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.
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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.
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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.
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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.
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• 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
Probability
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 – C2
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 (
a b
a b
b m
a
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
) ( b a
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
) ( b a
The Probability of Completing the Project on Time
2
) (
D Z
=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 .
2 5
Z X
Z Z
24 20
5 2 1 75
. .
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.
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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.
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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
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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.
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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.
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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.
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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
