Project Planning and Management

Agenda:

1. Motivation to study project planning

2. A Method: CPM/PERT

Project Planning: Motivation

Large scale projects (e.g. HK Disneyland)

Project requires completion of

hundreds of different activities by

several different groups or companies

Objective: Quickest completion of project

Project Planning and Management

What is the earliest time we can complete the entire project?

CPM/PERT

Critical Path Method

Program Evaluation and Review Technique

What is the latest time that we can begin an activity, without delaying the project?

Which activities are the bottlenecks?

Given an activity, what is the earliest we can begin to do it?

CPM/PERT: Example

Task Description I P Weeks

a Ecological survey - 6.2

b File environmental impact report;get approval

a 9.1

c Economic feasibility study a 7.3

d Preliminary design and cost estimation c 4.2

e Project approval b, d 10.2

f Call quotation for turbines, generators.. e 4.3

g Select supplier for equipment f 3.1

h Final design of project e 6.5

i Select construction contractor e 2.7

j Arrange construction materials supply h, i 5.2

k Dam building j 24.8

l Power station building j 18.4

m Power lines erection g, h 20.3

n Turbines, generators installation g, l 6.8

o Build-up reservoir water level k 2.1

p Commission the generators n, o 1.2

q Start supplying water m, p 1.1

s

B

A

C

a, 6.2

b, 9.1 c, 7.3

s

B

A

C

a, 6.2

b, 9.1 c, 7.3

EVENT

ACTIVITY

CPM/PERT: graphical representation

Task Description I P Weeks

a Ecological survey - 6.2

b File environmental impact report;get approval

a 9.1

c Economic feasibility study a 7.3

d Preliminary design, cost estimation c 4.2

e Project approval b, d 10.2

E

D

B

A

C

b, 9.1 c, 7.3

d, 4.2

e, 10.2

E

D

B

A

C

b, 9.1 c, 7.3

d, 4.2

e, 10.2

Dummy edge

CPM/PERT: graphical representation

Task Description I P Weeks

a Ecological survey - 6.2

b File environmental impact report;get approval

a 9.1

c Economic feasibility study a 7.3

d Preliminary design, cost estimation c 4.2

e Project approval b, d 10.2

J

H I

F

G

KL

M

N O

P

Q

s

a, 6.2

E

D

B

A

C

b, 9.1 c, 7.3

d, 4.2

e, 10.2

f, 4.3

g, 3.1

h, 6.5

i, 2.7

j, 5.2

k, 24.8l, 18.4

m, 20.3

o, 2.1n, 6.8

p, 1.2

q, 1.1

CPM/PERT

Complete graph

CPM/PERT: Forward Pass

Compute earliest start time for each task

E

e, 10.2

[27.9]

s

B

D

A

C

a, 6.2

b, 9.1 c, 7.3

d, 4.2

[6.2]

[13.5][15.3]

[17.7]

[0]

E

e, 10.2

[27.9]

s

B

D

A

C

a, 6.2

b, 9.1 c, 7.3

d, 4.2

[6.2]

[13.5][15.3]

[17.7]

[0]s

B

D

A

C

a, 6.2

b, 9.1 c, 7.3

d, 4.2

[6.2]

[13.5][15.3]

[17.7]

[0]Case 1

Case 2

J

H I

F

G

KL

M

N O

P

Q

f, 4.3

g, 3.1

h, 6.5

i, 2.7

j, 5.2

k, 24.8l, 18.4

m, 20.3

o, 2.1n, 6.8

p, 1.2

q, 1.1

[32.2]

[34.4][34.4]

[39.6]

[35.3]

[67.7]

[58.0] [64.4]

[66.5] [66.5]

[67.7]

[68.8]

E

e, 10.2

[27.9]

s

B

D

A

C

a, 6.2

b, 9.1 c, 7.3

d, 4.2

[6.2]

[13.5][15.3]

[17.7]

[0]

Forward Pass..

CPM/PERT: Backward Pass

Compute latest start time for each task

Case 1

- Start from the ‘finish project’ node

M

P

Q

p, 1.2

q, 1.1

[67.7, 67.7]

[67.7, 67.7]

[68.8, 68.8]

M

Latest start of ‘q’ = 68.8 – 1.1 =67.7 [WHY?]

CPM/PERT: Backward Pass

Compute latest start time for each task

Case 2

J

I

KL

j, 5.2

k, 24.8l, 18.4

[30.6, 34.4]

[39.6, 39.6]

[58.0, 59.7] [64.4, 64.4]

J

I

KL

j, 5.2

k, 24.8l, 18.4

[30.6, 34.4]

[39.6, 39.6]

[58.0, 59.7] [64.4, 64.4]

59.7 – 18.4 = 41.3

64.4 – 24.8 = 39.6

s

B

D

H

A

C

E

F

G

N O

a, 6.2

b, 9.1 c, 7.3

d, 4.2

e, 10.2

f, 4.3

g, 3.1

h, 6.5

i, 2.7

m, 20.3

o, 2.1n, 6.8

[6.2, 6.2]

[13.5, 13.5][15.3, 17.7]

[17.7, 17.7]

[27.9, 27.9]

[32.2, 44.3]

[34.4, 34.4]

[35.3, 47.4]

J

I

KL

j, 5.2

k, 24.8l, 18.4

[34.4, 34.4]

[39.6, 39.6]

[58.0, 59.7] [64.4, 64.4]

[66.5, 66.5] [66.5, 66.5]

M

P

Q

p, 1.2

q, 1.1

[67.7, 67.7]

[67.7, 67.7]

[68.8, 68.8]

[0, 0]

Backward Pass..

Critical Path

CPM/PERT: Project scheduling

What is the earliest time we can complete the entire project?

What is the latest time that we can begin an activity, without delaying the project?

Which activities are the bottlenecks?

Given an activity, what is the earliest we can begin to do it?

Example: activity ‘h’ cannot begin before 27.9

Week 68.8

All activities on critical path

Example: activity ‘g’ may be started as late as 44.3

CPM/PERT: Concluding remarks

(a) Difficult to estimate time for tasks

Use: (worst case, expected case, best case)

Probabilistic model- Difficult to estimate prob. distribution- Difficult to model correlated activities

(b) Activities share resources ?

Cannot model !

Use: resource constrained scheduling

next topic: Linear programming