management decision

  

Activities 10.1 and 10.2 in the slides for Chapter 10; they are developed in the course book.Please, solve each problem by utilizing QM for Windows and/or Excel QM. Capture the screenshots for the solution and other appropriate data. Explain the results.Activities 11.1 and 11.2 in the slides for Chapter 11; they are developed in the course book.Please, solve each problem by utilizing QM for Windows and/or Excel QM. Capture the screenshots for the solution and other appropriate data. Explain the results.session and we’ll discuss your answers in class (have a soft or hard copy to review in the classroom). Be prepared for an oral Q/A session!
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Management Decision Modeling
Chapter 11. Project Management
Dr. Jose Garcia-Rubia
Management Decision Modeling
Chapter 11. Project Management
LEARNING OBJECTIVES
After completing this chapter, students will be able to:
1. Understand how to plan, monitor, and control
projects with the use of PERT and CPM.
2. Determine earliest start, earliest finish, latest start,
latest finish, and slack times for each activity, along
with the total project completion time.
3. Reduce total project time at the least total cost by
crashing the network using manual or linear
programming techniques.
4. Understand the important role of software in
project management.
2
Management Decision Modeling
Chapter 11. Project Management
CHAPTER OUTLINE
11.1
11.2
11.3
11.4
11.5
Introduction
PERT/CPM
PERT/Cost
Project Crashing
Other Topics in Project Management
3
Management Decision Modeling
Chapter 11. Project Management
Introduction

Managing large-scale, complicated projects
effectively is a difficult problem and the stakes
are high
 The
first step in planning and scheduling a project is
to develop the work breakdown structure (WBS)
 Identify activities that must be performed and their
beginning and ending events
 Identify time, cost, resource requirements,
predecessors, and people responsible for each
activity
 A schedule for the project then can be developed
4
Management Decision Modeling
Chapter 11. Project Management
Introduction
The program evaluation and review technique
(PERT) and the critical path method (CPM) are
two popular quantitative analysis techniques for
complex projects
 PERT
uses three time estimates to develop a
probabilistic estimate of completion time
 CPM is a more deterministic technique
 They are so similar they are commonly considered
one technique, PERT/CPM
5
Management Decision Modeling
Chapter 11. Project Management
Six Steps of PERT/CPM
1.
2.
3.
4.
5.
6.
Define the project and all of its significant activities or
tasks.
Develop the relationships among the activities. Decide
which activities must precede others.
Draw the network connecting all of the activities.
Assign time and/or cost estimates to each activity.
Compute the longest time path through the network; this
is called the critical path.
Use the network to help plan, schedule, monitor, and
control the project.
6
Management Decision Modeling
Chapter 11. Project Management
Six Steps of PERT/CPM
1. Define the project and all of its significant activities or
tasks.
The critical path is important
2. Develop thesince
relationships
among
the activities.
any delay
in these
activities
Decide which
activities
mustcompletion
precede others.
can
delay the
of the
3. Draw the network
projectconnecting all of the 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.
7
Management Decision Modeling
Chapter 11. Project Management
PERT/CPM

Questions answered by PERT
1.
2.
3.
4.
5.
6.
7.
When will the entire project be completed?
What are the critical activities or tasks in the project, that is, the
ones that will delay the entire project if they are late?
Which are the noncritical activities, that is, the ones that can
run late without delaying the entire project’s completion?
If there are three time estimates, what is the probability that the
project will be completed by a specific date?
At any particular date, is the project on schedule, behind
schedule, or ahead of schedule?
On any given date, is the money spent equal to, less than, or
greater than the budgeted amount?
Are there enough resources available to finish the project on
time?
8
Management Decision Modeling
Chapter 11. Project Management
Activity 11.1 General Foundry Example




General Foundry, Inc. has long been trying to avoid the
expense of installing air pollution control equipment
The local environmental protection group has recently
given the foundry 16 weeks to install a complex air filter
system on its main smokestack
General Foundry was warned that it will be forced to
close unless the device is installed in the allotted period
They want to make sure that installation of the filtering
system progresses smoothly and on time
9
Management Decision Modeling
Chapter 11. Project Management
General Foundry Example
TABLE 11.1 – Activities and Immediate 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
B
E
Build high-temperature burner
C
F
Install control system
C
G
Install air pollution device
D, E
H
Inspect and test
F, G
10
Management Decision Modeling
Chapter 11. Project Management
Drawing the PERT/CPM Network

Two common techniques for drawing PERT
networks
(AON) – nodes represent activities
 Activity-on-arc (AOA) – arcs represent the activities
 The AON approach is easier and more commonly
found in software packages
 One node represents the start of the project, one
node for the end of the project, and nodes for each of
the activities
 The arcs are used to show the predecessors for each
activity
 Activity-on-node
11
Management Decision Modeling
Chapter 11. Project Management
Drawing the PERT/CPM Network
FIGURE 11.1 – Network for General Foundry
A
C
F
Build Internal
Components
Construct
Collection Stack
Install Control
System
Start
E
H
Build Burner
Inspect
and Test
B
D
G
Modify Roof
and Floor
Pour Concrete
and Install Frame
Install Pollution
Device
Finish
12
Management Decision Modeling
Chapter 11. Project Management
Activity Times

In some situations, activity times are known with
certainty
 CPM
assigns just one time estimate to each activity
and this is used to find the critical path

In many projects there is uncertainty about
activity times
 PERT
employs a probability distribution based on
three time estimates for each activity, and a weighted
average of these estimates is used for the time
estimate and this is used to determine the critical path
13
Management Decision Modeling
Chapter 11. Project Management
Activity Times

The time estimates in PERT are
Optimistic time (a) = time an activity will take if everything
goes as well as possible. There should
be only a small probability (say, 1/100) of
this occurring.
Pessimistic time (b) = time an activity would take assuming
very unfavorable conditions. There
should also be only a small probability
that the activity will really take this long.
Most likely time (m) = most realistic time estimate to complete
the activity.
14
Management Decision Modeling
Chapter 11. Project Management
Activity Times
• The time estimates in PERT are
PERT often assumes time
Optimistic time (a) = timeestimates
an activity follow
will takeaifbeta
everything
probability
distribution
goes
as well as possible.
There should
be only a small probability (say, 1/100) of
this occurring.
Pessimistic time (b) = time an activity would take assuming
very unfavorable conditions. There
should also be only a small probability
that the activity will really take this long.
Most likely time (m) = most realistic time estimate to complete
the activity.
15
Management Decision Modeling
Chapter 11. Project Management
Activity Times
FIGURE 11.2 – Beta Probability Distribution with Three Time Estimates
Probability
Probability of 1 in 100
of a Occurring
Probability of 1 in 100
of b Occurring
Activity Time
Most
Optimistic
Time
(a)
Most
Likely
Time
(m)
Most
Pessimistic
Time
(b)
16
Management Decision Modeling
Chapter 11. Project Management
Activity Times

To find the expected activity time (t), the beta
distribution weights the estimates as follows
a + 4m + b
t=
6
• To compute the dispersion or variance of activity
completion time
æb – aö
Variance = ç
÷
è 6 ø
2
17
Management Decision Modeling
Chapter 11. Project Management
Activity Times
TABLE 11.2 – Time Estimates (Weeks) for General Foundry, Inc.
ACTIVITY
OPTIMISTIC,
a
MOST
LIKELY,
m
PESSIMISTIC,
b
t = [(a + 4m + b)/6]
[(b – a)/6]2
A
1
2
3
2
4/36
B
2
3
4
3
4/36
C
1
2
3
2
4/36
D
2
4
6
4
16/36
E
1
4
7
4
36/36
F
1
2
9
3
64/36
G
3
4
11
5
64/36
H
1
2
3
2
4/36
EXPECTED
TIME,
VARIANCE,
25
18
Management Decision Modeling
Chapter 11. Project Management
Activity Times
FIGURE 11.3 – General Foundry’s Network with Expected Activity Times
A
2
C
2
F
E
3
4
H
Start
2
Finish
B
3
D
4
G
5
19
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path




We accept the expected completion time for
each task as the actual time
The total of 25 weeks does not take into account
that some of the tasks could be taking place at
the same time
To find out how long the project will take we
perform the critical path analysis for the network
The critical path is the longest path through the
network
20
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path

To find the critical path, determine the following
quantities for each activity
Earliest start (ES) time: the earliest time an activity
can begin without violation of immediate
predecessor requirements
2. Earliest finish (EF) time: the earliest time at which
an activity can end
3. Latest start (LS) time: the latest time an activity can
begin without delaying the entire project
4. Latest finish (LF) time: the latest time an activity
can end without delaying the entire project
1.
21
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path

Activity times are represented in the nodes
ACTIVITY
ES
LS
t
EF
LF
• Earliest times are computed as
Earliest finish time = Earliest start time
+ Expected activity time
EF = ES + t
Earliest start = Largest of the earliest finish times of
immediate predecessors
ES = Largest EF of immediate predecessors
22
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path


At the start of the project we set the time to zero
Thus ES = 0 for both A and B
A
ES = 0
t=2
EF = 0 + 2 = 2
B
ES = 0
t=3
EF = 0 + 3 = 3
Start
23
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path
FIGURE 11.4 – General Foundry’s Earliest Start (ES) and Earliest Finish (EF) Times
A
2
C
2
F
3
0
2
2
4
4
7
Start
E
4
H
2
4
8
13
15
B
3
D
4
G
5
0
3
3
7
8
13
Finish
24
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path
FIGURE 11.4 – General Foundry’s Earliest Start (ES) and Earliest Finish (EF) Times
Use a forward pass
through the network
A
2
C
2
F
3
0
2
2
4
4
7
Start
E
4
H
2
4
8
13
15
B
3
D
4
G
5
0
3
3
7
8
13
Finish
25
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path

Compute latest start (LS) and latest finish (LF) times for
each activity by making a backward pass through the
network
Latest start time = Latest finish time
– Expected activity time
LS = LF – t
Latest finish time = Smallest of latest start times
for following activities
LF = Smallest LS of following activities
For activity H
LS = LF – t = 15 – 2 = 13 weeks
26
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path
FIGURE 11.5 – General Foundry’s Latest Start (LS) and Latest Finish (LF) Times
A
2
C
2
F
3
0
2
2
4
4
7
0
2
2
4
10
13
Start
E
4
H
2
4
8
13
15
4
8
13
15
B
3
D
4
G
5
0
3
3
7
8
13
1
4
4
8
8
13
Finish
27
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path

Once ES, LS, EF, and LF have been determined, find the
amount of slack time for each activity
Slack = LS – ES, or Slack = LF – EF




Activities A, C, E, G, and H have no slack time
These are called critical activities and they are said to be on
the critical path
The total project completion time is 15 weeks
Industrial managers call this a boundary timetable
28
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path
TABLE 11.3 – General Foundry’s Schedule and Slack Times
ACTIVITY
EARLIEST
START,
ES
EARLIEST
FINISH,
EF
LATEST
START,
LS
LATEST
FINISH,
LF
SLACK,
LS – ES
ON
CRITICAL
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
29
Management Decision Modeling
Chapter 11. Project Management
How to Find the Critical Path
FIGURE 11.6 – General Foundry’s Critical Path (A–C–E–G–H)
A
2
C
2
F
3
0
2
2
4
4
7
0
2
2
4
10
13
Start
E
4
H
2
4
8
13
15
4
8
13
15
B
3
D
4
G
5
0
3
3
7
8
13
1
4
4
8
8
13
Finish
30
Management Decision Modeling
Chapter 11. Project Management
Probability of Project Completion

The critical path analysis helped determine the
expected project completion time of 15 weeks
 Variation
in activities on the critical path can affect
overall project completion
 If the project is not complete in 16 weeks, the foundry
will have to close

PERT uses the variance of critical path activities
to help determine the variance of the overall
project
Project variance =

variances of activities
on the critical path
31
Management Decision Modeling
Chapter 11. Project Management
Probability of Project Completion

From Table 11.2 we know
ACTIVITY
A
C
E
G
H
VARIANCE
4/36
4/36
36/36
64/36
4/36
• Hence, the project variance is
Project variance = 4/36 + 4/36 + 36/36 + 64/36 + 4/36 = 112/36 = 3.111
32
Management Decision Modeling
Chapter 11. Project Management
Probability of Project Completion

We know the standard deviation is the square root of the
variance, so
Project standard deviation = s T = Project variance
= 3.111 = 1.76 weeks
• We assume activity times are independent and that
total project completion time is normally distributed
• A bell-shaped curve can be used to represent project
completion dates
33
Management Decision Modeling
Chapter 11. Project Management
Probability of Project Completion
FIGURE 11.7 – Probability Distribution for Project Completion Times
Standard Deviation = 1.76 Weeks
15 Weeks
Expected Completion Time
34
Management Decision Modeling
Chapter 11. Project Management
Probability of Project Completion
FIGURE 11.8 – Probability of General Foundry’s Meeting the 16-Week Deadline
Expected Time is 15 Weeks
0.57 Standard Deviations
Excel QM
Probability
(T ≤ 16 Weeks)
Is 71.6%
Compute probs given cutoffs – 1 tailed
Parameter
Value
Mean
15
Standard deviation
1.76
Cutoff
16
Results
Probability to the left of the tail
Probability to the right of the tail
15
Weeks
16
Weeks
0.715044
0.284956
Time
35
Management Decision Modeling
Chapter 11. Project Management
What PERT Was Able to Provide
1.
2.
3.
4.
5.
The project’s expected completion date is 15 weeks
There is a 71.6% chance that the equipment will be in
place within the 16-week deadline
Five activities (A, C, E, G, H) are on the critical path
Three activities (B, D, F) are not critical but have some
slack time built in
A detailed schedule of activity starting and ending dates
has been made available
36
Management Decision Modeling
Chapter 11. Project Management
Using Excel QM
PROGRAM 11.1A –
Probability of General
Foundry’s Meeting the
16-Week Deadline
37
Management Decision Modeling
Chapter 11. Project Management
Using Excel QM
PROGRAM 11.1B –
Excel QM Input
Screen and Solution
for General Foundry
Example with
3 Time Estimates
38
Management Decision Modeling
Chapter 11. Project Management
Sensitivity Analysis and
Project Management

The time required to complete an activity can
vary from the projected or expected time
 If
the activity is on the critical path, the completion
time of the project will change
 This will also have an impact on ES, EF, LS, and LF
times for other activities
 Exact impact depends on the relationship between
the various activities
39
Management Decision Modeling
Chapter 11. Project Management
Sensitivity Analysis and
Project Management



A predecessor activity is one that must be
accomplished before the given activity can be
started
A successor activity is one that can be started
only after the given activity is finished
A parallel activity is one that does not directly
depend on the given activity
 Once
these have been defined, we can explore the
impact that an increase (decrease) in an activity time
for a critical path activity would have on other
40
activities in the network
Management Decision Modeling
Chapter 11. Project Management
Sensitivity Analysis and Project
Management
TABLE 11.4 – Impact of an Increase (Decrease) in an Activity Time for a Critical Path Activity
ACTIVITY TIME
SUCCESSOR
ACTIVITY
PARALLEL
ACTIVITY
PREDECESSOR
ACTIVITY
Earliest start
Increase (decrease)
No change
No change
Earliest finish
Increase (decrease)
No change
No change
Latest start
Increase (decrease)
Increase (decrease)
No change
Latest finish
Increase (decrease)
Increase (decrease)
No change
Slack
No change
Increase (decrease)
No change
41
Management Decision Modeling
Chapter 11. Project Management
PERT/COST


PERT is an excellent method of monitoring and
controlling project length but it does not consider
the very important factor of project cost
PERT/Cost is a modification of PERT that allows
a manager to plan, schedule, monitor, and
control cost as well as time
42
Management Decision Modeling
Chapter 11. Project Management
Four Steps of the Budgeting Process
1.
2.
Identify all costs associated with each of the activities.
Then add these costs together to get one estimated
cost or budget for each activity.
If you are dealing with a large project, several activities
can be combined into larger work packages. A work
package is simply a logical collection of activities. Since
the General Foundry project we have been discussing
is small, each activity will be a work package.
43
Management Decision Modeling
Chapter 11. Project Management
Four Steps of the Budgeting Process
3.
4.
Convert the budgeted cost per activity into a cost per
time period. To do this, we assume that the cost of
completing any activity is spent at a uniform rate over
time. Thus, if the budgeted cost for a given activity is
$48,000 and the activity’s expected time is four weeks,
the budgeted cost per week is $12,000
(=$48,000/4 weeks).
Using the earliest and latest start times, find out how
much money should be spent during each week or
month to finish the project by the date desired.
44
Management Decision Modeling
Chapter 11. Project Management
Budgeting for General Foundry

The Gantt chart below illustrates this process
Determine how much will be spent on each activity
during each week and fill these amounts into a chart in
place of the bars
A
FIGURE 11.9 – Gantt Chart for General Foundry Example
B
C
Activity

D
E
F
G
H
1
2
3
4
5
6
7
8
Week
9
10
11
12
13
14
15
45
Management Decision Modeling
Chapter 11. Project Management
Budgeting for General Foundry
TABLE 11.5 – Activity Cost for General Foundry, Inc.
ACTIVITY
EARLIEST
START,
ES
LATEST
START,
LS
EXPECTED
TIME, t
TOTAL
BUDGETED
COST ($)
BUDGETED
COST PER
WEEK ($)
A
0

0
2
22,000
11,000
B
0
1
3
30,000
10,000
C
2
2
2
26,000
13,000
D
3
4
4
48,000
12,000
E
4
4
4
56,000
14,000
F
4
10
3
30,000
10,000
G
8
8
5
80,000
16,000
H
13
13
2
16,000
8,000
T …
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