1. Dr. Ron Lembke Operations Management
Project Management
Dr. Ron Lembke
Operations Management

2. What’s a Project?
Changing something from the way it is to the desired state
Never done one exactly like this
Many related activities
Focus on the outcome
Regular teamwork focuses on the work process

3. Examples of Projects Building construction New product introduction
Software implementation
Training seminar
Research project

4. Why are projects hard? Resources- Planning People, materials
What needs to be done?
How long will it take?
What sequence?
Keeping track of who is supposedly doing what, and getting them to do it

5. IT Projects Half finish late and over budget
Nearly a third are abandoned before completion
The Standish Group, in Infoworld
Get & keep users involved & informed
Watch for scope creep / feature creep

6. Project Scheduling Establishing objectives
Determining available resources
Sequencing activities
Identifying precedence relationships
Determining activity times & costs
Estimating material & worker requirements
Determining critical activities

7. PERT & CPM Network techniques Developed in 1950’s
CPM by DuPont for chemical plants
PERT by U.S. Navy for Polaris missile
Consider precedence relationships & interdependencies
Each uses a different estimate of activity times

8. Questions Answered by PERT & CPM
Completion date?
On schedule? Within budget?
Probability of completing by ...?
Critical activities?
Enough resources available?
How can the project be finished early at the least cost?

9. PERT & CPM Steps Identify activities Determine sequence Create network
Determine activity times
Find critical path
Earliest & latest start times
Earliest & latest finish times
Slack

10. 3 1 2 Activity on Node (AoN) Project: Obtain a college degree (B.S.)
Attend class, study etc.
Receive diploma
Enroll 3 1 2
1 month
4? Years
1 day

11. 1 2 3 4 Activity on Arc (AoA) Project: Obtain a college degree (B.S.)
Attend class, study, etc.
Receive diploma
Enroll 1 2 3 4
1 month
4,5 ? Years
1 day

12. 1 2 3 4 AoA Nodes have meaning Project: Obtain a college degree (B.S.)
GraduatingSenior
Aluma
Alumnus
Applicant
Student

13. Precedence Relationships – Scenario 1a
Hierarchy of what needs to be done, in what order
Time required for each thing
For me, the hardest part
I’ve never done this before. How do I know what I’ll do when and how long it’ll take?
I think in phases
The farther ahead in time, the less detailed
Figure out the tricky issues, the rest is details
A lot will happen between now and then
It works not badly with no deadline

14. Precedence Relationships

15. Mudroom

16. Mudroom Remodel Big-picture sequence easy: Hard: can a sink fit?
Before:
Big-picture sequence easy:
Demolition
Framing
Plumbing
Electrical
Drywall, tape & texture
Slate flooring
Cabinets, lights, paint
Hard: can a sink fit? D W
After: D W

18. Project Scheduling Techniques
Gantt chart
Critical Path Method (CPM)
Program Evaluation & Review Technique (PERT)

19. Gantt Chart

22. What do these 3 guys have in common?
Day before Thanksgiving, 2015, late afternoon, 27ºF

23. Network Example
You’re a project manager for Bechtel. Construct the network.
Activity Predecessors A -- B A C A D B E B F C G D H E, F

24. Network Example - AON D G B A E Z C H F

25. Network Example - AON F H C A E Z B G D

26. Network Example - AON E H C G A Z F B D

27. Network Example - AOA D G 3 6 8 B E A 1 2 5 H 7 9 C F 4

28. AOA Diagrams
A precedes B and C, B and C precede D B A 1 2 3 D 4 C 3 B A 1 2 C 4 D 5
Add a phantom arc for clarity.

29. Scenario 1a
Task Description Days Pred A Drawings 1 -- B Get & Dye fabric 3 -- C Build stage 4 A D Sew fabric, frame back 2 B E Rent, deliver, hang lights 1 A F Paint stage 2 C G Test assembly 1 D,F H disassemble, deliver 1 G I Assemble, touch-up 1 E,H

30. Scenario 1a Network DiagramF 2
Finish
START C 4 B 3 H 1 G 1 D 2 3

31. Scenario 1a Longest Path
Paths: Days
AEI 3
ACFGHI 10
BDGHI 8
START A 1 B 3 E C 4 D 2 F G H I
Finish 3

32. Critical Path Analysis
Provides activity information
Earliest (ES) & latest (LS) start
Earliest (EF) & latest (LF) finish
Slack (S): Allowable delay
Identifies critical path
Longest path in network
Shortest time project can be completed
Any delay on critical activities delays the whole project
Activities have 0 slack

33. Critical Path Analysis Example

34. Network Solution B D E A G 2 6 3 1 1 C F 3 4

35. Earliest Start & Finish Steps
Begin at starting event & work forward
ES = 0 for starting activities
ES is earliest start
EF = ES + Activity time
EF is earliest finish
ES = Maximum EF of all predecessors for non-starting activities

36. Activity A Earliest Start SolutionD B C F G 1 6 2 3 4
For starting activities, ES = 0.

37. Earliest Start SolutionD B C F G 1 6 2 3 4

38. Latest Start & Finish Steps
Begin at ending event & work backward
LF = Maximum EF for ending activities
LF is latest finish; EF is earliest finish
LS = LF - Activity time
LS is latest start
LF = Minimum LS of all successors for non-ending activities

39. Earliest Start SolutionD B C F G 1 6 2 3 4

40. Latest Finish SolutionD B C F G 1 6 2 3 4
Latest Finish Solution

41. Compute Slack

42. Critical Path A E D B C F G 1 6 2 3 4

43. Scenario 1b ES/EF times E 1 1 2 A 1 0 1 I 1 9 10 F 2 5 7 Finish START
1 2 A 1
0 1 I 1
9 10 F 2
5 7
Finish
START C 4
1 5 B 3
0 3 H 1
8 9 G 1
7 8 D 2
3 5

44. Scenario 1c LF/LS times E 1 1 2 8 9 A 1 0 1 I 1 9 10 9 10 F 2 5 7
1 2
8 9 A 1
0 1 I 1
9 10
9 10 F 2
5 7
Finish
START C 4
1 5
1 5 B 3
0 3
2 5 H 1
8 9 G 1
7 8
7 8 D 2
3 5
5 7

45. Scenario 1c
START A 1
0 1 B 3
0 3
2 5 E
1 2
8 9 C 4
1 5
1 5 D 2
3 5
5 7 F G
7 8
7 8 H I
9 10
9 10
Finish

46. Other notation C 7 Compute ES, EF for each activity, Left to Right
LS LF
Compute ES, EF for each activity, Left to Right
Compute, LF, LS, Right to Left

47. Example #2
21 28
28 35
C 7
F 7
0 21
35 37
A 21
G 2
28 33
21 25
25 27
B 4
D 2
E 5

48. Example #2
21 28
28 35
C 7
F 7
0 21
35 37
A 21
G 2
28 33
21 25
25 27
B 4
D 2
E 5
F cannot start until C and D are done.
G cannot start until both E and F are done.

49. Example #2
21 28
28 35
C 7
F 7
21 28
28 35
0 21
35 37
A 21
G 2
0 21
35 37
28 33
21 25
25 27
B 4
D 2
E 5
22 26
26 28
30 35
E just has to be done in time for G to start at 35, so it has slack.
D has to be done in time for F to go at 28, so it has no slack.

50. Example #2
21 28
28 35
C 7
F 7
21 28
28 35
0 21
35 37
A 21
G 2
0 21
35 37
28 33
21 25
25 27
B 4
D 2
E 5
22 26
26 28
30 35
E just has to be done in time for G to start at 35, so it has slack.
D has to be done in time for F to go at 28, so it has no slack.

51. Gantt Chart - ES A C B D E F G

52. Gantt Chart - LS A C B D E F G

53. Another Example
B 4
E 6
G 7
A 1
C 3
I 4
F 2
D 7
H 9

54. Solved Problem 1 B 4 E 6 G 7 C 3 A 1 I 4 F 2 D 7 H 9 1 5 5 11 11 18
1 5
5 11
B 4
E 6
11 18
1 5
5 11
G 7
11 18
0 1
1 4
18 22
A 1
C 3
I 4
0 1
6 9
8 10
18 22
F 2
1 8
9 11
8 17
D 7
H 9
2 9
9 18

55. Can We Go Faster?

56. MacArthur Maze Key SF artery Day 8 – CC Meyers gets job
I-80 west to 880 south
April 29, 2007, 8,600 gal gas
Day 8 – CC Meyers gets job
Day 25 – opened to traffic
$876 k bid, $2.5m cost
$200,000 per day incentive
$5,000,000 bonus

57. Time-Cost Models 1. Identify the critical path
2. Find cost per day to expedite each node on critical path.
3. For cheapest node to expedite, reduce it as much as possible, or until critical path changes.
4. Repeat 1-3 until no feasible savings exist.

58. Time-Cost Example ABC is critical path=30 Crash cost Crash
D 8
A 10
B 10
C 10
ABC is critical path=30
Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 2
Cheapest way to gain 1
Week is to cut A

59. Time-Cost Example ABC is critical path=29 Crash cost Crash
D 8
A 9
B 10
C 10
ABC is critical path=29
Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 2
Wks Incremental Total
Gained Crash $ Crash $
Cheapest way to gain 1 wk
Still is to cut A

60. Time-Cost Example ABC is critical path=28 Crash cost Crash
D 8
A 8
B 10
C 10
ABC is critical path=28
Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 2
Wks Incremental Total
Gained Crash $ Crash $
,000
Cheapest way to gain 1 wk
is to cut B

61. Time-Cost Example ABC is critical path=27 Crash cost Crash
D 8
A 8
B 9
C 10
ABC is critical path=27
Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 2
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
Cheapest way to gain 1 wk
Still is to cut B

62. Time-Cost Example Critical paths=26 ADC & ABC Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 2
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
,600
To gain 1 wk, cut B and D,
Or cut C
Cut B&D = $1,900
Cut C = $5,000
So cut B&D

63. Time-Cost Example Critical paths=25 ADC & ABC Crash cost Crash
per week wks avail A B
C 5,000 2
D 1,100 1
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
,600
5 1,900 4,500
Can’t cut B any more.
Only way is to cut C

64. Time-Cost Example Critical paths=24 ADC & ABC Crash cost Crash
per week wks avail A B
C 5,000 1
D 1,100 1
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
,600
5 1,900 4,500
6 5,000 9,500
Only way is to cut C

65. Time-Cost Example Critical paths=23 ADC & ABC Crash cost Crash
per week wks avail A B
C 5,000 0
D 1,100 1
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
,600
5 1,900 4,500
6 5,000 9,500
7 5,000 14,500
No remaining possibilities to
reduce project length

66. Time-Cost Example
D 7
A 8
B 7
C 8
Now we know how much it costs us to save any number of weeks
Customer says he will pay $2,000 per week saved.
Only reduce 5 weeks.
We get $10,000 from customer, but pay $4,500 in expediting costs
Increased profits = $5,500
Wks Incremental Total
Gained Crash $ Crash $
,000
,800
,600
5 1,900 4,500
6 5,000 9,500
7 5,000 14,500
No remaining possibilities to
reduce project length

67. Ex. AOA

68. AON Paths: ABF: 18 CDEF: 20 C5 B 10 A 6 D 4 E 9 F2 Activity Avail Cost

69. Gantt charts to keep track
B10
A 6
D 4
E 9 F2
Original
Activity Avail Cost A
B 2 500
C 1 300
D 3 700
E 2 600 F
Consider CDEF 2
C is cheapest, crash 1 day
A 6
B 10
F 2
C 5
D 4
E 9
Revised Pictures:
Activity Avail Cost A
B 2 500
C 0
D 3 700
E 2 600 F
Consider
DEF
E cheapest
Crash E 1 day
A 6
B 10
C 4
D 4
E 9 1
F 2 C4
B10
A 6
D 4
E 9 F2

70. Keep Track with Gantt Charts
New Pictures:
Activity Avail Cost A
B 2 500
C 0
D 3 700
E 1 600
F 1 800 C4
B10
A 6
D 4 E8 F2
All Activities Critical
ABF: 18
CDEF: 18
A 6
B 10
C 4
D 4
E 8
F 2
Crash:
F $800
Crash:
B&D or B&E
E is cheaper than D
$500+$600 = $1,100 > 1,000
Cost > Benefit C4
B10
A 6
D 4 E8 F1
A 6
B 10
C 4
D 4
E 8
F 1
Stop after F!

71. Scenario 2 Task Normal Crash $/day B 3 2 $1,000 C 4 1 2,000 D 2 1 500
Now, need to do it in 7 days!
Task Normal Crash $/day
B 3 2 $1,000
C 4 1 2,000 D F
Not critical
$800 gain 1 day
Not critical
Cheapest
START A 1
0 1 B 3
0 3
2 5 E
1 2
8 9 C 4
1 5
1 5 D 2
3 5
5 7 F G
7 8
7 8 H I
9 10
9 10
Finish

72. Scenario 2 Task Normal Crash $/day B 3 2 $1,000 C 4 1 2,000 D 2 1 500
Now, need to do it in 7 days!
Task Normal Crash $/day
B 3 2 $1,000
C 4 1 2,000 D F
Not critical
Day 1 $800
Day 2 $2,000
Only option
Not critical
Used up E 1
1 2
8 8 A 1
0 1 I 1
8 9
8 9 F 1
5 6
Finish
START C 4
1 5
1 5 B 3
0 3
1 4 H 1
7 8 G 1
6 7 D 2
3 5
4 6

73. Scenario 2 Task Normal Crash $/day B 3 2 $1,000 C 3 1 2,000 D 2 1 500
Now, need to do it in 7 days!
Task Normal Crash $/day
B 3 2 $1,000
C 3 1 2,000 D F
Day 1 $800
Day 2 $2,000
Day 3 $2,500
Total $5,300
Used up
Something on both paths
C, and B or D, D cheaper E 1
1 2
8 8 A 1
0 1 I 1
7 8
7 8 F 1
4 5
Finish
START C 3
1 4
1 4 B 3
0 3 H 1
6 7 G 1
5 6 D 2
3 5

74. Scenario 2 Task Normal Crash $/day B 3 2 $1,000 C 2 1 2,000 D 1 1 500
Now, Done in 7 days!
Task Normal Crash $/day
B 3 2 $1,000
C 2 1 2,000 D F
Day 1 $800
Day 2 $2,000
Used up
Day 3 $2,500
Total $5,300
Used up E 1
1 2
5 6 A 1
0 1 I 1
6 7
6 7 F 1
3 4
Finish
START C 2
1 3
1 3 B 3
0 3 H 1
5 6 G 1
4 5 D 1
3 4

75. What about Uncertainty?

76.  PERT Activity Times 3 time estimates Follow beta distribution
Optimistic times (a)
Most-likely time (m)
Pessimistic time (b)
Follow beta distribution
Expected time: t = (a + 4m + b)/6
Variance of times: v = (b - a)2/36


77. Example Activity a = 2, m = 4, b = 6
E[T] = (2 + 4*4 + 6)/6 = 24/6 = 4.0
σ2 = (6 – 2)2 / 36 = 16/36 = 0.444

78. Example C B A Activity a m b E[T] variance A 2 4 8 4.33 1
6.48
7.67
Activity a m b E[T] variance A B C
Project
Complete in 18.5 days, with a variance of 4.

79. Sum of 3 Normal Random Numbers
Average value of the sum is
equal to the sum of the averages
Variance of the sum is equal to
the sum of the variances
Notice curve of sum is more spread
out because it has large variance

80. Back to the Example: Probability of <= 21 wks
Average time = 18.5, st. dev = 2
21 is how many standard deviations
above the mean?
= 2.5.
St. Dev = 2,
so 21 is 2.5/2 = 1.25 standard
deviations above the mean
Book Table says area between
Z=1.25 and –infinity is
Probability <= 21 wks
= = 89.44%

81. Benefits of PERT/CPM Useful at many stages of project management
Mathematically simple
Use graphical displays
Give critical path & slack time
Provide project documentation
Useful in monitoring costs

82. Limitations of PERT/CPM
Clearly defined, independent, & stable activities
Specified precedence relationships
Activity times (PERT) follow beta distribution
Subjective time estimates
Over emphasis on critical path

83. Conclusion Explained what a project is Drew project networks
Compared PERT & CPM
Determined slack & critical path
Found profit-maximizing crash decision
Computed project probabilities