PERT/CPM Models for Project Management

Chapter 16: Hillier and Hillier

Agenda

What is Project Management Discuss PERT/CPM Motivating Case Study: The Reliable

Construction Company Ways of Finding the Critical Path Considering Time-Cost Trade-Offs

What is Project Management

Project management can be defined as the coordination of activities with the potential use of many organizations, both internal and external to the business, in order to conduct a large scale project from beginning to end.

There are two management science techniques that are used for project management: – Program and Evaluation Review Technique (PERT) – Critical Path Method (CPM)

PERT/CPM

PERT – PERT was designed to examine projects from the

standpoint of uncertainty. CPM

– CPM was designed to examine projects from the standpoint of costs.

PERT and CPM techniques have been combined over time.

PERT and CPM both rely heavily on the use of networks to help plan and display the coordination of all the activities for a project.

The Reliable Construction Company

Reliable has just secured a contract to construct a new plant for a major manufacturer.

The contract is for $5.4 million to cover all costs and any profits.

The plant must be finished in a year. – A penalty of $300,000 will be assessed if Reliable does

not complete the project within 47 weeks. – A bonus of $150,000 will be paid to Reliable if the

plant is completed within 40 weeks.

Needed Terminology

Activity – A distinct task that needs to be performed as

part of the project. Start Node

– This is a node that represents the beginning of the project.

Finish Node – This node represents the end of the project.

Needed Terminology Cont.

Immediate Predecessor – These are activities that must be completed by no later

than the start time of the given activity. Immediate Successor

– Given the immediate predecessor of an activity, this activity becomes the immediate successor of each of these immediate predecessors.

– If an immediate successor has multiple immediate predecessors, then all must be finished before an activity can begin.

Activity List for Reliable Construction

Activity Activity Description Immediate

Predecessors Estimated

Duration (Weeks) A Excavate — 2

B Lay the foundation A 4

C Put up the rough wall B 10

D Put up the roof C 6

E Install the exterior plumbing C 4

F Install the interior plumbing E 5

G Put up the exterior siding D 7

H Do the exterior painting E, G 9

I Do the electrical work C 7

J Put up the wallboard F, I 8

K Install the flooring J 4

L Do the interior painting J 5

M Install the exterior fixtures H 2

N Install the interior fixtures K, L 6

Questions Needed to be Answered

How can the project be displayed graphically? How much time is required to finish the project if

no delays occur? When is earliest start and finish times for each

activity if no delays occur? What activities are critical bottleneck activities

where delays must be avoided to finish the project on time?

Questions Needed to be Answered Cont.

For non bottleneck activities, how much can an activity be delayed and yet still keep the project on time?

What is the probability of completing the project by the deadline?

What is the least amount of money needed to expedite the project to obtain the bonus?

How should costs be monitored to keep the project within budget?

Project Network

A project network is a network diagram that uses nodes and arcs to represent the progression of the activities is a project from start to finish.

Three pieces of information needed: – Activity information – Precedence relationship – Time information

Project Network Cont.

Two types of project networks – Activity-on-Arc (AOA)

• On this diagram, the activity is represented on an arc, while a node is used to separate an activity from its immediate predecessors.

– Activity-on-Node (AON) • On this diagram, the activity is represented by the

node, while the arc is used to showed the precedence relationship between the activities.

A

START

G

H

M

F

J

K L

N

Activity Code

A. Excavate

B. Foundation

C. Rough wall

D. Roof

E. Exterior plumbing

F. Interior plumbing

G. Exterior siding

H. Exterior painting

I. Electrical work

J. Wallboard

K. Flooring

L. Interior painting

M. Exterior fixtures

N. Interior fixtures

2

4

10

746

7

9

5

8

4 5

6

2

0

0FINISH

D IE

C

B

Microsoft Project Visual Diagram: Gantt Chart

Scheduling Using PERT/CPM

A path through a project network is a route that follows a set of arcs from the start node to the finish node.

The length of a path is defined as the sum of the durations of the activities of the path. – What are the paths and their corresponding

lengths for Reliable?

Critical Path

This is the path that has the longest length through the project.

The shortest time that a project can conceivably be finished is the critical path. – Why?

More Terminology

Earliest start time of an activity (ES) – The time at which an activity will begin if there are no

delays in a project. Earliest finish time of an activity (EF)

– The time at which an activity will finish if there are no delays in a project.

Latest start time of an activity (LS) – The latest possible time that an activity can start

without delaying the project.

More Terminology Cont.

Latest finish time of an activity (LF) – The latest possible time that an activity can be

completed without delaying the project. Forward pass

– The process of moving through a project from start to finish to determine the earliest start and finish times for the activities in the project.

More Terminology Cont.

Backward pass – The process of moving through a project from finish to

start to determine the latest start and finish times for the activities in the project.

Slack for an activity – The amount of time that a particular activity can be

delayed without delaying the whole project. – It is calculated by taking the difference between the

latest finish time with the earliest finish time.

More Terminology Cont.

Earliest start time rule – The earliest start time for an activity is equal to

the largest of the earliest finish times of its immediate predecessors.

Latest finish time rule – The latest finish time is equal to the smallest of

the latest start times of its immediate successors.

Procedure for Obtaining Earliest Times

Step 1: For the activity that starts the project, assign an earliest start time of zero, i.e., ES=0.

Step 2: For each activity whose ES has just been obtained, calculate its earliest finish time as ES plus duration of the activity.

Step 3: For each new activity whose immediate predecessors have EF values, obtain its ES by using the earliest start time rule.

Procedure for Obtaining Earliest Times Cont.

Step 4: Apply step 2 to calculate EF. Step 5: Repeat step 3 until ES and EF have

been obtained for all activities including the finish node.

Procedure for Obtaining Latest Times

Step 1: For each of the activities that together complete the project, set its latest finish time equal to the earliest finish time of the finish node.

Step 2: For each activity whose LF value has just been obtained, calculate its latest start time as LS equals LF minus the duration of the activity.

Procedure for Obtaining Latest Times Cont.

Step 3: For each new activity whose immediate successors now have LS values, obtain its LF by applying the latest finish time rule.

Step 4: Apply step 2 to calculate its LS. Step 5: Repeat step 3 until LF and LS have

been obtained for all activities.

A

START

G

H

M

F

J

FINISH

K L

N

D IE

C

B

2

4

10

746

7

9

5

8

4 5

6

2

S = (0, 0) F = (2, 2)

S = (2, 2) F = (6, 6)

S = (16, 20) F = (22, 26)

S = (16, 16) F = (20, 20)

S = (16, 18) F = (23, 25)

S = (20, 20) F = (25, 25)

S = (22, 26) F = (29, 33)

S = (6, 6) F = (16, 16)

S = (0, 0) F = (0, 0)

S = (25, 25) F = (33, 33)

S = (33, 33) F = (38, 38)

S = (38, 38) F = (44, 44)

S = (33, 34) F = (37, 38)

S = (29, 33) F = (38, 42)

S = (38, 42) F = (40, 44)

S = (44, 44) F = (44, 44)

0

0

Ways of Finding the Critical Path

Examine all the paths and find the path with the maximum length.

Calculate the slack for an activity. – If the slack is zero, it is on the critical path. – If the slack is positive, it is not on the critical

path.

Time-Cost Trade-Offs

Reliable had an incentive bonus of $150,000 to finish the project in 40 weeks. – Is it worth while for Reliable to speed-up the

project?

Crashing

Crashing an activity refers to taking on extra expenditures in order to reduce the duration of an activity below its expected value.

Crashing a project refers to crashing a number of activities to reduce the duration of the project.

CPM Method of Time-Cost Trade-Offs

This is a method concerned with whether it is worthwhile to crash activities to reduce the anticipated duration of the project to a desired value.

This assumes that there is a trade-off between time and cost that has an inverse relationship.

More Terminology

Normal Point is the time and cost of an activity when it is performed in a normal way.

Crash point show the time and cost when the activity is fully crashed.

Graph of Normal and Crash Points

Activity duration

Activity cost

Crash cost

Normal cost Normal

Crash

Crash time Normal time

Marginal Cost Analysis

It is a method of using the marginal cost of crashing individual activities on the current critical path to determine the least expensive way of reducing the project duration to an acceptable level.

This method requires you to calculate the cost per desired time unit and compare each cost with the other costs.

Time (weeks) Cost Maximum Reduction

in Time (weeks)

Crash Cost per Week

Saved Activity Normal Crash Normal Crash A 2 1 $180,000 $280,000 1 $100,000

B 4 2 320,000 420,000 2 50,000

C 10 7 620,000 860,000 3 80,000

D 6 4 260,000 340,000 2 40,000

E 4 3 410,000 570,000 1 160,000

F 5 3 180,000 260,000 2 40,000

G 7 4 900,000 1,020,000 3 40,000

H 9 6 200,000 380,000 3 60,000

I 7 5 210,000 270,000 2 30,000

J 8 6 430,000 490,000 2 30,000

K 4 3 160,000 200,000 1 40,000

L 5 3 250,000 350,000 2 50,000

M 2 1 100,000 200,000 1 100,000

N 6 3 330,000 510,000 3 60,000

Marginal Cost Analysis Cont.

Once the marginal cost for crashing each activity has been conducted, you next want to choose the crashing that has the smallest marginal cost.

Next, calculate the effect that the crash has on each path. – Note: Crashing can potentially cause another

path to become a critical path.

Solving Crashing Problems Using LP

There are three decisions to be made: – The start time of each activity – The reduction in each activity due to crashing – The finish time of the project

LP model will be examined in class.