Project Scheduling: PERT/CPM

Managers are often responsible for planning, scheduling and controlling projects that consist of numerous separate jobs or tasks performed by a variety of individuals or departments.

Project managers must schedule and coordinate the activities that make up the project to ensure the project is completed on time.

A complicating factor is the interdependence of the activities• Some activities must be completed before

others can be started.

PERT/CPM

PERT• Program Evaluation and Review Technique• Developed by U.S. Navy for Polaris missile

project• Developed to handle uncertain activity times

CPM• Critical Path Method• Developed by Du Pont & Remington Rand• Developed for industrial projects for which

activity times generally were known Today’s project management software packages

have combined the best features of both approaches.

PERT/CPM

PERT and CPM have been used to plan, schedule, and control a wide variety of projects:• R&D of new products and processes• Construction of buildings and highways• Maintenance of large and complex

equipment• Design and installation of new systems

PERT/CPM

PERT/CPM is used to plan the scheduling of individual activities that make up a project.

Projects may have as many as several thousand activities.

A complicating factor in carrying out the activities is that some activities depend on the completion of other activities before they can be started.

PERT/CPM

Project managers rely on PERT/CPM to help them answer questions such as:• What is the total time to complete the project?• What are the scheduled start and finish dates

for each specific activity?• Which activities are critical and must be

completed exactly as scheduled to keep the project on schedule?

• How long can noncritical activities be delayed before they cause an increase in the project completion time?

PERT/CPM

First step: develop a list of the activities that make up the project.

Then identify the immediate predecessor- the activities that must be completed immediately prior to the start of that activity.

Estimate the activity time for each activity

Shopping Center Project

Activity Activity Description

Immediate Predecessor

Activity Time

A Prepare architectural drawings

-- 5

B Identify potential new tenants

-- 6

C Develop prospectus for new tenants

A 4

D Select contractor A 3

E Prepare building permits

A 1

F Obtain approval for building permits

E 4

G Perform construction

D,F 14

H Finalize contracts with tenants

B,C 12

I Tenants move in G,H 2

Total 51

Draw Project Network

Start

B

A

E

D

C

F

G

H I Finish

Determining the Critical Path (forward pass)

Find the earliest start time and a latest start time for all activities in the network• ES – earliest start time for an activity• EF = earliest finish time for an activity• T = activity time

EF = ES + t• Activity A: ES = 0, t = 5, EF = 5

An activity cannot be started until all immediately preceding activities have been finished.

ES = the largest of the earliest finish times for all its immediate predecessors.

Determining the Critical Path

Activity B: ES = 0, EF = ES + t = 0 + 6 = 6 Activity C: earliest finish time for activity A is 5,

so the earliest start time for activity C must be 5• ES = 5, t = 4• EF = ES + t = 5 + 4 = 9

Activity H: Both B and C are predecessors.• ES = the largest of the earliest finish times

for activities B and C• EF = 6 for activity B, and EF = 9 for activity

C, t = 12• Thus ES for H is 9

• EF (for H): ES + t = 9 + 12 = 21

Critical Path (forward pass)

A 0 5

5

C 5 9

4

STARTH 9

21

12

Forward pass

Activity ES EF

A 0 5

B 0 6

C 5 9

D 5 8

E 5 6

F 6 10

G 10 24

H 9 21

I 24 26

Forward pass

Thus, the project can be completed in 26 weeks.

Backward Pass

Begin the backward pass with a latest finish time of 26 for activity I

Once the latest finish time is known, the latest start time can be computed:• LS = latest start time for an activity• LF = latest finish time for an activity

Beginning with activity I, LF = 26, t = 2 LS = LF – t = 26 – 2 = 24

I 24(ES) 26(EF)

2 (t) 24(LS) 26(LF)

Backward Pass

Activity Time (t) ES EF LS LF

A 5 0 5 0 5

B 6 0 6 6 12

C 4 5 9 8 12

D 3 5 8 7 10

E 1 5 6 5 6

F 4 6 10 6 10

G 14 10 24 10 24

H 12 9 21 12 24

I 2 24 26 24 26

SLACK

Slack is the length of time an activity can be delayed without increasing the project completion time.

Slack = LS – ES = LF = EF Activity C: LS – ES = 8 – 5 = 3 weeks

• Thus activity C can be delayed up to 3 weeks and the entire project can still be completed in 26 weeks

Activity E: LS – ES = 5 – 5 = 0• Activity E has no slack. This activity cannot

be delayed without increasing the completion time for the entire project.

• Activity E is a critical activity, and on the “critical path.”

Critical Path

Critical activities are those with zero slack Activities with zero slack are on the critical

path.

Critical Path

Activity

ES LS EF LF SlackLS-ES

Critical

Path?

A 0 0 5 5 0 Yes

B 0 6 6 12 6 No

C 5 8 9 12 3 No

D 5 7 8 10 2 No

E 5 5 6 6 0 Yes

F 6 6 10 10 0 Yes

G 10 10 24 24 0 Yes

H 9 12 21 24 3 No

I 24 24 26 26 0 Yes

Project Network

A project network can be constructed to model the precedence of the activities.

The nodes of the network represent the activities.

The arcs of the network reflect the precedence relationships of the activities.

A critical path for the network is a path consisting of activities with zero slack.

Example: Frank’s Fine Floats

Frank’s Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to use PERT/CPM to help them manage the project .

The table on the next slide shows the activities that comprise the project. Each activity’s estimated completion time (in days) and immediate predecessors are listed as well.

Frank wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

Example: Frank’s Fine Floats

Immediate Completion

Activity Description Predecessors Time (days) A Initial Paperwork --- 3 B Build Body A 3 C Build Frame A 2 D Finish Body B 3 E Finish Frame C 7 F Final Paperwork B,C 3 G Mount Body to Frame D,E 6 H Install Skirt on Frame C 2