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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
Network TechniquesNetwork TechniquesCPMCPM
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 TechniquesNetwork TechniquesCPMCPM
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
Source: Badiru & Pulat, 1995
Network Network -- DefinitionsDefinitions
Source: Badiru & Pulat, 1995
Finish
I
H
G
D
E
F
Start
A
B
C
Arc
Node (Activity)
Milestone
Dummy
Merge Point
Burst Point
Network Network -- DefinitionsDefinitions
Source: Badiru & Pulat, 1995
•Predecessor Activity of D•Successor Activity of F
Finish
I
H
G
D
E
F
Start
A
B
C
Definitions (ContDefinitions (Cont’’d)d)
Source: Badiru & Pulat, 1995
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
Definitions (ContDefinitions (Cont’’d)d)
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
Source: Badiru & Pulat, 1995
Definitions (ContDefinitions (Cont’’d)d)
Source: Badiru & Pulat, 1995
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
Network TechniquesNetwork TechniquesCPMCPM
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
Source: Badiru & Pulat, 1995
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
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 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?
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)
Activity Predecessor Duration (days)A - 2B - 6C - 4D A 3E C 5F A 4G B,D,E 2
CPM ExampleCPM Example
Source: Badiru & Pulat, 1995
Draw AON network
A2
F4
B6
C4
D3
G2
E5
End
Start
Forward PassForward Pass
Source: Badiru & Pulat, 1995
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
Source: Badiru & Pulat, 1995
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
Source: Badiru & Pulat, 1995
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
Source: Badiru & Pulat, 1995
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
Source: Badiru & Pulat, 1995
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
Source: Badiru & Pulat, 1995
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