Project Scheduling: Prof. Jiang Zhibin Dept. Of Ie, Sjtu

Project Scheduling Prof. Jiang Zhibin Dept. of IE, SJTU

What’s a Project? • • • •

•

Bringing about change is hard Many related activities Hard to plan production A project focuses on the outcome Regular teamwork focuses on the work process

Examples of Projects • • • • •

Building construction New product introduction Software implementation Training seminar Research project

Project Scheduling • • • •

•

•

•

Establishing objectives Determining available resources Sequencing activities Identifying precedence relationships Determining activity times & costs Estimating material & worker requirements

Project Scheduling Techniques

• •

•

Gantt chart Critical Path Method (CPM) Program Evaluation & Review Technique (PERT)

Gantt Chart Activity Design Build Test

J

Time Period F M A

M

J

J

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

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?

PERT & CPM Steps • • • • •

Identify activities Determine sequence Create network Determine activity times Find critical path • • •

Earliest & latest start times Earliest & latest finish times Slack

Activity on Node (AoN) Project: Obtain a college degree (B.S.) Enroll

1 1 month

Attend class, study etc.

Receive diploma

2

3

4? Years

1 day

Activity on Arc (AoA) Project: Obtain a college degree (B.S.)

1

Enroll 1 month

2

Attend class, study, etc. 4,5 ? Years

Receive diploma

3

4 1 day

AoA Nodes Have Meaning Project: Obtain a college degree (B.S.)

1 Applicant

2 Student

3 Graduating Senior

4 Alum

Activity Relationships

3 1

2

1-2 must be done before 2-3 or 3-4 can start

4

Activity Relationships 2-3 must be done before 3-4 or 3-5 can start

1

3 5

2 4

Activity Relationships 2-4 and 3-4 must be done before 4-5 can start

1

3 5

2 4

Activity Relationships

3 1

When 5-6 is done, project is complete.

5

2 4

6

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

Predecessors -A A B B C D E, F

Network Example - AON

D

B A

G

E

C

F

Z H

Network Example - AOA

B 1

A

2

3

C

F 4

D E 5

6 H

G

8 7

9

AOA Diagrams A precedes B and C, B and C precede D

1

A

B 2

3

C

1

2

4

3

B A

D

C

Add a phantom arc for clarity.

4

D

5

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 activities delays project Activities have 0 slack

Critical Path Analysis Example

Event ID

A B C D E F G

Pred. None

A B B D C C

Description

Time (Wks)

Prepare Site Pour fdn. & frame Buy shrubs etc. Roof Do interior work Landscape Move In

1 6 3 2 3 4 1

Network Solution

A 1

B

D

E

6

2

3

C

F

3

4

G 1

Earliest Start & Finish Steps •

•

Begin at starting event & work forward ES = 0 for starting activities •

•

EF = ES + Activity time •

•

ES is earliest start EF is earliest finish

ES = Maximum EF of all predecessors for non-starting activities

Activity A Earliest Start Solution Activity A B C D E F

ES 0

EF 1

LS

A 1

LF

Slack

B

D

E

6

2

3

C

F

3

4

For starting activities, ES = 0.

G 1

Earliest Start Solution Activity A B C D E F G

ES 0 1 1 7 10 4 12

EF 1 7 4 9 12 8 13

LS

A 1

LF

Slack

B

D

E

6

2

3

C

F

3

4

G 1

Latest Start & Finish Steps •

•

Begin at ending event & work backward LF = Maximum EF for ending activities •

•

LS = LF - Activity time •

•

LF is latest finish; EF is earliest finish LS is latest start

LF = Minimum LS of all successors for non-ending activities

Earliest Start Solution Activity A B C D E F G

ES 0 1 1 7 9 4 12

EF 1 7 4 9 12 8 13

LS

LF

Slack

B D E A

6

2

1 C 3

3 G F 1 4

13

Latest Finish Solution Activity ES EF A B0 D E1 B A 61 2 73 C 1 4 1 C F D 7 9 3 4 E 9 12 F 4 8 G 12 13

G 1

LS 0 1 4 7 9 7 12

LF 1 7 7 9 12 12 13

Slack

Compute Slack Activity A B C D E F G

ES 0 1 1 7 9 4 12

EF 1 7 4 9 12 8 13

LS 0 1 4 7 9 7 12

LF 1 7 7 9 12 12 13

Slack 0 0 3 0 0 3 0

Critical Path

A 1

B

D

E

6

2

3

C

F

3

4

G 1

New notation ES EF

C7 LS LF •

•

Compute ES, EF for each activity, Left to Right Compute, LF, LS, Right to Left

PERT Activity Times •

3 time estimates • • •

• •

•



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

Project Times •

Expected project time (T) •

•

Sum of critical path activity times, t

a + 4m + b ET = 6

b−a σ =  Project variance (V)  6  • Sum of critical path activity variances, v 2

2

PERT Probability Example You’re a project planner for Sun Microsystems. A software project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the project in 50 weeks or less?

Converting to Standardized Variable D − T 50 − 40 Z= = = 2.0 σ 5 From Normal Distribution Table, Probability = 0.5 + 0.4772 = 0.9772

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.

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

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

Conclusion • •

• • • •

Explained what a project is Summarized the 3 main project management activities Drew project networks Compared PERT & CPM Determined slack & critical path Computed project probabilities