2. ORGANISING PROCUREMENT
ACTIVITIES
For big projects or procurements, the activities needs to
be well organised prior execution if the procurement is
to be successful.
Organising activities in a procurement alternatively can
be viewed as project management
3. THE IMPORTANCE OF PROJECT
MANAGEMENT
Wherever your carrier takes you, one of the most useful tools
you can have as a manager, is the ability to manage a project.
Projects are a common part of our everyday life e.g. planning a
wedding, or a surprise birthday party etc
The management of projects involves three phases:
1. Planning: This phase includes goal setting, defining the
project, and team organisation
2. Scheduling: This phase relates to people, money, and supplies
to specific activities and relates activities to each other
3. Controlling: Here the firm monitors resources, costs, quality,
and budgets. It also revise or changes plans and shifts
resources to meet time and cost demands.
Three popular techniques to allow managers plan, schedule, and
control are Gantt charts, Project Evaluation Review Technique
(PERT), and Critical Path Method (CPM).
4. PROJECT PLANNING
Projects can be defined as a series of related tasks
directed toward a major output.
One of the activities of the project management team is to
carefully establish the project’s objectives, then break the
project down into manageable parts.
This work breakdown structure (WBS) defines the project
by diving it into its major subcomponents (or tasks), which
are then subdivided into more detailed components, and
finally into a set of activities and their related costs.
The division of the project into smaller and smaller tasks
can be difficult, but is critical to managing the project and
to scheduling success.
Gross requirements of people, supplies and equipment are
also estimated in this planning phase.
5. PROJECT SCHEDULING
Project scheduling involves sequencing and allocating time to
all project activities.
At this stage, managers decide how long each activity will
take and compute the resources needed at each stage of
production.
One popular project scheduling approach is the Gantt chart.
Gantt charts are low costs means of helping managers make
sure that:
1. Activities are planned
2. Order of performance is documented
3. Activity time estimates are recorded
4. Overall project time is developed
Although Gantt charts are simple, they do not adequately
illustrate the relationships between the activities and the
resources. Therefore, PERT CPM are two widely used network
techniques.
6. Passengers
Baggage
Fueling
Cargo and mail
Galley servicing
Lavatory servicing
Drinking water
Cabin cleaning
Cargo and mail
Flight services
Operating crew
Baggage
Passengers
Deplaning
Baggage claim
Container offload
Pumping
Engine injection water
Container offload
Main cabin door
Aft cabin door
Aft, center, forward
Loading
First-class section
Economy section
Container/bulk loading
Galley/cabin check
Receive passengers
Aircraft check
Loading
Boarding
0 15 30 45 60
Minutes
SERVICE FOR A DELTA JET
7. PROJECT SCHEDULING
Whatever the approach taken by a project manager,
project scheduling serves several purposes:
1. It shows the relationship of each activity to others
and to the whole project
2. It identifies the precedence relationships among
activities
3. It encourages the setting of realistic time and cost
estimates for each activity
4. It helps make better use of people, money, and
material resources by identifying critical bottlenecks
in the project
8. PROJECT CONTROLLING
The control of projects, like the control of any
management system, involves close monitoring of
resources, costs, quality, and budgets.
Control also means using a feedback loop to revise the
project plan and having the ability to shift resources to
where they are needed most.
9. PROJECT MANAGEMENT TECHNIQUES:
PERT AND CPM
Program Evaluation and Review Technique (PERT)
and the Critical path Method (CPM) were both
developed in the 1950s to help managers to
schedule, monitor and control large and complex
projects/procurements.
PERT is a project management technique that uses
three time estimates for each activity. These time
estimates are used to compute expected values and
standard deviations for the activity.
CPM is a project management technique that uses
only one time factor per activity. It makes the
assumption that, activity times are known with
certainty and hence requires only one time factor
for each activity.
10. THE FRAMEWORK OF PERT &
CPM
PERT and CPM both follow six basic steps:
1. Define the project and prepare the work breakdown
structure
2. Develop relationships among the activities. Decide
which must precede and which must follow others
3. Draw the network connecting all activities
4. Assign time and/ or cost estimates to each activity
5. Compute the longest time path through the network.
This is called the critical path
6. Use the network to help plan, schedule, monitor and
control the project.
11. PROJECT MANAGEMENT
TECHNIQUES: PERT AND CPM
1. When will the entire project be completed?
2. What are the critical activities or tasks in the project –
that is, which activities will delay the entire project if
they are late?
3. Which are the non critical activities – the ones that
can run late without delaying the whole project’s
completion?
4. What is the probability that the project will be
completed by a specific date?
5. At any particular date, is the project on schedule,
behind schedule, or ahead of schedule?
6. On any given date, is the money spent equal to or
less than, or greater than the budgeted amount?
7. Are there enough resources available to finish the
project on time?
12. NETWORK DIAGRAMS AND APPROACHES
There are two approaches of drawing a project network:
i. Activity On Node (AON)
ii. Activity On Arrow (AOA)
Under AON convection nodes designate activities.
Under AOA arrows designate activities
Activities consume time and resources
The basic difference between AON and AOA is that, nodes in an
AON diagram represents activities. In an AOA network, the
nodes represents the starting and finishing times of an activity
and are also called events
So nodes in AOA neither consume time or resources
Although both AON and AOA are popular in practice, many of
the project management software packages, including
Microsoft Project, use AON networks. Therefore, our major
focus will be on AON
13. A COMPARISON OF AON AND
AOA NETWORK CONVENTIONS
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
A comes before
B, which comes
before C
(a) A B C
B
A C
A and B must both
be completed
before C can start
(b)
A
C
C
B
A
B
B and C cannot
begin until A is
completed
(c)
B
A
C
A
B
C
14. EXAMPLE 1
PREDECESSOR RELATIONSHIPS FOR POLLUTION
CONTROL AT KADOMA PAPER
Kadoma Paper Manufacturing had long delayed the
expense of installing advanced computerized air
pollution control equipment in its facility. But when
the board of directors adopted a new proactive
policy on sustainability, it did not just authorize the
budget for the state of the art equipment. It
directed the plant manager, Julie Annie Williams, to
complete installation in time for a major
announcement of the policy, on a new public
holiday Earth Day, exactly 16 weeks away! Under
strict deadlines from her bosses, Williams needs to
be sure that installation of the filtering system
progresses smoothly and on time.
Given the following information, develop a table
15. EXAMPLE 1
Kadoma Paper has identified the eight activities that need to be
performed in order for the project to be completed:
When the project begins, two activities can be simultaneously started:
Building the internal components for the device (activity A) and the
modifications necessary for the floor and roof activity (activity B)
The construction of the collection stack (activity C) can begin when the
internal components are completed. Pouring the concrete floor and
installation of the frame (activity D) can be started as soon as the
internal components are completed and the roof and floor have been
modified.
After the collection stack has been constructed , two activities can
begin: building high temperature burner (activity E) and installing the
pollution control system (activity F).
The air pollution device can be installed (activity G) after the concrete
floor has been poured, the frame has been installed, and the high
temperature burner has been built.
Finally, after the control system and pollution device have been
installed, the system can be inspected and tested (activity H)
16. SOLUTION TO EXAMPLE 1
Activities and precedence relationships may seem rather
confusing when they presented in this descriptive form.
It is therefore, convenient to list all the activity
information in a table, as below.
17. KADOMA PAPER MANUFACTURING'S
ACTIVITIES AND PREDECESSORS
Activity Description
Immediate
Predecessors
A Build internal components —
B Modify roof and floor —
C Construct collection stack A
D Pour concrete and install frame A, B
E Build high-temperature burner C
F Install pollution control system C
G Install air pollution device D, E
H Inspect and test F, G
18. NB:
When there are many activities in a project with fairly
complicated precedence relationships, it is difficult for
an individual to comprehend the complexity of the
project from just the tabular information.
In such cases, a visual representation of the project,
using a project network is convenient and useful.
A project network is a diagram of all the activities and
the precedence relationships that exist between these
activities in a project.
19. AON NETWORK FOR KADOMA
PAPER
In an AON approach, we denote each activity by a
node.
The arrows or lines represents the precedence
relationships between the activities
In this case, there are two activities (A and B) that
do not have predecessors. We draw separate nodes
for each of these activities. Although not required,
it is usually convenient to have a unique starting
activity for a project.
We have therefore include a dummy activity called
start
Dummy activity does not really exist and takes up
zero time and resources.
Therefore, start activity serves as a predecessor for
both activities A and B
20. AON NETWORK FOR
MILWAUKEE PAPER
A
Start
B
Start Activity
Activity A
(Build Internal Components)
Activity B
(Modify Roof and Floor)
21. AON NETWORK FOR KADOMA
PAPER
C
D
A
Start
B
Activity A Precedes Activity C
Activities A and B Precede
Activity D
23. DETERMINING THE PROJECT
SCHEDULE
Once the project network has been drawn to show all the
activities and their precedence relationships, the next step is
to determine the project schedule.
That is, we need to identify the planned starting time and
ending time for each activity.
Lets assume Kadoma Paper Manufacturing estimates the time
required for each activity, in weeks, as shown below.
24. DETERMINING THE PROJECT
SCHEDULE
Perform a Critical Path Analysis
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25
Table 3.2
25. DETERMINING THE PROJECT
SCHEDULE
Critical Path is the longest time path through
the network.
Any delay in critical path activities delays the
project
Critical path activities have no slack time
To find the critical path, we calculate two
distinct starting and ending times for each
activity.
These are defined as follows:
26. DETERMINING THE PROJECT
SCHEDULE
Perform a Critical Path Analysis
Table 3.2
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25
Earliest start (ES) = earliest time at which an activity can start,
assuming all predecessors have been
completed
Earliest finish (EF) = earliest time at which an activity can be
finished
Latest start (LS) = latest time at which an activity can start
so as to not delay the completion time of
the entire project
Latest finish (LF) = latest time by which an activity has to be
finished so as to not delay the completion
time of the entire project
27. DETERMINING THE PROJECT
SCHEDULE
We use a two-pass process, consisting of a forward pass
and backward pass, to determine these time schedules
for each activity.
The early start and finish times (ES and EF) are
determined during the forward pass.
The late start and finish times (LS and LF) are determined
during the backward pass.
28. DETERMINING THE PROJECT
SCHEDULE
Perform a Critical Path Analysis
A
Activity Name or
Symbol
Earliest
Start ES
Earliest
Finish
EF
Latest
Start
LS Latest
Finish
LF
Activity Duration
2
29. FORWARD PASS
Begin at starting event and work forward
Earliest Start Time Rule:
If an activity has only one immediate predecessor, its ES
equals the EF of the predecessor
If an activity has multiple immediate predecessors, its ES
is the maximum of all the EF values of its predecessors
ES = Max (EF of all immediate predecessors)
30. FORWARD PASS
Begin at starting event and work forward
Earliest Finish Time Rule:
The earliest finish time (EF) of an activity is the sum of its
earliest start time (ES) and its activity time
EF = ES + Activity time
31. ES/EF NETWORK FOR KADOMA
PAPER
Start
0
0
ES
0
EF = ES + Activity time
Since activity start has no predecessors, we begin by setting
Its ES to 0. That is activity Start can begin at time 0. It activity
Start has an ES of 0, its EF is also 0, since its activity time is 0
32. ES/EF NETWORK FOR KADOMA
PAPER
Start
0
0
0
A
2
2
EF of A =
ES of A + 2
0
ES
of A
33. B
3
ES/EF NETWORK FOR KADOMA
PAPER
Start
0
0
0
A
2
2
0
3
EF of B =
ES of B + 3
0
ES
of B
37. E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
D
4
3 7
C
2
2 4
ES/EF NETWORK FOR KADOMA
PAPER
B
3
0 3
Start
0
0
0
A
2
2
0
Since H is the last activity in the project, this also implies
That the earliest time in which the entire project can be
Completed is 15 weeks
38. FORWARD PASS
Although the forward pass allows us to determine the
earliest project completion time, it does not identify the
critical path.
To identify this path, we need to conduct the backward
pass to determine the LS and LF values of all activities.
39. BACKWARD PASS
Just as the forward pass began with first activity in the
project, the backward pass begins with the last activity in
the project.
For each activity, we first determine its LF value, followed
by its LS value
40. BACKWARD PASS
Begin with the last event and work backwards
Latest Finish Time Rule:
If an activity is an immediate predecessor for just a single
activity, its LF equals the LS of the activity that immediately
follows it
If an activity is an immediate predecessor to more than one
activity, its LF is the minimum of all LS values of all activities
that immediately follow it
LF = Min (LS of all immediate following activities)
41. BACKWARD PASS
Begin with the last event and work backwards
Latest Start Time Rule:
The latest start time (LS) of an activity is the difference of its
latest finish time (LF) and its activity time
LS = LF – Activity time
42. LS/LF TIMES FOR KADOMA
PAPER
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
LF = EF
of Project
15
13
LS = LF – Activity time
43. LS/LF TIMES FOR KADOMA
PAPER
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
LF = Min(LS of following
activity)
10 13
44. LS/LF TIMES FOR KADOMA
PAPER
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
LF = Min(4, 10)
4
2
45. LS/LF TIMES FOR KADOMA
PAPER
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
46. COMPUTING SLACK TIME
After computing the ES, EF, LS, and LF times for
all activities, compute the slack or free time for
each activity
Slack is the length of time an activity can be delayed without
delaying the entire project
Slack = LS – ES or Slack = LF – EF
47. COMPUTING SLACK TIME
The activities with zero slack are called critical activities
and are said to be on the critical path.
The critical path is a continuous path through the project
network that:
Start at the first activity in the project (Start in our
example)
Terminates at the last activity in the project (H in our
example)
Includes only critical activities (activities with n slack
time)
48. COMPUTING SLACK TIME
Earliest Earliest Latest Latest On
Start Finish Start Finish Slack Critical
Activity ES EF LS LF LS – ES Path
A 0 2 0 2 0 Yes
B 0 3 1 4 1 No
C 2 4 2 4 0 Yes
D 3 7 4 8 1 No
E 4 8 4 8 0 Yes
F 4 7 10 13 6 No
G 8 13 8 13 0 Yes
H 13 15 13 15 0 Yes
49. CRITICAL PATH FOR KADOMA
PAPER
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
50. CRITICAL PATH FOR KADOMA
PAPER
The total project completion time is 15 weeks which
corresponds to the longest path in the network.
The path start at A-C-E-G-H
51. VARIABILITY IN ACTIVITY TIMES
In identifying all earliest and latest times so far, and the
associated critical path(s), we have adopted the CPM approach of
assuming that all activity times are known and fixed constants.
That is there is no variability in activity times.
However, in practice, it is likely that activity completion times
vary depending on various factors.
For example, building internal components (activity A) for
Kadoma Paper Manufacturing is estimated to finish in 2 weeks.
Clearly, supply chain issues such as late arrival of materials,
absence of key personnel and so on could delay this activity.
This means that we cannot ignore the impact of variability in
activity times when deciding the schedule for a project.
PERT addresses this issue.
PERT’s ability to handle three time estimates for each activity
enables us to compute the probability that we can complete the
project by a target date
52. THREE TIME ESTIMATES IN PERT
Three time estimates are required
Optimistic time (a) – time an activity will take if
everything goes according to plan. In estimating this
value, there should be only a small probability (say
1/100) that the activity time will be <a
Most–likely time (m) – most realistic estimate to
complete an activity
Pessimistic time (b) – time an activity will take
assuming very unfavorable conditions. In estimating
this value, there should be only a small probability (say
1/100) that the activity time will be < b
In PERT we employ a probability distribution based on three
estimates for each activity
When using PERT, we often assume that activity time estimates
follow the beta probability distribution.
This continuous distribution is often appropriate for
determining the expected value and variance for activity
completion times
53. VARIABILITY IN ACTIVITY TIMES
Estimate follows beta distribution
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b − a)/6]2
Probability of
1 in 100 of > b
occurring
Probability of
1 in 100 of
< a occurring
Probability
Optimistic
Time (a)
Most Likely Time
(m)
Pessimistic Time
(b)
Activity
Time
54. VARIABILITY IN ACTIVITY TIMES
Estimate follows beta distribution
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b – a)/6]2
55. VARIABILITY IN ACTIVITY TIMES
The time t (expected activity time) for each activity is
used to in the project network to compute all earliest and
latest times
56. COMPUTING VARIANCE
Most Expected
Optimistic Likely Pessimistic Time Variance
Activity a m b t = (a + 4m + b)/6 [(b – a)/6]2
A 1 2 3 2 .11
B 2 3 4 3 .11
C 1 2 3 2 .11
D 2 4 6 4 .44
E 1 4 7 4 1.00
F 1 2 9 3 1.78
G 3 4 11 5 1.78
H 1 2 3 2 .11
57. PROBALITY O PROJECT
COMPLETION
The critical path analysis helped us determine that
Kadoma paper’s expected project completion time is 15
weeks
However, Williams knows that there is significant
variation in the time estimates for several activities.
Variation of the activities on the critical path can affect
the overall project completion time – possibly delaying it.
PERT uses the variance of critical path activities to help
to determine the variance of the overall project.
58. PROBABILITY OF PROJECT
COMPLETION
Project variance is computed by
summing the variances of critical
activities
s2 = Project variance
= (variances of activities
on critical path)
p
59. PROBABILITY OF PROJECT
COMPLETION
Project variance is computed by summing the variances of critical
activities because activities are independent and then take the square
root to determine the standard deviation
Project variance
s2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
Project standard deviation
sp = Project variance
= 3.11 = 1.76 weeks
p
Management now has an estimate not only of expected completion time
for the project but also of the standard deviation of the estimate
60. PROBABILITY OF PROJECT
COMPLETION
How can this information be used to help answer
questions regarding the probability of finishing
the project on time?
PERT makes two more assumptions:
Total project completion times follow a normal
probability distribution
Activity times are statistically independent
With these assumptions, the bell shaped normal
curve can be used to represent project
completion dates.
The normal curve implies that, there is 50%
chance that the manufacture’s project completion
time will be less than 15 weeks and 50% chance
62. PROBABILITY OF PROJECT
COMPLETION
What is the probability this project can be
completed on or before the 16 week
deadline?
Z= – /sp
= (16 wks – 15 wks)/1.76
= 0.57
due expected date
date of completion
Where Z is the number of standard
deviations the due date lies from the
mean
63. WHAT IS THE PROBABILITY THIS PROJECT CAN BE
COMPLETED ON OR BEFORE THE 16 WEEK
DEADLINE?
Z= − /sp
= (16 wks − 15 wks)/1.76
= 0.57
due expected date
date of completion
Where Z is the number of standard
deviations the due date lies from the
mean
.00 .01 .07 .08
.1 .50000 .50399 .52790 .53188
.2 .53983 .54380 .56749 .57142
.5 .69146 .69497 .71566 .71904
.6 .72575 .72907 .74857 .75175
From Appendix I
65. DETERMINING PROJECT
COMPLETION TIME FOR A GIVEN
LEVEL
Let’s say Williams is worried that there is 71.57% chance
that the population control equipment can be put in place in
16 weeks or less.
She thinks that it may be possible to plead with board of
directors for more time.
However, before she approaches the board, she wants to
arm herself with sufficient information about the project.
Specifically she wants to find deadline by which she has a
99% chance of completing the project.
Clearly, this due date would be greater than 16 weeks.
However, what is the exact value of this new due date?.
To answer this question, we again use the assumption that
Kadoma paper’s Project completion follows a normal
distribution with mean of 15 weeks and standard deviation
of 1.76 weeks
66. DETERMINING PROJECT
COMPLETION TIME FOR A GIVEN
CONFIDENCE LEVEL
First compute the Z value corresponding to 99%
Starting with the standard normal equation on slide 62
we can solve the due date and rewrite the equation as:
Due date = Expected completion time + (z x SD)
= 15 +(2.33x1.76)
= 19.1 weeks
68. WHAT PROJECT MANAGEMENT
HAS PROVIDED SO FAR
The project’s expected completion time
is 15 weeks
There is a 71.57% chance the equipment
will be in place by the 16 week deadline
Five activities (A, C, E, G, and H) are on
the critical path
Three activities (B, D, F) have slack time
and are not on the critical path
A detailed schedule is available
69. COST-TIME TRADE-OFFS AND
PROJECT CRASHING
While managing a project, it is uncommon for a
project manager to be faced with either (or
both) of the following situations:
The project is behind schedule, and
The scheduled project completion time has
been moved forward.
In either situation, some or all of the remaining
activities need to be speeded up (usually by
adding resources) to finish the project by the
desired due date.
The process by which we shorten the duration
of a project in the cheapest manner possible is
called project crashing
70. COST-TIME TRADE-OFFS AND
PROJECT CRASHING
CPM is a technique in which each activity has a normal
or standard time.
Associated with this normal time is the normal cost of
the activity.
However, another time in project management is the
crash time.
Associated with this crash time is the crash cost of the
activity.
Usually we shorten an activity by adding extra
resources (e.g. equipment, people etc) to it. Bear in
mind that not all activities can be shortened
Hence it is logical for crashing cost of an activity to be
71. COST-TIME TRADE-OFFS
AND PROJECT
CRASHING
When choosing which activities to to crash, and by how
much, we need to ensure the following:
The amount by which the activity is crashed is
Taken together, the shortened activity durations will
enables us to finish the project by the due date
The cost of crashing is as small as possible.
72. STEPS IN PROJECT CRASHING
1. Compute the crash cost per time period for
each activity in the network.
Crash cost
per period =
(Crash cost – Normal cost)
(Normal time – Crash time)
2. Using current activity times, find the critical
path and identify the critical activities
73. STEPS IN PROJECT CRASHING
3. If there is only one critical path, then
select the activity on this critical path
that:
(a) can still be crashed, and
(b) has the smallest crash cost per
period.
If there is more than one critical path,
then select one activity from each
critical path such that
(a) each selected activity can still be
crashed, and (b) the total crash cost of
all selected activities is the smallest.
74. STEPS IN PROJECT CRASHING
4. Update all activity times. If the desired
due date has been reached, stop. If not,
return to Step 2.
75. PROJECT CRASHING TO MEET A
DEADLINE AT KADOMA PAPER
Suppose the plant manager at Kadoma paper
Manufacturing has been given only 13 weeks (instead of
16 weeks) to install the new pollution control equipment.
As you recall, the length of Julie Ann Williams’s critical
path was 15 weeks, but she must now complete the
project in 13 weeks
Naturally, Williams is interested in speeding up the
project by 2 weeks at the least additional costs.
The company’s normal and crash times, and normal and
crash costs, are shown in the table below
76. CRASHING THE PROJECT
Time (Wks) Cost ($) Crash Cost Critical
Activity Normal Crash Normal Crash Per Wk ($) Path?
A 2 1 22,000 22,750 750 Yes
B 3 1 30,000 34,000 2,000 No
C 2 1 26,000 27,000 1,000 Yes
D 4 2 48,000 49,000 500 No
E 4 2 56,000 58,000 1,000 Yes
F 3 2 30,000 30,500 500 No
G 5 2 80,000 84,500 1,500 Yes
H 2 1 16,000 19,000 3,000 Yes
77. CRASHING THE PROJECT
The current critical path using the normal times is Start–
A–C-E-G-H in which start is just a dammy starting
activity.
Of these critical activities, activity A has the lowest crash
cost per week of $750.
Williams will therefore, crash activity A by 1 week to
reduce the project completion time to 14 weeks.
Note that activity A cannot be crashed any further, since
it has reached its crash limit of 1 week.
78. CRASHING THE PROJECT
At this stage, the original path Start-A-C-E-G-H remains
critical with a completion time of 14 weeks. However, a new
path Start-B-D-G-H is also critical now, with completion
time of 14 weeks.
Any further crashing must be done on both critical paths
On each of these e need to identify one activity that can still
be crashed
We also want the total cost of crashing an activity on each
path to be the smallest.
Pick the activities with the smallest crash cost per period in
each path.
If we do this we could select activity C from the first path
and activity D from the second path.
The total crash cost will then be $2000 (= $1000 + $1000)
79. CRASHING THE
PROJECT
But we also spot that activity G is common to
both paths. That is by crashing activity G, we will
simultaneously reduce the completion time of
both paths.
Even though $1500 crash cost for activity G is
higher than that for activities C and D, we could
still prefer crashing G, since the total crashing
cost will now be only $1500 (compared with
$2000 if we crash C and D)
To crash project down to 13 weeks, Williams
should crash activity A by 1 week and activity G
by 1 week.
The total additional cost will be $2250 (=$750 +
$1500)
This is important because many projects include
80. ADVANTAGES OF PERT/CPM
Some features operations managers need to be aware of
1. Especially useful when scheduling and controlling large
projects
2. Straightforward concept and not mathematically
complex
3. Graphical networks help to perceive relationships among
project activities
4. Critical path and slack time analyses help pinpoint
activities that need to be closely watched
81. ADVANTAGES OF PERT/CPM
5. Project documentation and graphics
point out who is responsible for various
activities
6. Applicable to a wide variety of projects
7. Useful in monitoring not only schedules
but costs as well
82. LIMITATIONS OF PERT/CPM
1. Project activities have to be clearly
defined, independent, and stable in their
relationships
2. Precedence relationships must be
specified and networked together
3. Time estimates tend to be subjective
and are subject to fudging by managers
4. There is an inherent danger of too much
emphasis being placed on the longest,
or critical, path
