Pert and Cpm

1.040/1.4011.040/1.401

Project ManagementProject ManagementSpring 2007Spring 2007

Deterministic Planning Part IDeterministic Planning Part I

Dr. SangHyun Lee

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental EngineeringMassachusetts Institute of Technology Massachusetts Institute of Technology

Project Management PhaseProject Management Phase

FEASIBILITY DEVELOPMENT CLOSEOUT OPERATIONS

Fin.&Eval.

RiskEstimating

Planning&SchedulingPlanning&Scheduling

DESIGNDESIGNPLANNING PLANNING

Organization

OutlineOutline

ObjectiveObjective

Bar ChartBar Chart

Network TechniquesNetwork TechniquesCPMCPM

ObjectiveObjective

What are some of the Different Representations for DeterministicWhat are some of the Different Representations for DeterministicSchedules ?Schedules ?

What are some Issues to Watch for?What are some Issues to Watch for?

OutlineOutline

ObjectiveObjective

Bar ChartBar Chart


Gantt Chart Characteristics

Bar Chart

Henry L. Gantt

World War I - 1917

Ammunition Ordering and Delivery

Activities Enumerated in the Vertical Axis

Activity Duration Presented on the Horizontal Axis

Easy to Read

Simple Gantt ChartSimple Gantt Chart

TimePhase Year 1 Year 2 Year 3

1. Concept and feasibility studies

2. Engineering and design

3. Procurement

4. Construction

5. Start-up and implementation

6. Operation or utilization

.

Figure by MIT OCW.

Gantt (Bar) ChartsGantt (Bar) Charts

Very effective communication tool

Very popular for representation of simpler schedules

Can be cumbersome when have >100 activities

Key shortcoming: No dependencies captured

Most effective as reporting format rather than representation

Hierarchy of Gantt ChartsHierarchy of Gantt ChartsLevel one plan

Level two plans

Level three plans

Figure by MIT OCW.

Activity AggregationActivity Aggregation

Source: Shtub et al., 1994

Hammock ActivitiesHammock Activities

A graphical arrangement which includes a summary of a A graphical arrangement which includes a summary of a group of activities in the project. group of activities in the project.

Duration equal to longest sequence of activitiesDuration equal to longest sequence of activities

Activity AggregationActivity Aggregation

Source: Shtub et al., 1994

MilestonesMilestones

A task with a zero duration that acts as a reference point A task with a zero duration that acts as a reference point marking a major project event. Generally used to mark: marking a major project event. Generally used to mark: beginning & end of project, completion of a major phase, or a beginning & end of project, completion of a major phase, or a task for which the duration is unknown or out of control.task for which the duration is unknown or out of control.

Flag the start or the successful completion of a set of activitiFlag the start or the successful completion of a set of activitieses

OutlineOutline

ObjectiveObjective

Bar ChartBar Chart


Network SchedulingNetwork Scheduling

A network is a graphical representation of a project plan, A network is a graphical representation of a project plan, showing the intershowing the inter--relationships of the various activities. relationships of the various activities. When results of time estimates & computations are added to a When results of time estimates & computations are added to a network, it may be used as a project schedule.network, it may be used as a project schedule.

Source: Badiru & Pulat, 1995

ActivityA

Event i Event j

Activity on ArrowAOA

Activity on NodeAON

Activity A

Activity B

AdvantagesAdvantages

CommunicationsCommunicationsInterdependencyInterdependencyExpected Project Completion DateExpected Project Completion DateTask Starting DatesTask Starting DatesCritical Activities Critical Activities Activities with Slack Activities with Slack ConcurrencyConcurrencyProbability of Project CompletionProbability of Project Completion


Network Network -- DefinitionsDefinitions


Finish

I

H

G

D

E

F

Start

A

B

C

Arc

Node (Activity)

Milestone

Dummy

Merge Point

Burst Point

Network Network -- DefinitionsDefinitions


•Predecessor Activity of D•Successor Activity of F

Finish

I

H

G

D

E

F

Start

A

B

C

Definitions (ContDefinitions (Cont’’d)d)


ActivityTime and resource consuming effort with a specific time required to perform the task or a set of tasks required by the project

DummyZero time duration event used to represent logical relationships between activities

MilestoneImportant event in the project life cycle

NodeA circular representation of an activity and/or event


ArcArcA line that connects two nodes and can be a representation of anA line that connects two nodes and can be a representation of an event or an activityevent or an activity

Restriction / PrecedenceRestriction / PrecedenceA relationship which establishes a sequence of activities or theA relationship which establishes a sequence of activities or the start or end of an start or end of an activityactivity

Predecessor ActivityPredecessor ActivityAn activity that immediately precedes the one being consideredAn activity that immediately precedes the one being considered

Successor ActivitySuccessor ActivityAn activity that immediately follows the one being consideredAn activity that immediately follows the one being considered

Descendent ActivityDescendent ActivityAn activity restricted by the one under considerationAn activity restricted by the one under consideration

Antecedent ActivityAntecedent ActivityAn activity that must precede the one being consideredAn activity that must precede the one being considered




Merge PointMerge PointExists when two or more activities are predecessors to a single Exists when two or more activities are predecessors to a single activity activity (the merge point)(the merge point)

Burst PointBurst PointExists when two or more activities have a common predecessor (thExists when two or more activities have a common predecessor (the e burst point)burst point)

NetworkNetworkGraphical portrayal of the relationship between activities and Graphical portrayal of the relationship between activities and milestones in a projectmilestones in a project

PathPathA series of connected activities between any two events in a netA series of connected activities between any two events in a networkwork

OutlineOutline

ObjectiveObjective

Bar ChartBar Chart


Critical Path Method (CPM)Critical Path Method (CPM)

DuPont, Inc., and UNIVAC Division of Remington RandDuPont, Inc., and UNIVAC Division of Remington Rand

Scheduling Maintenance Shutdowns in Chemical Processing Scheduling Maintenance Shutdowns in Chemical Processing PlantsPlants

~1958~1958

Construction ProjectsConstruction Projects

Time and Cost ControlTime and Cost Control

Deterministic TimesDeterministic Times

CPM ObjectiveCPM Objective

Determination of the critical path: the minimum time for a projeDetermination of the critical path: the minimum time for a projectct

CPM PrecedenceCPM Precedence


Technical PrecedenceTechnical Precedence

Caused by the technical relationships among activities (e.g., inCaused by the technical relationships among activities (e.g., in conventional conventional construction, walls must be erected before roof installation)construction, walls must be erected before roof installation)

Procedural PrecedenceProcedural Precedence

Determined by organizational policies and procedures that are ofDetermined by organizational policies and procedures that are often ten subjective with no concrete justification subjective with no concrete justification

Imposed PrecedenceImposed Precedence

E.g., Resource Imposed (Resource shortage may require one task tE.g., Resource Imposed (Resource shortage may require one task to be before o be before another)another)

CPM: AOA & AONCPM: AOA & AON

Activity-on-Arrow

Activity-on-NodeExcavate Footings

Source: Feigenbaum, 2002Newitt, 2005

Mobilize

Clear & Grub

Fabricate Forms Footings

Fabricate Rebar Footings

Form FootingsStart

Finish

1Start Form

Footings

5

7ExcavateFootings 6Fabricate Footings

Forms at Site Workshop

Clear & Grub

2 3Mobilize

4

Fabricate RebarFootings

8

Fini

sh

Arc

Arrow

ActivityDummyActivity

Event

DummyActivity

CPM CalculationsCPM Calculations

Source: Hegazy, 2002Hendrickson and Au, 1989/2003

Forward PassForward PassEarly Start Times (ES)Early Start Times (ES)

Earliest time an activity can start without violating precedenceEarliest time an activity can start without violating precedence relationsrelations

Early Finish Times (EF)Early Finish Times (EF)Earliest time an activity can finish without violating precedencEarliest time an activity can finish without violating precedence relationse relations

Forward Pass Forward Pass -- IntuitionIntuition

ItIt’’s 8am. Suppose you want to know the earliest time you can s 8am. Suppose you want to know the earliest time you can arrange to meet a friend after performing some tasksarrange to meet a friend after performing some tasks

Wash hair (5 min)Wash hair (5 min)

Boil water for tea (10 min)Boil water for tea (10 min)

Eat breakfast (10 min)Eat breakfast (10 min)

Walk to campus (5 min)Walk to campus (5 min)

What is the earliest time you could meet your friend?What is the earliest time you could meet your friend?

CPM CalculationsCPM Calculations

Source: Hegazy, 2002Hendrickson and Au, 1989/2003

Backward PassBackward PassLate Start Times (LS)Late Start Times (LS)

Latest time an activity can start without delaying the completioLatest time an activity can start without delaying the completion of the projectn of the project

Late Finish Times (LF)Late Finish Times (LF)Latest time an activity can finish without delaying the completiLatest time an activity can finish without delaying the completion of the on of the projectproject

Backward Pass Backward Pass -- IntuitionIntuition

Your friend will arrive at 9am. You want to know by what time Your friend will arrive at 9am. You want to know by what time you need to start all thingsyou need to start all things





What is the latest time you should start?What is the latest time you should start?

Slack or FloatSlack or Float

ItIt’’s 8am, and you know that your friend will arrive at 9am. How s 8am, and you know that your friend will arrive at 9am. How much do you have as free time? much do you have as free time?





Activity Predecessor Duration (days)A - 2B - 6C - 4D A 3E C 5F A 4G B,D,E 2

CPM ExampleCPM Example


Draw AON network

A2

F4

B6

C4

D3

G2

E5

End

Start

Forward PassForward Pass


0 0ES EF

ES(kES(k) = ) = Max{EF(iMax{EF(i)}, i )}, i P(kP(k) ) EF(kEF(k) = ) = ES(kES(k) + ) + D(kD(k))

∋

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11


Forward PassForward Pass

ES(kES(k) = ) = Max{EF(iMax{EF(i)}, i )}, i P(kP(k) ) EF(kEF(k) = ) = ES(kES(k) + ) + D(kD(k))

∋

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11


Backward PassBackward Pass

11 11LS LF

LF(kLF(k) = ) = Min{LS(jMin{LS(j)} j )} j S(kS(k) )

LS(kLS(k) = ) = LF(kLF(k) ) –– D(kD(k))

∋

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11


Backward PassBackward Pass

11 11

0 4 4 9

6 9

3 9

7 11

9 11

4 6

0 0

LF(kLF(k) = ) = Min{LS(jMin{LS(j)} j )} j S(kS(k) )

LS(kLS(k) = ) = LF(kLF(k) ) –– D(kD(k))

∋

Slack or FloatSlack or Float

The amount of flexibility an activity possessesThe amount of flexibility an activity possesses

Degree of freedom in timing for performing task Degree of freedom in timing for performing task

Source: Hendrickson and Au, 1989/2003

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11

0 0

0 4 4 9

9 11

11 114 6

6 9

3 9

7 11

4

Total Slack or FloatTotal Slack or Float

Total Slack or Float (TS or TF)Total Slack or Float (TS or TF)Max time can delay w/o delaying the projectMax time can delay w/o delaying the project

TS(kTS(k) = {) = {LF(kLF(k) ) -- EF(kEF(k)} or {)} or {LS(kLS(k) ) -- ES(kES(k)})}

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11

0 0

0 4 4 9

9 11

11 114 6

6 9

3 9

7 11

TS = 4

Free Slack or FloatFree Slack or Float

Free Slack or Float (FS or FF)Free Slack or Float (FS or FF)Max time can delay w/o delaying successorsMax time can delay w/o delaying successors

FS(kFS(k) = ) = Min{ES(jMin{ES(j)} )} -- EF(kEF(k) j ) j S(kS(k))

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11

0 0

0 4 4 9

9 11

11 114 6

6 9

3 9

7 11

FS = 3∋

Independent Slack or FloatIndependent Slack or Float

Independent Slack or Float (IF)Independent Slack or Float (IF)Like Free float but assuming worstLike Free float but assuming worst--case finish of predecessorscase finish of predecessors

IF(kIF(k) = Max { 0, ( ) = Max { 0, ( Min(ES(jMin(ES(j)) )) -- Max(LF(iMax(LF(i)) )) –– D(kD(k) ) } j ) ) } j S(kS(k), i ), i P(kP(k))

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11

0 0

0 4 4 9

9 11

11 114 6

6 9

3 9

7 11

IF = 1

∋ ∋

CPM AnalysisCPM Analysis

Adapted from: Badiru & Pulat, 1995

Activity Duration ES EF LS LF TS FS IF CriticalA 2 0 2 4 6 4 0 0B 6 0 6 3 9 3 3 3C 4 0 4 0 4 0 0 0 YesD 3 2 5 6 9 4 4 0E 5 4 9 4 9 0 0 0 YesF 4 2 6 7 11 5 5 1G 2 9 11 9 11 0 0 0 Yes

Critical PathCritical Path

The path with the least slack or float in the networkThe path with the least slack or float in the network

Activities in that path: critical activitiesActivities in that path: critical activities

For algorithm as described, at least one such pathFor algorithm as described, at least one such path

Must be completed on time or entire project delayedMust be completed on time or entire project delayed

Determines minimum time required for projectDetermines minimum time required for project

Consider nearConsider near--critical activities as well!critical activities as well!

A2

F4

B6

C4

D3

G2

E5

End

Start0 0

0 22 6

0 6

0 4

2 5

9 11

4 9

11 11

0 0

0 4 4 9

9 11

11 114 6

6 9

3 9

7 11

Critical PathCritical Path


If EFi = ESj, then activity i is a critical activity (here, activity i is an immediate predecessor of activity j

Path CriticalityPath Criticality

= minimum total float

= maximum total float

= total float or slack in current path

Rank paths from more critical to less criticalRank paths from more critical to less critical

( )100%mm inax ααβαλ

−−

=max

minα

axmα

β

%1000−=λ


Calculate Path CriticalityCalculate Path Criticalityααminmin = 0, = 0, ααmaxmax = 5= 5

Path 1: [(5Path 1: [(5--0)/(50)/(5--0)](100 %) = 100 %0)](100 %) = 100 %

Path 2: [(5Path 2: [(5--3)/(53)/(5--0)](100 %) = 40 %0)](100 %) = 40 %

Path 3: [(5Path 3: [(5--4)/(54)/(5--0)](100 %) = 20 %0)](100 %) = 20 %

Path 4: [(5Path 4: [(5--5)/(55)/(5--0)](100 %) = 0 %0)](100 %) = 0 %

Path Number Activities on Path Total Slack λ1 Start,C,E,G,End 0 1002 Start,B,G,End 3 403 Start,A,D,G,End 4 204 Start,A,F,End 5 0

Path Criticality Path Criticality -- ExampleExample

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Pert and Cpm