt Chart • A programme chart, a bar chart, a graphical time-scale of the schedule, developed by Henry L. Gantt. • Characteristics: • Simple, easy to use/interpret, does not require extensive interrelationships of activities • Difficult and require significant time to update, does not show interdependences of activities, does not integrate costs or resources with the schedule • An effective technique for overall project scheduling, but has limited application for detailed contraction work. 16 • The activities involved in a project and the time taken for each activity is displayed in this chart.
  • 18. Network Analysis Method (NAS) • Provides a comprehensive method for project planning, scheduling, and controlling. • A general title for the technique of defining and coordinating work by a graphical diagram that shows work activities and the interdependences of activities. • Steps of CPM/PERT: 1. Define the project and all of its significant activities or tasks 2. Develop relationships among the activities (Decide which activities must precede and which must follow others) 3. Draw the network connecting all of the activities 4. Assign time and cost estimates to each activity 5. Compute the longest time path through the network – the critical path 6. Use the network to help plan, schedule, monitor, and control the project 18
  • 19. Critical Path Method (CPM) • Developed in 1956, now commonly used in engineering and construction industry. • The most commonly used NAS for project management. • Characteristics: • Simple concept, computations only require basic arithmetic, a large number of computer programs are available to automate the work required of CPM scheduling. • The most difficult task is identifying and interfacing the numerous activities that are required to complete a project, i.e. development of the CPM network diagram. • If a well-defined WBS is developed first, the task of developing a CPM diagram is greatly simplified. 19 (Activity-on-node/AON network) (Activity-on-arrow/AOA network)
  • 20. 20
  • 23. Method 2: Activity-On-Arrow (AOA) • Use of dummy activity – it consumes neither time nor resource! 23
  • 24. Dummy Activity • Only in Arrow Diagram 24
  • 26. Node • Determine the activity information • Earliest Start time (ES) & Earliest Finish time (EF) • Latest Start time (LS) & Latest Finish time (LF) • For an activity, the times can be presented as shown: • Total Float is the allowable delay of an activity. • Identify the critical path • Longest path in network • Shortest time project can be completed • Any delay on critical path activities delays project • Critical path activities have zero slack 26
  • 27. Computation a. Forward Pass Computation • Involves the computation of the Earliest Start time (ES) of each activity. • When two activities merge, the later of the Earliest Finish time (EF) becomes the ES of the successor activity. • The Earliest Finish time (EF) of the last node is the overall duration of the project. b. Backward Pass Computation • Provides the Latest Finish time (LF) by which an activity must be completed if there is to be no delay in the project. 27
  • 28. Forward Pass Procedure • Determine ES & EF times for each activity, 1. EFi = ESi + Di 2. ESi = Maximum EFj of predecessor(s) 28
  • 29. Forward Pass Procedure • Determine ES & EF times for each activity, 1. EFi = ESi + Di 2. ESi = Maximum EFj of predecessor(s) 29 +2 +6 +4
  • 30. Forward Pass Procedure • Determine ES & EF times for each activity, 1. EFi = ESi + Di 2. ESi = Maximum EFj of predecessor(s) 30 +5 +3 +4
  • 31. Forward Pass Procedure • Determine ES & EF times for each activity, 1. EFi = ESi + Di 2. ESi = Maximum EFj of predecessor(s) 31 +2
  • 32. Backward Pass Procedure • Determine LS & LF times for each activity, 1. LSi = LFi – Di 2. LFi = Minimum LSj of successor(s) 32
  • 33. Backward Pass Procedure • Determine LS & LF times for each activity, 1. LSi = LFi – Di 2. LFi = Minimum LSj of successor(s) 33 -2 -4
  • 34. Backward Pass Procedure • Determine LS & LF times for each activity, 1. LSi = LFi – Di 2. LFi = Minimum LSj of successor(s) 34 -5 -3 -6
  • 35. Backward Pass Procedure • Determine LS & LF times for each activity, 1. LSi = LFi – Di 2. LFi = Minimum LSj of successor(s) 35 -4 -2
  • 36. Critical Path Analysis • Float = LS – ES or LF – EF 36
  • 37. Gantt Chart Method • Earliest Start time (ES) • Critical Path Start  C  E  G  End 37
  • 38. Gantt Chart Method • Latest Start time (LS) • Critical Path Start  C  E  G  End 38
  • 39. Gantt Chart Method • Earliest Start time with Float 39
  • 40. Cost Distribution • The distribution of costs with respect to time 40
  • 42. Cost Distribution • Some of the S-curves are calculated based on the Start times (ES & LS) instead of the Finish times (EF & LF). • Each activity may have its expenses distributed either evenly or in a certain pattern: • e.g. Activity A costs $20,000 for 2-day work i.e. each day costs = $20,000/2 days average = $10,000/day Or Day 1 = $15,000 and Day 2 = $5,000 • The target schedule is the midpoint between Earliest Start (ES) and Latest Start (LS): • e.g. for Activity D, ES = Day 2, LS = Day 6 Target schedule = Day 4 42
  • 43. Cost Distribution • Illustrative S-Curve for cumulative cost curve on Early Start and Late Start, and Target Schedule 43
  • 44. PERT • Program Evaluation and Review Technique (PERT) • The application of the critical path method (CPM) to calculate project duration with uncertainty. • It uses three quantities in estimating the duration of a single activity: 1. The optimistic time 2. The pessimistic time 3. The most likely time 44 • Similarity with CPM • Both make use of a network diagram and use critical path analysis to represent and analyze a project. • Difference from CPM • CPM uses only a single time estimate for an activity. • PERT is usually applied to projects which are carried out under considerable uncertainty and is used to predict the probability of completion of a certain project within a certain period of time.
  • 45. PERT • Probability concept • The optimistic time (a) , i.e. the shortest duration which could be anticipated for an activity • The pessimistic time (b), i.e. the duration of the activity when everything takes a long time to complete • The most likely time (m) 45 • It is empirical that when an activity is repeating many times, the activity durations recorded will follow a β-distribution. • The optimistic and pessimistic times could only occur once when under hundred times. • Hence, the two vertical lines (i.e. a and b) divide the area under the β-curve into the ratio of 1:99.
  • 46. PERT • Probability concept • The activity duration time (te) of an activity is given by the expected time or mean time required to complete the activity: 46 • The vertical line through te in the β-curve divides the area under the curve into two equal halves. • The standard deviation (s) and the variance ( ) of the β-distribution are given by: te = a + 4m + b 6 s b a 6 s b a 6
  • 47. PERT • Although the duration of an individual activity follows a β-distribution, the completion time for a series of activities in a chain takes the form of a normal distribution (this is also empirical). 47 • Normal distribution for the project completion time, where Te is the expected project completion time.
  • 48. PERT Analysis • Example (based on the same example for CPM) 48 Given Calculated
  • 49. PERT Network • A PERT network is constructed based on te (instead of using m). • Forward pass and backward pass procedures similar to those used in the CPM are performed. • The total duration is found to be 11.83 days. 49
  • 51. Uncertainty Analysis • When the times of individual activity are uncertain, the total project completion time becomes uncertain. • It is assumed that the variance in the total project completion time (V) can be computed by adding the variances along the critical path, V = S2 = ∑ s2 for all activities on the critical path • In the example, V = S2 = sC 2 + sE 2 + sG 2 = 1.000 + 0.250 + 0.444 = 1.694 S = V = 1.694 = 1.302 51
  • 52. Uncertainty Analysis • It is also assumed that the distribution of project completion time is normal based on central limit theorem. 52 Normal distribution μ = mean σ = standard deviation Probability density function = f x = 1 σ 2π exp 1 2 x μ σ Boundaries Area under normal curve μ ± σ 0.683 μ ± 2σ 0.954 μ ± 3σ 0.997
  • 53. Uncertainty Analysis • Knowing the mean and standard deviation of a normal distribution, the probability of completing the project by a particular target time can be computed. 53
  • 54. Uncertainty Analysis • Example 1 • Probability of completing the project on or before 13 days, P(T ≤ 13) = 0.5 + P(Z ≤ (13 – 11.83)/1.302) = 0.5 + P(Z ≤ 0.90) = 0.5 + 0.3159 = 0.8159 • Example 2 • Probability of completing the project on or before 11 days, P(T ≤ 11) = 0.5 + P(Z ≤ (11 – 11.83)/1.302) = 0.5 + P(Z ≤ –0.64) = 0.5 – P(Z ≤ 0.64) = 0.5 – 0.2389 = 0.2611 54
  • 55. Checklist • Can you 1. Differentiate between project planning and project scheduling? 2. Suggest the advantages of using a well-defined WBS? 3. Describe the expected outcomes of planning and scheduling? 4. Identify the responsibilities of the various parties in planning? 5. Plot a Gantt Chart? 6. Determine the critical path of a project? 7. Determine the overall duration of a project? 8. Determine the cost distribution of a project? 9. Determine the probability that a project will complete on or before a certain numbers of days? 55
  • 56. Reference • Oberlender G.D. (2014) “Project Management for Engineering and Construction”. New York: McGraw Hill Education. 56 • Tang S.L et al. (2003) “Modern Construction Project Management”. HK: HKU Press.