Download Project Management Overview

Project Management
presented by
Miles Hamby, PhD
Copyright©2012 Miles M. Hamby
1
Topics
• The Nature of Project Management
• The Elements of Project Management
• The Project Proposal Document
• SOW, OBS, RAM, CPM/PERT Networks
• Weighted Average & Probabilistic Activity Times
• Cost-Benefit and Earned Value Analysis
• Project Costs & Project Crashing
• Using Excel to create Gantt charts
2
Nature of
Project Management
3
Nature of Project Management
What is a project?
 Unique (one-time effort)
 Fixed duration
 Specific goal
4
The Project Team
 Includes engineers, line workers, HR personnel, budget
experts, technical experts, outside consultants
 Headed by the Project Manager
• Must coordinate various skills of team members into
single, focused effort
• Great pressure due to uncertainty inherent in project
schedule, budget, and quality.
5
Nature of Project Management
Why manage a project?
Murphy’s Law
If anything can go wrong – it will!
• Complete on-time
• In budget
• Meet expectations (quality)
6
Nature of Project Management
 Controlling an activity for a relatively short period of time
until project is completed, then operations begin.
 Project manager not involved in operations.
 3 components of PM:
• Planning
• Scheduling
• Controlling individual activities.
7
The Project Management Process
PLANNING
SCHEDULING
CONTROLLING
ON TIME
PERT/CPM
SOW
2
5
6
START
FINISH
1
4
3
OBS
IN BUDGET
GANTT
PM
Bull Run Defenses
11
10
HR
Design
9
Const
8
Activity
7
6
5
4
3
Move Eng Div
receive orders
Activity
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Days
RESOURCES
RAM
TASK
HR
DESIGN
CONST
1
O.P
S
S
2
S
P
O
3
P
O
S
MEETS
EXPECTATIONS
8
Project Control
 Process of ensuring progress toward successful completion ~
on time, in budget, meet expectations.
 Monitoring project to minimize deviations from project plan and
schedule.
 Corrective actions necessary if deviations occur.
 Key elements of project control
• Time management
• Cost management
• Performance management
• Earned value analysis.
9
The Project Planning Document
- a document for the customer,
individuals, team members, groups,
departments, subcontractors and
suppliers, describing what is required
for successful completion - on time, in
budget, meet expectations.
10
The Project Planning Document













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Cover page
TOC
SOW and Scope
OBS
RAM
Work Breakdown Schedule (WBS)
PERT/CPM – AON diagram & Gantt Chart
Budgeting
Resources (Human and Materials)
Technology
Cost-Benefit and Earned Value Analysis (EVA)
Execution and Control Plan (Quality Assurance)
Protection of the Environment
Risk Assessment and Management
11
SOW and Scope
 Statement of Work (SOW) – statement of work to
be performed, justification describing the factors
giving rise to need for project, expected duration
(on time), total cost (budget), and performance
standards (meeting expectations).
 Scope – identification of boundaries and
limitations on specific aspects of the project,
including size, resources, work to be performed
and performance standards
12
Organizational Breakdown Structure (OBS)
Wilson Bridge Renovation Project
Acme Construction Company
Organization Breakdown Structure (OBS)
Project Manager
Bob Smith
Design Manager
Jane Doe
Construction Mgr
Bill Jones
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
(Tasking)
Electrical Mgr
Rene Flemming
Resources Mgr
John Henry
13
Responsibility Assignment Matrix (RAM)

OBS leads to the responsibility assignment matrix (RAM)

RAM is a table or a chart showing which organizational
units are responsible for work items.

Project Manager assigns work elements to organizational
units, departments, groups, individuals or subcontractors.

RAM shows who is responsible for oversight (O),
performance (P), and support (S) of each task
14
Responsibility Assignment Matrix (RAM)
ACME Construction Company
Wilson Bridge Renovation
Responsibility Assignment Matrix (RAM)
Key: O = Oversight, P = Performance, S = Support
Activity
1 – Design
2 - Acquire materials
OBS Unit
Design
Construction
O, P
S
S
3 - Prepare foundation
4 - Set piles
Electrical
O, P
O, P
S
Resources
S
S
O, P
5 - Construct piers
P
6 - Construct roadway
P
15
Activity Scheduling
 Project Schedule evolves from planning documents, with focus
on timely completion.
 Scheduling is the source of most conflicts and problems.
 Schedule development steps:
1. Define activities
2. Sequence activities
3. Estimate activity times
4. Construct schedule.
 Gantt chart and CPM/PERT techniques used.
 Computer software packages available, e.g. Microsoft Project.
16
Work Breakdown Schedule (WBS)
 Basis for project development, management ,
schedule, resources and modifications.
 WBS breaks down project into major modules.
 Modules are further broken down into activities
and, finally, into individual tasks.
 Identifies activities, tasks, resource requirements
and relationships between modules and
activities.
17
Work Breakdown Structure (WBS)
ACME Construction Company
Wilson Bridge Renovation
Activity Schedule
ACTVITY
PREDESSOR
EARLY START
DURATION (months)
1 – Design
--
0
14
2 - Acquire materials
1
6
1
3 - Prepare foundation
1
12
1
4 - Set piles
3
14
3
5 - Construct piers
4
20
8
6 - Construct roadway
5
28
4
18
CPM/PERT
CPM – Critical Path Method
PERT – Project Evaluation and Review Technique
AON – Activity on Node
19
CPM/PERT – Activity on Node
Activity-on-Node (AON) Network
 A node represents the beginning and end of activities,
referred to as events.
 Each node depicts ID and duration (often more info)
 Branches in the network indicate precedence relationships.
 When an activity is completed at a node, it has been
realized.
WILSON
BRIDGE
Project
-- / B / -4.8 GET MATERIALS
-- / 3 / --
0
/ A / -PLAN & DESIGN
0 / 14 /
--/ D / -0 SINK PILINGS
-- / 8 / --
21.2 / E / 24.2
2 LAY SPAN
-- / 3 / --
-- / F / -0 FINISH
ROADBED
--/ 3 / --
-- / C / -1 CONSTRUCT APP
-- / 7 / --
20
AON Concurrent Activities
 Activities can occur at the same time (concurrently).
 A dummy activity shows a precedence relationship but
reflects no passage of time.
 Two or more activities cannot share the same start and end
nodes.
WILSON
BRIDGE
Project
0
/ A / 14
0 PLAN & DESIGN
0 / 14 / 14
14 / B / 17
5 GET MATERIALS
19 / 3 / 22
14 / D / 22
0 SINK PILINGS
14 / 8 / 22
22 / E / 25
0 LAY SPAN
22 / 3 / 25
25 / F / 28
0 FINISH ROADBED
25 / 3 / 28
14 / C / 21
1 CONSTRUCT APP
15/ 7 / 22
21
The Critical Path Method (CPM)
 The critical path is the longest path through the network; the
minimum time the network can be completed
Path A:
AB E F
14 + 1 + 8 + 4 = 27 months
Path B:
ACEF
14 + 1 + 8 + 4 = 27 months
Path C:
ADEF
14 + 3 + 8 + 4 = 29 months  Critical Path
22
Activity Early Start Schedule
(for Gantt Chart)
ACME Construction Company
Wilson Bridge Renovation
Activity Schedule
ACTVITY
PREDESSOR
EARLY START
DURATION (months)
1 – Design
--
0
14
2 - Acquire materials
1
6
1
3 - Prepare foundation
1
12
1
4 - Set piles
3
14
3
5 - Construct piers
4
20
8
6 - Construct roadway
5
28
4
23
Gantt Chart
 Bar chart developed by Henry Gantt (1914).
 A visual display of project schedule showing activity
start and finish times and where extra time is
available.
 Based on Early Start of activities – order, duration,
predecessors
 Drawback: precedence relationships are not always
discernible.
24
Gantt Chart for Wilson Bridge Project
Wilson Bridge Renovation Gantt Chart
Duration (months)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1 Design
Activity
2 Acquire materials
3 Prepare foundation
4 Set piles
5 Construct piers
6 Construct roadway
25
AON Earliest/Latest Times Configuration
ES
Earliest Start
Activity
0
Slack
9
12 RECRUITING
2
LS
Latest Start
/ A /
EF
Earliest Finish
/ 9 /
Duration
11
LF
Latest Finish
26

AON Earliest/Latest Times Configuration
 ES: Earliest an activity can start
 EF: ES + duration
 LF: Latest time an activity can finish
 LS: LF – duration
 Slack: LS - ES
0
/ A /
9
12 RECRUITING
12
/ 9 /
11
27
Activity Schedule
Wilson Bridge Project
Task
DUR
ES
EF
LS
LF
Slack
A
13
0
13
0
13
0
B
3
13
16
18
21
13
C
7
13
20
20
27
7
D
8
13
21
13
22
0
E
3
21
24
21
24
2
F
2
24
27
24
27
0
*Critical Activities
28
AON Diagram for Wilson Bridge
WILSON BRIDGE
/ A /
/
B / 15
2 GET MATERIALS
Project
0
14
16
14
14 /
/ 1 / 17
D / 15
17 /
E / 25
0 PLAN & DESIGN
2 SINK PILINGS
0 LAY SPAN
0 / 14 / 14
16 / 1 / 17
17 / 8 / 25
14 /
25
/
F / 29
0 FINISH ROADBED
25 /
4
/ 29
C / 17
0 CONSTRUCT APP
14 / 3 / 17
29
Weighted Average
&
Probabilistic Activity Times
30
Weighted Average
ACME Computer Network Project
Work Breakdown Structure (WBS)
Activity
Optimistic
(a)
Most
Probable
(m)
Pessimistic
(b)
A – Recruiting
6
8
10
B – Development
3
6
9
C – System Training
1
3
5
D – System Training
2
4
12
E – Equipment Test
2
3
4
F – System Test
3
4
5
G – Equipment Mod
2
2
2
H – System Debug
3
I – Equipment Change
2
4
6
J – Pre-interface
1
4
7
K – Interface
1
10
13
Weighted
Mean Time
(t)
Variance
(v)
11
31
Probabilistic Activity Times
 Activity time estimates usually cannot be made with
certainty.
 PERT used for probabilistic activity duration times.
 In PERT, three time estimates are used: most likely time
(m), the optimistic time (a) , and the pessimistic time (b).
 These provide an estimate of the mean and variance of a
beta distribution:
• Weighted Mean (expected time):t  Op  4*MP  Ps
6

2
• Variance: v   Ps - Op 

6 

32
WBS – Computer Network Example
Computer Network Project Work Breakdown Structure (WBS)
Activity
Optimistic
(a)
Most
Probable
(m)
Pessimistic
(b)
Weighted
Mean Time
(t)
Variance
(v)
A – Equipment Installation
6
8
10
8
.44 (4/9)
B – System Development
3
6
9
6
1
C – Position Recruiting
1
3
5
3
.44 (4/9)
D – Equip testing & Mod
2
4
12
5
2.78 (25/9)
E – Manual Testing
2
3
4
3
.11 (1/9)
F – Job Training
3
4
5
4
.11 (1/9)
G – Orientation
2
2
2
2
1.78 (0)
H – System training
3
11
7
2.11 (16/9)
I – System Testing
2
4
6
4
.44 (4/9)
J – Final Debugging
1
4
7
4
1 (9/9)
K – System Changeover
1
10
13
9
4 (36/9)
33
AON – Computer Network Example
0/A/9
2.8 RECRUTING
2.8/8/11.8
ACME CORP
Computer Network
Activity on Node
0/C/9
2.8 RECRUTING
2.8/3/11.8
0/D/9
2.8 34
RECRUTING
2.8/5/11.8
0/J/9
2.8 RECRUTING
2.8/4/11.8
0/K/9
2.8 RECRUTING
2.8/9/11.8
START
0/E/9
2.8 RECRUTING
2.8/3/11.8
0/B/9
2.8 RECRUTING
2.8/6/11.8
LEGEND
ES’/A/EF
Sl ECRUTING
LS/Dur/LF
0/F/9
2.8 RECRUTING
2.8/4/11.8
0/G/9
2.8 RECRUTING
2.8/2/11.8
0/H/9
2.8 RECRUTING
2.8/7/11.8
0/I/9
2.8 RECRUTING
2.8/4/11.8
FINISH
Critical Path for Computer Network Example
Critical Path is the path with the longest mean time and is also
the Expected Time to Completion (ETC)
Path
Mean Times
ADJ
8 + 5 + 4 = 17 weeks
BEH
6 + 3 + 7 = 16 weeks
BEIK
6 + 3 + 4 + 9 = 22 weeks CPM
CFH
CEIK
3 + 4 + 7 = 14 weeks
3 + 4 + 4 + 9 = 20 weeks
CGK
3 + 2 + 9 = 14 weeks
35
ETC and Variance
The Project Variance (vp) is the sum of the variances of the
critical path activities.
Critical Path:
BEIK
Project time:
6+ 3 + 4 + 9
Variance:
=
22 weeks
.44 + .11 + 2.11 + 4 = 7.22 weeks
Standard Deviation: Sqrt of Variance = 2.69
36
Probability Analysis of a Project Network
 ETC is assumed to be normally distributed (based on central
limit theorem).
 As such, the ETC and variance (vp) are interpreted as the
mean () and variance (2) of a normal distribution
Project time: 6+3+4+9 = 22 weeks
Variance: .44+.11+2.11+4 = 7.22 weeks
Std Dev: Sqrt 7.22 = 2.69
-3 = 13.93 weeks
 = 22 weeks
3 = 30.07 weeks
Time (Weighted Average Duration)
37
Probability Analysis of a Project Network
Example 1
From Computer Network example:
Critical Path:
2  5  9  11
Project time:
Variance:
6+ 3+ 4+
9 = 22 weeks
.44 + .11 + 2.11 + 4 = 7.22 weeks
What is the probability that the new order processing system
will be ready in 20 weeks?
µ = 22 weeks
2 = 7.22, therefore,  = 2.69 weeks
Z = (x-)/  = (20 - 22)/2.69 = -.74
38
Table of Areas (p-values)
+/- Z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
0.00
0.0000
0.0398
0.0793
0.1179
0.1554
0.1915
0.2257
0.2580
0.2881
0.3159
0.3413
0.3643
0.3849
0.4032
0.4192
0.4332
0.4452
0.4554
0.4641
0.4713
0.4772
0.4821
0.4861
0.4893
0.4918
0.4938
0.4953
0.4965
0.4974
0.4981
0.4987
0.01
0.0040
0.0438
0.0832
0.1217
0.1591
0.1950
0.2291
0.2611
0.2910
0.3186
0.3483
0.3665
0.3869
0.4049
0.4207
0.4345
0.4463
0.4564
0.4649
0.4719
0.4778
0.4826
0.4864
0.4896
0.4920
0.4940
0.4955
0.4966
0.4975
0.4982
0.4987
0.02
0.0080
0.0478
0.0871
0.1255
0.1628
0.1985
0.2324
0.2642
0.2939
0.3212
0.3461
0.3686
0.3888
0.4066
0.4222
0.4357
0.4474
0.4573
0.4656
0.4726
0.4783
0.4830
0.4868
0.4898
0.4922
0.4941
0.4956
0.4967
0.4976
0.4982
0.4987
0.03
0.0120
0.0517
0.0910
0.1293
0.1664
0.2090
0.2357
0.2673
0.2967
0.3238
0.3485
0.3708
0.3907
0.4082
0.4236
0.4370
0.4484
0.4582
0.4664
0.4732
0.4788
0.4834
0.4871
0.4901
0.4925
0.4943
0.4957
0.4968
0.4977
0.4983
0.4988
0.04
0.0160
0.0557
0.0948
0.1331
0.1700
0.2054
0.2389
0.2704
0.2995
0.3264
0.3508
0.3729
0.3925
0.4099
0.4251
0.4382
0.4495
0.4591
0.4671
0.4738
0.4793
0.4838
0.4875
0.4904
0.4927
04945
0.4959
0.4969
0.4977
0.4984
0.4988
0.05
0.0199
0.0596
0.0987
0.1368
0.1736
0.2088
0.2422
0.2734
0.3023
0.3289
0.3531
0.3749
0.3944
0.4115
0.4265
0.4394
0.4505
0.4599
0.4678
0.4744
0.4798
0.4842
0.4878
0.4906
0.4929
0.4946
0.4960
0.4970
0.4978
0.4984
0.4989
0.06
0.0239
0.0636
0.1026
0.1406
0.1772
0.2123
0.2454
0.2764
0.3051
0.3315
0.3554
0.3770
0.3962
0.4131
0.4279
0.4406
0.4515
0.4608
0.4686
0.4750
0.4803
0.4846
0.4881
0.4909
0.4931
0.4948
0.4961
0.4971
0.4979
0.4985
0.4989
0.07
0.0279
0.0675
0.1064
0.1413
0.1808
0.2157
0.2486
0.2794
0.3078
0.3340
0.3577
0.3790
0.3980
0.4147
0.4292
0.4418
0.4525
0.4616
0.4693
0.4756
0.4808
0.4850
0.4884
0.4911
0.4932
0.4949
0.4962
0.4972
0.4979
0.4985
0.4989
0.08
0.0319
0.0714
0.1103
0.1480
0.1844
0.2190
0.2517
0.2823
0.3106
0.3365
0.3599
0.3810
0.3997
0.4162
0.4306
0.4429
0.4535
0.4625
0.4699
0.4761
0.4812
0.4854
0.4887
0.4913
0.4934
0.4951
0.4963
0.4973
0.4980
0.4986
0.4990
0.09
0.0359
0.0753
0.1141
0.1517
0.1879
0.2224
0.2549
0.2850
0.3133
0.3389
0.3621
0.3830
0.4015
0.4177
0.4319
0.4441
0.4545
0.4633
0.4706
0.4767
0.4817
0.4857
0.4890
0.4916
0.4936
0.4952
0.4964
0.4974
0.4981
0.4986
0.4990
39
Probability Analysis of a Project Network
Z value of -.74 corresponds to probability of .2704 (table of
areas under the curve). Therefore, the probability of
completing the project in 20 weeks is .5000 - .2704 = .2296.
Z=
x-µ

=
20 - 22
2.69
P = .2704
.5 - .2704 = .2296
Z= -.74 (20 weeks)
 = 22 weeks
Time (Duration)
40
Cost – Benefit Analysis
41
Cost – Benefit Analysis
Given an amount of capital to invest, what is the
cost and what is the benefit?
• Project Owner’s perspective ~ is the project
worth doing, or do we invest in something
else, like another project or the market?
• Project Manager’s perspective ~ what do I do
with money waiting to be spent on the project
– keep it in the bank, or invest it?
42
Cost - Benefit
Project – replace old computerized production
control system for an auto assembly plant
• The project will cost $3M over 3 years and
save $7M over 10 years
• However, if we invest $3M over ten years, we
make $8M, but lose $5M in extra costs from
the outdated system
ITEM
BENEFIT
($M)
COST
($M)
GAIN or (LOSS)
(Benefit-Cost)
New
System
7 (in savings)
3 (install new system)
4
Old
System
8 (from investment)
5 (using old system)
3
43
Earned Value Analysis (EVA)
Measures progress of a project in terms of:
•
Planned Value (PV) or Budgeted Cost Work
Scheduled (BCWS) – what is supposed to be done
•
Earned Value (EV) or Budgeted Cost, Work
Performed (BCWP) – what has actually been done
•
Actual Cost (AC) or Work Performed (ACWP) –
actual labor and materials expended
44
Earned Value - Example
Project: Build a deck
PV: 40 labor-hours x $20/hr = $800
+ $600 materials
$1,400 PV (BCWS)
Changes after work begun: Labor rate now $22/hr,
materials price increase to $700, project only 95%
completed after 40 hours
EV: 95% completed x $1,400 = $1,330 EV(BCWP)
AC:
40 hrs x $22/hr = $880 labor
+ 700 materials
$1,580 AC (ACWP)
45
Earned Value
Should be proportionate to project time
Project Time
Monitoring Schedule
1 week
1 month
6 months
> 6 months
Daily
Twice weekly
Weekly
Monthly
46
Project Costs
&
Project Crashing
47
Project Crashing and Time-Cost Trade-Off
 Project crashing is a method for shortening project duration
by reducing one or more critical activities to a time less than
normal activity time.
 Achieved by devoting more resources to ‘crashed’
(compressed) activities
 However, total cost of project will increase.
 Crashing cost – original cost plus cost of additional
resources
 Decision to crash is based on analysis of trade-off between
time and cost.
48
Project Crashing
 Project crashing costs and indirect costs have an
inverse relationship.
 Indirect costs decrease as the project duration
crashes (decreases) while Direct costs increase.
 Optimal project time is at minimum point on the
total cost curve.
49
Optimum Time-Cost Trade-Off
Optimum project Time is
at minimum Total Cost
$
TIME
Crash
Cost
– Time
Tradeoff
Crash
Cost
per Unit
of Time Saved
Project crash cost is
Activity
Planned
Duration
Crash
Time
Planned
Cost
Crash
Cost
Time
Saved
(weeks)
Crash Cost
per Week
(*Crit. Path)
(weeks)
(weeks)
1*
12
7
$3,000
$5,000
5
$400
2*
8
5
2,000
3,500
3
500
3
4
3
4,000
7,000
1
3,000
4*
12
9
50,000
71,000
3
7,000
5
4
1
500
1,100
3
200
6
4
1
500
1,100
3
200
7*
4
3
15,000
22,000
3
7,000
TOTAL
69
75,000
108,700
21
(Crash CostPlanned
Cost/Time Saved)
51
Project Cost
 Each activity incurs a cost.
 Project cost is total of costs of all activities
$3000
$2000
Project Activity Costs
2
8
Total Cost = $75,000
$50,000
4
12
1
12
$4000
3
4
$15,000
$500
5
4
$500
7
12
6
4
52
Project Cost
 Each activity incurs a cost.
 Project cost is total of costs of all activities
$2000
$3000
2
8
Project Activity Costs
$50,000
4
12
1
12
$4000
3
4
$15,000
$500
5
4
$500
7
4
6
4
53
Project Cost
Depending on which Critical Path activities are crashed,
a new Critical Path could emerge
$2000
$3000
2
8
Project Activity Costs
$50,000
4
12>9
1
12
$4000
3
4
$500
5
4
$15,000
$500
7
4
6
4
54
End
55
PERT/CPM
on
MS Project™ 2003
56
Analysis with Microsoft Project (1 of 13)
Microsoft Project handles only AON networks.
57
Analysis with Microsoft Project
(2 of 13)
58
Analysis with Microsoft Project (3 of 13)
59
Analysis with Microsoft Project (4 of 13)
Exhibit 8.6
60
Analysis with Microsoft Project (5 of 13)
Figure 8.7
61
Analysis with Microsoft Project (6 of 13)
62
Analysis with Microsoft Project (7 of 13)
Exhibit 8.9
63
Analysis with Microsoft Project (8 of 13)
64
Analysis with Microsoft Project (9 of 13)
Exhibit 8.11
65
Analysis with Microsoft Project (10 of 13)
Figure 8.12
66
Analysis with Microsoft Project (11 of 13)
67
Analysis with Microsoft Project (12 of 13)
Exhibit 8.14
68
Analysis with Microsoft Project (13 of 13)
Exhibit 8.15
69
Formulating PERT/CPM
as a
Linear Programming Model
70
Linear Programming Model
The objective is to minimize the project duration (i.e., the
critical path time).
General linear programming model with AOA convention:
Minimize Z = xi
i
subject to:
xj - xi  tij for all activities i  j
xi, xj  0
Where:
xi = earliest event time of node i
xj = earliest event time of node j
tij = time of activity i  j
71
Project Crashing with QM for Windows
Exhibit 8.16
72
The CPM/PERT Network
Example Problem Formulation and Data (1 of 2)
Figure 8.24
CPM/PERT Network for the House-Building Project with Earliest Event Times
73
The CPM/PERT Network
Example Problem Formulation and Data (2 of 2)
Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7
subject to:
x2 - x1  12
x3 - x2  8
x4 - x2  4
x4 - x3  0
x5 - x4  4
x6 - x4  12
x6 - x5  4
x7 - x6  4
x i, x j  0
74
The CPM/PERT Network
Example Problem Solution with Excel (1 of 4)
B6:B12
Exhibit 8.17
75
The CPM/PERT Network
Example Problem Solution with Excel Solver
Exhibit 8.18
76
The CPM/PERT Network
Example Problem Solution with Excel Solver
Exhibit 8.19
77
The CPM/PERT Network
Example Problem Solution with Excel Solver
Exhibit 8.20
78
Project Crashing with Linear Programming
Example Problem – Model Formulation
 Objective is to minimize the cost of crashing
xi = earliest event time of node I
xj = earliest event time of node j
yij = amount of time by which activity i  j is crashed
Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46
+ 200y56 + 7000y67
subject to:
y12  5
y23  3
y24  1
y34  0
y45  3
y46  3
y56  3
y67  1
y12 + x2 - x1  12
y23 + x3 - x2  8
y24 + x4 - x2  4
y34 + x4 - x3  0
y45 + x5 - x4  4
y46 + x6 - x4  12
y56 + x6 - x5  4
x67 + x7 - x6  4
x7  30
xi, yij ≥ 0
79
Project Crashing with Linear Programming
Excel Solution (1 of 3)
Exhibit 8.21
80
Project Crashing with Linear Programming
Excel Solver (2 of 3)
Exhibit 8.12
81
CPM/PERT Analysis with QM for Windows & Excel QM (1 of 2)
82
CPM/PERT Analysis with QM for Windows & Excel QM (2 of 2)
Exhibit 8.1
83
Project Crashing with Linear Programming
Excel Solver (3 of 3)
Exhibit 8.23
84
Project Crashing and Time-Cost Trade-Off
Example Problem (2 of 5)
Crash cost and
crash time have
linear relationship:
total crash
cost/total crash
time = $2000/5
= $400/wk
Figure 8.20
Time-Cost Relationship for Crashing Activity 1
85
House Building Project Example
No.
Activity
Predecessor
Duration (Months)
1. Design house and
obtain financing
-
3
2. Lay foundation
1
2
3. Order Materials
1
1
4. Build house
2, 3
3
5. Select paint
2, 3
1
5
1
4, 6
1
6. Select carpet
7. Finish work
86
Project Crashing and Time-Cost Trade-Off
Normal Activity Times and Activity Crashing Costs
87
Project Crashing and Time-Cost Trade-Off
Example Problem (5 of 5)
As activities are crashed, the critical path may change and
several paths may become critical.
Figure 8.22
Revised Network with Activity 1 Crashed
88