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TRANSCRIPT
Scheduling
Resources
and Costs
CHAPTER EIGHT
Student Version
Copyright © 2011 by The McGraw-Hill Companies, Inc. All
rights reserved.
McGraw-Hill/Irwin
Gannt Chart
• Developed by Henry Gannt in 1916
• is used to determine the timing of individual activities in a
project,
• is a graphical representation of the duration of tasks against the
progression of time,
• The purpose is to place tasks and activities (groups of tasks
gathered into broad tasks) as horizontal bars against a time line
to show start and end dates for the tasks
• is a type of bar chart that illustrates a project schedule,
• illustrates the start and finish dates of the terminal elements and
summary elements of a project,
–Terminal elements and summary elements comprise the work
breakdown structure of the project.
8–2
Gannt Chart
Planning and Scheduling
• Use a Gantt chart to plan how
long a project should take.
• A Gantt chart lays out the order in
which the tasks need to be carried
out.
• Early Gantt charts did not show
dependencies between tasks but
modern Gantt chart software
provides this capability.
Monitoring a Project
• A Gantt chart lets you see
immediately what should have been
achieved at any point in time.
• A Gantt chart lets you see how
remedial action may bring the project
back on course.
• Most Gantt charts include
"milestones" which are not part of a
traditional Gantt Chart.
• However, for representing deadlines
and other significant events, it is very
useful to include this feature on a
Gantt chart.
8–3
A Gantt Chart is a Matrix
• The Gantt chart is constructed with a horizontal axis
representing the total time span of the project, broken
down into increments (days, weeks, or months).
• A Gantt chart is a horizontal bar chart to graphically portray
WBS task duration.
• The Gantt chart is constructed with a vertical axis
representing the tasks that make up the project.
• The Gantt chart is constructed with a graph area which
contains horizontal bars for each task connecting the
period start and period ending symbols.
8–4
A Gantt Chart has variants
• Milestones: important checkpoints or interim goals for a
project.
• Resources: for team projects, it often helps to have an
additional column containing numbers or initials which
identify who on the team is responsible for the task.
• Status: the projects progress, the chart is updated by filling
in the task's bar to a length proportional to the amount of
work finished.
• Dependencies: an essential concept that some activities
are dependent on other activities being completed first. 8–5
Guidelines
1. What is the total length of the project?
– Let that time be the length of the time axis (x-axis).
2. How long is the shortest task?
– Let that time help you set the divisions on the x-axis. (Use your
judgment if you have a few tasks much shorter than most. They’ll
show up as points in time—or vertical lines).
3. What are the tasks of the project?
– List them sequentially along the y-axis (either by short title or
identifying number). Also, you can choose to list your tasks
sequentially by starting date or by number.
4. Estimate the duration for each task in your task list.
When does the task begin? When does the task end? Represent
start date and end date by an empty bar horizontal to the x-axis for
each task. The time between start date and end date is the duration
of the task. 8–6
• F:\BİM 405 Project MAnagement_Spring
2012\IME614_ek\HAK_PM_book.pdf
8–7
Figure 5-23 A Gantt Chart of a Sample
Project
Figure 5-24 A Gantt Chart of Sample Project
Showing Critical Path, Path Connections, Slack,
EST, LST, EFT, and LFT
Figure 5-25 A Gantt Chart of a Day Care Project
Showing Expected Durations, Critical Path,
Milestone, and Resource Requirements
Figure 5-26 A Progress Report on a Day Care
Project Showing Actual Progress Versus Baseline
Basic Gantt Chart
8–12
Gantt Chart with Dependencies
8–13
Using PERT
• PERT is used when activity times are uncertain.
– Decision making under risk (“P” for probabilistic)
– Three time estimates are required for each activity.
• OPTIMISTIC TIME: Best time if everything goes
perfectly
• REALISTIC TIME: Most likely time
• PESSIMISTIC TIME: A worst-case situation
B + 4M + P Expected Time = ------------------- 6
In this example, the most likely time is given a weight of 4, and the other two times
(pessimistic and optimistic) are each given weights of 1. Software allows you to change
these as needed, but the denominator must be the total of the weights given.
• If the activity times are risky, the project team must make
three time estimates for each activity and use PERT.
• Risky activity times enable the use of a probability
distribution and risk assessment.
– For this sample project the times will be certain. (CPM)
• Activity slack is the maximum length of time that an
activity can be delayed without delaying the entire
project. (The difference between the earliest time we can start an activity and the
latest time we can start it without delaying the project.)
– For St. Adolf’s we can’t go beyond 69 weeks since that is the
project length.
St. Adolf’s Hospital
Developing the schedule
• Earliest Start Time (ES) for an activity is the earliest finish
time of the immediately preceding activity.
• Earliest Finish Time (EF) for an activity is its earliest start
time plus how long it takes to do it (estimated duration).
• Latest Start Time (LS) is the latest you can finish the
activity minus the activity’s estimated duration.
• Latest Finish Time (LF) is the latest start time of the
activity that immediately follows it. (Latest start and finish times
for each activity are computed starting at the project’s last
activity completion time and working forward.)
• For simplicity, all projects start at time zero.
St. Adolf’s Hospital
Developing the schedule
Earliest Start and Earliest Finish Times
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0
Earliest start time
12
Earliest finish time
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69
© 2012 Lew Hofmann
Earliest Start and Earliest Finish Times
Critical Path
The Critical Path
takes 69 weeks
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
Path Time (wks)
A-I-K 33
A-F-K 28
A-C-G-J-K 67
B-D-H-J-K 69
B-E-J-K 43
© 2012 Lew Hofmann
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
Latest Start and Latest Finish Times (Working from the last activity toward the first activity)
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
Latest
finish
time
63 69
Latest
start
time
© 2012 Lew Hofmann
Activity Slack
Analysis
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
63 69
Slack is the difference between
LS and ES or the EF and LF.
Node Duration ES LS Slack
A 12 0 2 2
B 9 0 0 0
C 10 12 14 2
D 10 9 9 0
E 24 9 35 26
F 10 12 53 41
G 35 22 24 2
H 40 19 19 0
I 15 12 48 36
J 4 59 59 0
K 6 63 63 0
© 2012 Lew Hofmann
ANALYZING PROBABILITIES
• What is the probability that our sample project
will finish in 69 weeks as scheduled?
100% (Why?)
–Because we used CPM!
• (This means we were certain of all of our activity times.)
–If we weren’t certain, we should have used PERT
• You can’t do risk analysis if you use CPM
PERT and PROBABILITIES
• With PERT’s three time-estimates, we get a mean
(average) time and a variance for each activity and
each path.
–We also get a project mean time and variance.
• In order to compute probabilities (assuming a normal
distribution) we need the activity means and
variances.
– Most computer packages calculate this for you.
Probability
of Project Completion
• The probability of a project being completed by a given
date is a function of the mean activity times and variances
along the critical path(s).
• The probability of any specific activity being completed
by a given date is a function of the mean activity times
and variances along the longest path leading up to that
activity.
• If you have more than one critical path, focus on the path
with the greatest variance.
–A near-critical path may also be a problem, depending
on the mean and variance of it’s activities.
Distributions & Probability
• A Beta distribution is often used for the three
estimates of each activity
– This allows skewed distributions.
Optimistic------Most likely -----------------------Pessimistic
(3 ------------- 5 ---------------------------------- 11)
• Normal distributions are needed for probabilities.
• A distribution of activity-means is a normal
distribution, even though each activity time may be a
beta distribution.
Beta Distribution
Mean
m a b Time
Pro
ba
bili
ty
Pessimistic Optimistic
Each activity may have its three time
estimates skewed (Beta Distribution), but the
path along which this activities lie has a
normal distribution and thus a mean and
variance.
Figuring Probabilities
• Assume a PERT project critical path takes 40 days, and that the
variance of this path is 2.147
– You wish to know the probability of the project going over 42 days.
• Compute the standard deviation of the critical path. (Take the
square root of the variance of 2.147) Std. Dev. = 1.465
– POM/QM software gives you the variance of the critical path.
• Compute the Z value: Z = (absolute time difference) / Std. Dev.
In this example, Z = (42 days - 40 days) / 1.465 = 1.365
• Look up the Z value of 1.365 in a Normal Distribution table to get
the probability of the project taking 42 days.
• Subtract it from 100% to get the probability of going over 42.
Look up the Z value (1.365) in the table of normal distribution.
(In this case you need to interpolate between the Z values of .9313 and .9147)
.9139 or 91.39% is the probability of the project taking up to 42 days.
Going over 42 days is thus 100 - 91.39 = 8.61%
Project duration (weeks)
40 42
Probability of
meeting the
schedule in 42
weeks is
91.39%
Length of
critical path
is 40 weeks
Normal distribution: Sum of
Variances along critical
path = 2.147
Std. Dev. = 1.465 weeks
Probability of
exceeding 42
weeks is 8.61%
2 = (variances of activities along critical path) z =
T – C
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z = 72 – 69
11.89
What is the Probability of it taking 72 weeks?
Critical Path = B - D - H - J – K = 69 weeks
T = 72 weeks C = 69 weeks
St. Adolf’s Hospital A 69-week Project
Look up Z value in normal distribution table Pz = .8078 or 80.78%
(Probability of it taking 72 weeks) Z = 0.870
Critical
Path
Variance
Look up the Z value (0.870) in the table of normal distribution.
.8078 or 80.78% is the probability of the project taking up to 72 wks.
Going over 72 weeks would be 100 – 80.78 = 19.22%
Project duration (weeks)
69 72
Probability of
taking 72 weeks is
0.8078 or 80.78%
Length of
critical path is
69 weeks
Normal distribution:
Mean = 69 weeks;
= 3.45 weeks
Probability of
exceeding 72
weeks is 0.1922
or 19.22%
St. Adolf’s Hospital Probability of Completing Project On Time
The Statistical Distribution of all
Possible Times for an Activity
Activity Expected Time and Variance
2
2
E
6
)(Var
6
)(
6
)4(T
ab
ab
bma
95 Percent Level
• Task will be a or lower 5 percent of the time
• Task will be b or greater 5 percent of the time
3.3
)( ab
90 Percent Level
• Task will be a or lower 10 percent of the time
• Task will be b or greater 10 percent of the time
6.2
)( ab
The Probability of Completing the Project on
Time
2
)(
DZ
=NORMDIST(D,,,TRUE)
Figure 5-18 The Statistical Distribution of
Completion Times of the Path a-b-d-g-h
Completion Time Distribution for Tennis
Tournament
Critical Path
Activities D V
A 2 4/36
C 3 4/36
E 10 144/36
I 3 36/36
J 2 0
= 20 188/36 = 5.2 =
2
15-38
Probability of Overrun
What is the probability of an overrun if a 24 day completion time is promised?
24
P (Time > 24) = .5 - .4599 = .04 or 4%
Days
2.52
ZX
Z
Z
24 20
52
175
.
.
15-39
8–40
The Resource Problem
• Resources and Priorities
–Project network times are not a schedule
until resources have been assigned.
• The implicit assumption is that resources will be available in the required amounts when needed.
• Adding new projects requires making realistic judgments of resource availability and project durations.
–Cost estimates are not a budget
until they have been time-phased.
8–41
The Resource Problem (cont’d)
• Resource Smoothing (or Leveling)
–Involves attempting to even out varying demands
on resources by using slack (delaying noncritical
activities) to manage resource utilization when
resources are adequate over the life of the project.
• Resource-Constrained Scheduling
–The duration of a project may be increased by
delaying the late start of some of its activities if
resources are not adequate to meet peak demands.
8–42
Types of Project Constraints
• Technical or Logic Constraints
– Constraints related to the networked sequence
in which project activities must occur.
• Physical Constraints
– Activities that cannot occur in parallel or are affected by
contractual or environmental conditions.
• Resource Constraints
– The absence, shortage, or unique interrelationship and
interaction characteristics of resources that require a particular
sequencing of project activities
• Kinds of Resource Constraints
– People, materials, equipment
8–43
Classification of A Scheduling Problem
• Classification of Problem
–Using a priority matrix will help determine if
the project is time or resource constrained.
• Time-Constrained Project
–Must be completed by an imposed date.
• Time is fixed, resources are flexible: additional resources are required to ensure project meets schedule.
• Resource-Constrained Project
–Is one in which the level of resources available
cannot be exceeded.
• Resources are fixed, time is flexible: inadequate resources will delay the project.
8–44
Resource Allocation Methods
• Limiting Assumptions
–Splitting activities is not allowed—once an
activity is start, it is carried to completion.
–Level of resources used for an activity cannot
be changed.
• Risk Assumptions
–Activities with the most slack pose the least risk.
–Reduction of flexibility does not increase risk.
–The nature of an activity (easy, complex)
doesn’t increase risk.
8–45
Resource Allocation Methods (cont’d)
• Time-Constrained Projects
–Must be completed by an imposed date.
–Require use of leveling techniques that focus
on balancing or smoothing resource demands.
–Use positive slack (delaying noncritical activities)
to manage resource utilization over the duration
of the project.
• Peak resource demands are reduced.
• Resources over the life of the project are reduced.
• Fluctuation in resource demand is minimized.
8–46
Resource Allocation Methods (cont’d)
• Resource Demand Leveling Techniques
for Time-Constrained Projects
–Advantages
• Peak resource demands are reduced.
• Resources over the life of the project are reduced.
• Fluctuation in resource demand is minimized.
–Disadvantages
• Loss of flexibility that occurs from reducing slack.
• Increases in the criticality of all activities.
8–47
Resource Allocation Methods (cont’d)
• Resource-Constrained Projects
– Resources are limited in quantity or availability.
– Activities are scheduled using heuristics
(rules-of-thumb) that focus on:
1. Minimum slack
2. Smallest (least) duration
3. Lowest activity identification number
– The parallel method is used to apply heuristics
• An iterative process starting at the first time period of the project and scheduling period-by-period the start of any activities using the three priority rules.
8–48
The Impacts of Resource-Constrained
Scheduling
• Reduces delay but reduces flexibility.
• Increases criticality of events.
• Increases scheduling complexity.
• May make the traditional critical path
no longer meaningful.
• Can break sequence of events.
• May cause parallel activities to become
sequential and critical activities with slack
to become noncritical.
8–49
Splitting
• Splitting
– A scheduling technique use to get a better project
schedule and/or increase resource utilization.
• Involves interrupting work on an activity to employ the resource on another activity, then returning the resource to finish the interrupted work.
• Is feasible when startup and shutdown costs are low.
• Is considered the major reason why projects fail to meet schedule.
8–50
Multiproject Resource Schedules
• Multiproject Scheduling Problems
1. Overall project slippage
• Delay on one project create delays for other projects
2. Inefficient resource application
• The peaks and valleys of resource demands create scheduling problems and delays for projects.
3. Resource bottlenecks
• Shortages of critical resources required for multiple projects cause delays and schedule extensions.
8–51
Multiproject Resource Schedules (cont’d)
• Managing Multiproject Scheduling:
–Create project offices or departments to oversee
the scheduling of resources across projects.
–Use a project priority queuing system: first come,
first served for resources.
–Centralize project management: treat all projects
as a part of a “megaproject.”
–Outsource projects to reduce the number
of projects handled internally.
8–52
Key Terms
Heuristic
Planned value (PV)
Resource-constrained projects
Smoothing
Splitting
Time-constrained projects
Time-phased budget baseline