3. What is a Project?
• A project is a “temporary endeavor undertaken to create
a unique product or service”.
• Project characteristics
– Temporary
• Every project has a definite beginning and a definite end,
the duration is finite, not “short”
– Unique
• The uniqueness of the deliverable requires a special
approach in that there may not be a pre-existing blueprint
for the project’s execution
– Progressive elaboration
• Developing in steps, and continuing by increments
3
项目是“为创造独特的产品或服务而
做出的临时性努力”。
每个项目都有明确的开始
和结束，持续时间是有限
的，而不是“短暂的”。
交付物的独特性需要一种特殊的方法
，因为可能没有预先存在的项目执行
蓝图
逐步细化
循序渐进，循序渐进地发展
4. Examples of Projects
• Construction of dams, warehouse, freeways, railways,
etc.
• Design of new models of products, such as new cars,
ships, and aircraft.
• Development of computer systems, software, etc.
• New product marketing, advertising campaigns, global
mergers, capital acquisitions, etc.
• Set-up of a new enterprise, organization, department,
office, etc.
• Performing major maintenance or repair.
Project management spans both the manufacturing and
service sectors. 4
进行重大维护或维修。
5. Project Management
The means, techniques, and the concepts used to run a
project and achieve its objectives subject to various
constraints and limits on time, resources, technology,
and personnel.
• Key decisions:
– Deciding which projects to implement
– Selecting a project manager
– Selecting a project team
– Planning and designing the project
– Managing and controlling project resources
– Deciding if and when a project should be terminated
5
在时间、资源、技术和人员方面的各种限制和限制
下，用于运行项目和实现其目标的手段、技术和概
念。
项目实施
决定项目是否以及何时应
该终止
6. What is a Project Manager?
• The project manager is ultimately responsible for the
success or failure of the project
• The project manager must effectively manage:
– The work
– The human resources
– Communications
– Quality
– Time
– Costs
6
Project
manager
Client
Government
agencies
Other
organizations
Consultants
Subcontractors
Project
team
Functional
managers
Top
management
8. Project Failure: Microsoft’s “Kin” Phones
• Kin One & Kin Two
– Social networking, cloud
storage
– No downloadable apps or
games
– Target: between ages 15~30
– Invested US$1 billion
8
• Introduced to the market in May 2010
• Was discontinued in August 2011 because of poor sales
– Lack basic functions users required
– High cost of data and texting plans
– Lack of marketing, senior management support
– Tough competition 激烈的竞争
9. Factors Affecting Project Success
• Project mission and goals
• Top management support
• Project planning
• Client consultation
• Personnel issues
• Technical issues
• Client acceptance
• Project control
• Communication
• Troubleshooting
9
n. 解决纷争；发现并修理故障
10. Work Breakdown Structure
• Work Breakdown Structure (WBS) is an important aid
in planning and managing the project
– A hierarchical listing of what must be done during the project
– Complicated tasks is subdivided into several smaller tasks.
Process continued until task can no longer be subdivided
• A project can be structured as different WBSs. The
choice depends on how you would like the project to be
executed
10
分层列表
11. Work Breakdown Structure: Example
• A university initiates a project to design a new MBA
program
– Approach 1: Divide the entire project directly into work
packages (lowest level of WBS)
11
12. Work Breakdown Structure: Example
• Approach 2: Divide the entire project by functional area and then
further divide the work content in each area into specific work
packages
12
13. Work Breakdown Structure: Example
• Approach 3: Divide the entire project according to the year in the
program, then functional areas, and then specific work packages
13
14. Project Planning and Scheduling Tools
• Gantt chart
– Developed by Henry L. Gantt in 1917
– Popular for simple projects
– Major limitation: inability to show task dependencies
14
主要限制:无法显示任务依赖关系
15. Project Planning and Scheduling Tools
• PERT (Program Evaluation and Review Technique)
and CPM (Critical Path Method)
– Two of the most widely used techniques for large-scale
projects developed in 1950’s
– Both approaches work on a network diagram, which
graphically portrays the activities of the project and their
relationships
– Each uses a different estimate of activity times
• CPM deals with purely deterministic problems
• PERT allows randomness in the activity times
15
16. The Network Diagram – Terminology
• Activities
– Project steps that consume resources and/or time.
• Activity-On-Arrow (AOA)
– Use an arc to represent an activity
– Nodes represent the events, which are the starting and
finishing of activities
• Activity-On-Node (AON)
– Use a node to represent an activity
16
1 2
A
3 4
B C
A B C
activity
event
17. Example 1: A simple network
• Consider the list of four activities for making a simple
product, draw a AON diagram of the project
– Immediate predecessors for a particular activity are the
activities that, when completed, enable the start of the activity
in question
17
Activity Description Immediate predecessors
A Buy Plastic Body -
B Design Component -
C Make Component B
D Assemble product A,C
18. AOA vs. AON
18
AOA Interpretation AON
C is preceded by A and B
B is preceded by A
C is preceded by A
C is preceded by A and B
D is preceded by A and B
A
B
C
A
B
C
A
B
C
D
A
B
C
A
B
C
A
B
C
D
C前面是A和B
19. Example 2 (1/2)
• Suppose a project consists of five activities A, B, C, D
and E that satisfy the following precedence
relationships:
– 1. Neither A nor B has any immediate predecessors.
– 2. A is an immediate predecessor of C.
– 3. A and B is immediate predecessors of D.
– 4. C and D are immediate predecessors of E.
• Draw a AOA diagram of the project
19
1 2 3 4
Correct?
A
B
C
D
E
20. Example 2 (2/2)
• With the dummy activity P, node 3 corresponds to the
completion of both activities A and B
– Dummy activities have no resources (time, labor, machinery,
etc.). They are used to eliminate possible confusion of two or
more activities having the same starting and ending nodes
20
1
2
3
4 5
E
A
B
P
C
D
虚拟活动没有资源(时间、劳动力、机器等)。它们用于消除具有相同开始节点
和结束节点的两个或多个活动之间可能出现的混淆
21. Exercise 1
• Draw the AOA network using the data in the following
Table.
21
Tasks Immediate predecessors
A. Perform market survey
B. Design graphic icons A
C. Develop flowchart A
D. Design input/output screens B, C
E. Module 1 coding C
F. Module 2 coding C
G. Module 3 coding E
H. Module 4 coding E, F
I. Merge models and graphic and test D, G, H
23. Exercise 2
• Draw the AOA diagram so that the following
precedence relations are satisfied:
– E is preceded by B and C
– F is preceded by A and B
23
B
A
C
F
E
P1
P2
End
Start
24. Critical Path Analysis
• Path: Sequence of activities that leads from the starting
node to the finishing node
• Project is completed: all paths from the initial node to
the final node must be traversed
• Critical path
– Longest path in the network
– Shortest time project can be completed
– Any delay on activities delays project (critical activities)
• Activity slack time
– The amount of time by which the activity may be delayed
without delaying the project
– Critical activities have zero slack
24
从开始节点到结束节点的活动序列
必须遍历从初始节点到最终节点的
所有路径
25. A Simple Case
• The length of each path?
• The critical path?
• The amount of slack time for each path?
25
1
2
3
4
5 6
8 weeks
6 weeks
3 weeks
4 weeks
9 weeks
11 weeks
1 week
Move in
26. Earliest Start & Earliest Finish Times
• ES: the earliest time activity can start, assuming all
preceding activities start as early as possible
• EF: the earliest time the activity can finish
• Earliest start time rule:
– ES=0 for starting activities
– The earliest start time for an activity leaving a particular node
is equal to the largest of the earliest finish times for all
activities entering the node:
ES of an activity = max{EF of its immediate predecessors}
– EF = ES + Activity time
• Finding ES and EF times involves a forward pass
through the network
26
活动可以最早开始的
时间，假设前面的所
有活动都尽可能早地
开始
离开某个特定节点的活动的最早开始时间等于所有
进入该节点的活动最早结束时间中的最大时间:
求ES和EF时间涉及到网络
的前向传递
27. Arc with ES & EF Times
27
1
2
Activity
ES = earliest start time
EF = earliest finish time
t = activity time
29. Latest Start & Latest Finish Times
• LS: the latest time the activity can start and not delay
the project
• LF: the latest time the activity can finish and not delay
the project
• Latest finish time rule:
– LF=maximum EF for ending activities
– The latest finish time for an activity entering a particular node
is equal to the smallest of the latest start times for all
activities leaving the node:
LF of an activity = min{LS of its immediate successors}
– LS = LF – Activity time
• Finding LS and LF times involves a backward pass
through the network 29
一个进入特定节点的活动的最遲
结束时间等于所有离开该节点的活动的最
遲开始时间的最小值:
30. ES, EF, LS, LF
30
2
3
Activity
ES = earliest start time
EF = earliest finish time
LF = latest finish time
LS = latest start time
32. Activity Slack
• Slack (float) is the length of time an activity can be
delayed without affecting the completion date for the
entire project.
– E.g. Slack for C = 3 weeks, i.e Activity C can be delayed up
to 3 weeks (start anywhere between weeks 5 and 8).
32
ES
5
LS
8
EF
9
LF-EF = 12 –9 =3
LS-ES = 8 – 5 = 3
LF-ES-t = 12-5-4 = 3
LF
12 2
3
Slack(浮动)是指在不影响整个项目完成日期的情况下，
某个活动可以被延迟的时间长度。
33. Activity Schedule
33
Activity ES LS EF LF Slack
A 0 0 5 5 0
B 0 6 6 12 6
C 5 8 9 12 3
D 5 7 8 10 2
E 5 5 6 6 0
F 6 6 10 10 0
G 10 10 24 24 0
H 9 12 21 24 3
I 24 24 26 26 0
What is the total time to complete the project?
What activities are critical ?
How long can non-critical activities be delayed before
they cause a delay in the project’s completion time?
34. Importance of Slack and Critical Path
• Slack shows how much allowance each activity has, i.e
how long it can be delayed without affecting
completion date of project
• If any activity on the critical path is shortened or
extended, project time will be shortened or extended
accordingly
• If can spend resources to speed up some activity, do so
only for critical activities.
• If resources can be saved by lengthening some
activities, do so for non-critical activities, up to limit of
float.
34
Slack表示每个活动有多少余量，即在不影响
项目完成日期的情况下可以延迟多长时间
如果关键路径上的任何活动被缩短或延长，项目时间将相应地
缩短或延长
如果可以花费资源来加速某些活动，那么只
对关键的活动这样做。
如果可以通过延长某些活动来节省资源，那么对非关键活动
也这样做，直到限制浮动
37. Project Crashing: Time-Cost Trade-Offs
• It is possible to reduce the length of activity by adding
additional resources
• Shortening the duration of the project is called project
crashing
– Normal time: time for completing an activity
– Crash time: minimum possible time required
• Approach
– Crash the project one period at a time.
– Crash the least expensive activity that is on the critical path.
– Successively crash the project time if the saving of shortening
the project outweighs the additional cost of crashing, until no
further reductions are possible
37
项目崩溃:时间和成本的权衡
省的錢>用於加速的錢=good
38. Crashing Activities
• Crashing activities
reduce indirect
project costs and
increase direct costs;
the optimum amount
of crashing results in
minimizing the sum
of these two types of
costs.
38
坠毁活动降低了间接项目
成本，增加了直接成本;
最优碰撞量的结果是使这
两种类型的成本之和最小
化。
39. Example (1/4)
• Develop the optimal time-cost solution
– Suppose the benefit of crashing is $1000 per day
39
Activity Normal Time (days) Crash Time (days) Cost per day to crash ($)
A 6 6
B 10 8 500
C 5 4 300
D 4 1 700
E 9 7 600
F 2 1 800
1
4
A B
C
6
2
3
5
D
E
F
40. Example (2/4)
• Initially, we have the following:
• Shorten the project, one day at a time, and check after
each reduction to see which path is critical
40
Project
time
Critical
path
Critical
activities
Normal
Time (days)
Crash Time
(days)
Crash Cost
(per day)
20 C-D-E-F C 5 4 $300
D 4 1 $700
E 9 7 $600
F 2 1 $800
一天一天地缩短项目，并在每次缩减后检查哪条路径是关键
的
41. Example (3/4)
• Shorten activity C one day at a cost of $300
41
Project
time
Critical
path
Critical
activities
Current
time (days)
Crash
Time (days)
Crash Cost
(per day)
19 C-D-E-F C 4 4 $300
D 4 1 $700
E 9 7 $600
F 2 1 $800
42. Example (4/4)
• Shorten activity E one day at a cost of $600
• Which activity to crash?
42
Project
time
Critical
path
Critical
activities
Current
time (days)
Crash
Time (days)
Crash Cost
(per day)
18 C-D-E-F C 4 4 $300
D 4 1 $700
E 8 7 $600
F 2 1 $800
18 A-B-F A 6 6
B 10 8 $500
F 2 1 $800
43. PERT (1/3)
• PERT is a generalization of CPM to allow uncertainty
in the activity times
• The three time estimates used by PERT for each
activity are:
𝑡𝑜 = optimistic time, which is the estimate of the
time if the execution goes extremely well.
𝑡𝑝 = pessimistic time, which is the estimate of the
time if everything goes badly
𝑡𝑚 = most likely time, which is the estimate of the
time if the execution is normal. 43
允许活动时间的不确定性
乐观时间，这是在执行非常顺利的情况下对时间的估计。
悲观时间，这是如果一切都不顺利的估计时间
最可能的时间，如果执行正常，这是对时间的估计。
44. PERT (2/3)
• A beta distribution is used to describe probabilistic time
estimates.
• Expected time of an activity, 𝑡𝑒 =
𝑡𝑜+4𝑡𝑚+𝑡𝑝
6
• Standard deviation, 𝜎 =
𝑡𝑝−𝑡𝑜
6
44
45. PERT (3/3)
• In PERT, one assumes that the distribution of the total
project time is normal (central limit theorem)
• Expected duration of a path is equal to the sum of the
expected times of the activities on that path
• Variance of the expected time for each path:
45
t= 𝑡𝑒𝑖
𝜎𝑝𝑎𝑡ℎ
2
= 𝜎𝑖
2
N>30=nomal
46. Example (1/3)
• The network diagram for a project is shown in the
accompanying figure, with three time estimates for each
activity. Activity times are in weeks.
46
a) Compute the expected
time for each activity and
the expected duration for
each path.
b) Identify the critical path.
c) Compute the variance of
each activity and the
variance and standard
deviation of each path.
47. Example (2/3)
47
Times
te = (to+4tm+tp)/6
Path Activity to tm tp Path Total
a 1 3 4 2.83
a-b-c b 2 4 6 4.00 10.00
c 2 3 5 3.17
d 3 4 5 4.00
d-e-f e 3 5 7 5.00 16.00
f 5 7 9 7.00
g 2 3 6 3.33
g-h-i h 4 6 8 6.00 13.50
i 3 4 6 4.17
48. Example (3/3)
48
Times
𝝈𝑝𝑎𝑡ℎ
𝟐 𝝈 𝒑𝒂𝒕𝒉
Path Activity to tm tp
a 1 3 4 (4-1)2/36=9/36
a-b-c b 2 4 6 (5-2)2/36=16/36 34/36=0.944 0.97
c 2 3 5 (6-2)2/36=9/36
d 3 4 5 (5-3)2/36=4/36
d-e-f e 3 5 7 (7-3)2/36=16/36 36/36=1.00 1.00
f 5 7 9 (9-5)2/36=16/36
g 2 3 6 (6-2)2/36=16/36
g-h-i h 4 6 8 (8-4)2/36=16/36 41/36=1.139 1.07
i 3 4 6 (6-3)2/36=9/36
𝝈𝟐 =
𝒕𝒑 − 𝒕𝒐
𝟐
𝟑𝟔
49. Determining Path Probabilities
• Probability Calculation:
𝑧 =
Specified time−Path mean
𝜎𝑝𝑎𝑡ℎ
– The resulting value of z indicates how many standard
deviations of the path distribution that specified time is
beyond the expected path duration.
49
If the z is +3.00 or more, treat the
probability of path completion by
the specified time as 100%
50. Determining Path Probabilities
• Noncritical path may take longer than the critical path
because of the variability of the activity times
– Assuming independent of two or more paths is more accurate
than assuming a single critical path
– Independence: activity times are independent of each other
and each activity is only on one path
50
Can the paths be considered
independent? Why?
51. Exercise
• Using the information from the previous example,
answer the following questions:
a) What is the probability that the project can be completed
within 17 weeks of its start?
b) What is the probability that the project will be completed
within 15 weeks of its start?
c) What is the probability that the project will not be completed
within 15 weeks of its start?
51
53. Answer (2/2)
b)
P(finish by week 15) = 1.00 (0.1587) (0.9192) = 0.1459
c) The probability of not finishing before week 15 is the
complement of the probability obtained in part b: 1 - 0.1459 =
0.8541 53
55. Takeaways
• Understand the nature and management of projects
• Understand work breakdown structure (WBS)
• Construct network diagrams
• Understand project planning and scheduling techniques:
Gantt Chart, CPM, and PERT
• Describe activity "crashing" and solve typical problems
• Analyze networks with deterministic times and
probabilistic times
55
