project scheduling a. a. elimam

Project Project SchedulingScheduling

A. A. ElimamA. A. Elimam

FinishStart

Project SchedulingProject Scheduling

Need to plan and Need to plan and control large/time control large/time consuming projectsconsuming projects

Projects CharacteristicsProjects Characteristics

Projects are uniqueProjects are unique Time Estimation DifficultyTime Estimation Difficulty ControlControl

• Decomposition into smaller tasksDecomposition into smaller tasks

• Responsibility of a task given to a Responsibility of a task given to a specific individualspecific individual

Project Management: StagesProject Management: Stages

1.1. Define:Define: Describe goalDescribe goal

or Final outcome of Projector Final outcome of Project

2.2. Plan:Plan: Identify tasks / resources / Identify tasks / resources / timetime

3.3. Execute / Control:Execute / Control:

Time-cost Trade-offTime-cost Trade-off

ActivityActivity

The smallest unit of work The smallest unit of work effort consuming both effort consuming both timetime and and resources resources that the that the project manager can project manager can schedule and control.schedule and control.

Precedence RelationshipPrecedence Relationship

A sequencing constraint A sequencing constraint between interrelated activities between interrelated activities by which one activity cannot by which one activity cannot start until a preceeding activity start until a preceeding activity has been completed.has been completed.

ScheduleSchedule

A plan that sets priorities, A plan that sets priorities, determines determines start and finish start and finish timestimes, and allocates , and allocates resourcesresources to accomplish to accomplish the activities.the activities.

ExamplesExamples Constructing a building or amusement parkConstructing a building or amusement park Constructing a road, dam, or oil pipelineConstructing a road, dam, or oil pipeline Renovating a blighted urban areaRenovating a blighted urban area Developing a prototype for a new airplaneDeveloping a prototype for a new airplane Installing a large computer systemInstalling a large computer system Introducing a new productIntroducing a new product Organizing a state fairOrganizing a state fair Redesigning an office layoutRedesigning an office layout

Measuring Success of a projectMeasuring Success of a project

ConformanceConformance

TimeTime

BudgetBudget

Basic Questions

1.1. Project completion time?Project completion time?

2.2. Critical activities?Critical activities?

3.3. Activities that can be delayed?Activities that can be delayed?

How Long?How Long?

4.4. Starting / ending time of each activity?Starting / ending time of each activity?

5.5. Range of $’s spent on project?Range of $’s spent on project?

6.6. Time-cost trade-offTime-cost trade-off

Project ManagementProject ManagementBasic StepsBasic Steps

i.i. Describe projectDescribe project

ii.ii. Draw a network diagramDraw a network diagram

iii.iii. Provide time estimatesProvide time estimates

iv.iv. Analyze networkAnalyze network

v.v. Develop project planDevelop project plan

vi.vi. Update project planUpdate project plan

i. Describe projecti. Describe project

Activities / precedenceActivities / precedence end pointsend points

ii. Draw a network diagramii. Draw a network diagram

AOA: AOA: Arcs: Arcs: ActivitiesActivitiesNodes: Nodes: EventEvent

AON: AON: Nodes: Nodes: Activities ActivitiesArcs: Arcs: SequenceSequence

AOA and AON relationshipsAOA and AON relationships

1

2

AA

BB

CC3 4

(a) AOA approach: Event 4 cannot(a) AOA approach: Event 4 cannottake place until activities A, B andtake place until activities A, B andC have been completed.C have been completed.

(b) AON approach: Activity C(b) AON approach: Activity Ccannot take place until cannot take place until activities A and B completed.activities A and B completed.

A

B

C

Event

Event

Event Event

Activity

Activity

Activity

Implies time and resource consumption

Software

Activity RelationshipsActivity RelationshipsActivity Relationship

AOA AON


S precedes T, which precedes U.

AOA AON

1 2S

3T

4U

S T U


S and T must be completed before U can be started.

AOA AON

S

T

U

1

2

3T

S

4U


T and U cannot begin until S has been completed.

AOA AON

T

U

S

3

4

1

T

U2S


U and V cannot begin until both S and T have been completed.

AOA AON

1

2

4

5

U

V

S

T 3

S

T

U

V


U cannot begin until both S and T have been completed; V cannot begin until T has been completed.

AOA AON

S

T

U

V

1 3

Dummy

5

2 4 6

S U

T V


T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed.

AOA AON

1 2 4

3

S T5

V

UDummy

S T V

U

iii. Provide Time Estimatesiii. Provide Time Estimates

Deterministic Deterministic CPMCPM

CCritical ritical PPath ath MMethodethod

oror Probabilistic Probabilistic PERT PERT

PProgram rogram EEvaluation and valuation and RReview eview TTechnique echnique then CPMthen CPM

iv. Analyze Networkiv. Analyze Network

Identify critical path (CP) and Identify critical path (CP) and activities on it activities on it

Estimate probability of Estimate probability of completing project on timecompleting project on time

Explore time-cost trade-offExplore time-cost trade-off

v. Develop project plan

Schedule each activity Schedule each activity (particularly on CP)(particularly on CP)

Monitor actual Monitor actual planned. planned.

vi. Update project planvi. Update project plan

Adjust schedule on Adjust schedule on

the basis of actualsthe basis of actuals

St. Adolf’s HospitalSt. Adolf’s HospitalImmediate

Activity Description Predecessor(s)

ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop and information system.JInstall the equipment.KTrain nurses and support staff.



ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J




AON Network

A

Start




AON Network

A

B

Start




AON Network

A

C

B

Start




AON Network

A

C

DB

Start




AON Network

A

C

D

E

B

Start




AON Network

A F

C

D

E

B

Start




AON Network

A F

C G

D

E

B

Start




AON Network

A F

C G

D

E

HB

Start




AON Network

A F

I

C G

D

E

HB

Start




AON Network

A F

I

C G

D

E

HB J

Start




AON Network

A F

I

C G

D

E

HB J

K

Start




AON Network

A F

I

C G Finish

D

E

HB J

K

Start




Completion Time

FinishStart

A 12

C 10

G 35

H 40

D 10

E 24

J 4

K 6

F 10

I 15

B 9

St. Adolf’s HospitalSt. Adolf’s Hospital

FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

F

10

Earliest StartandEarliest Finish Times


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0

I

15

F

10


Earliest start time


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10


Earliest start time Earliest finish time


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

0 9



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

9 33

0 9 9 19



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22

9 33

0 9 9 19

12 22



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22

19 59

9 33

0 9 9 19

12 22



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22

22 57

19 59

9 33

0 9 9 19

12 22



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22

22 57

59 6319 59

9 33

0 9 9 19

12 22



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

Latest StartandLatest Finish Times



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

63 69 Latestfinishtime



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

63 69

Lateststarttime

Latestfinishtime


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

59 63Latest StartandLatest Finish Times


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

24 59

19 59

35 59



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

53 63 63 69

14 24 24 59

9 19 19 59

35 59



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59



FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Activity Slack Analysis


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


LS - ES = S


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


LS - ES = S63 - 63 = 0


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


LF - EF = S69 - 69 = 0


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


0


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


0000 00 00

0


FinishStart

A

12

K

6

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 69

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 69

14 24 24 59

0 9 9 19 19 59

35 59

59 63


0000 00 00

22

22

2626

4141

3636

0

22


FinishStart

A

12

C

10

G

35

E

24

0 12

I

15

F

10

12 27

12 22

22 57

9 33

12 22

48 63

2 14 53 63

14 24 24 59

35 59

0000 00 00

22

22

2626

4141

3636

0

22

B

9

0 9

0 9

D

10

9 19

9 19

H

40

19 5919 59

J

4

59 6359 63

K

6

63 6963 69

Critical Path

Probabilistic Time EstimatesProbabilistic Time Estimates


Time

Pro

bab

ility


Mean

ma bTime

Pro

bab

ility


Mean

Time

Pro

bab

ility

a bm 3s 3s


A F

I

C G Finish

D

E

HB J

K

Start

Probabilistic Time Estimates


Activity B

MostOptimistic Likely Pessimistic

(a) (m) (b)7 8 15


A F

I

C G Finish

D

E

HB J

K

Start


Activity B


(a) (m) (b)7 8 15


te = = 9 weeks7 + 4(8) + 15

6

A F

I

C G Finish

D

E

HB J

K

Start


Activity B


(a) (m) (b)7 8 15


te = = 9 weeks7 + 4(8) + 15

6

2 = = 1.78( )15 - 7

6

2

A F

I

C G Finish

D

E

HB J

K

Start


Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )

Time Estimates (wk) Activity Statistics

A F

I

C G Finish

D

E

HB J

K

Start


Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )

Time Estimates (wk) Activity Statistics

A 11 12 13 12 0.11B 7 8 15 9 1.78C 5 10 15 10 2.78D 8 9 16 10 1.78E 14 25 30 24 7.11F 6 9 18 10 4.00G 25 36 41 35 7.11H 35 40 45 40 2.78I 10 13 28 15 9.00J 1 2 15 4 5.44K 5 6 7 6 0.11

A F

I

C G Finish

D

E

HB J

K

Start

St. Adolf’s HospitalSt. Adolf’s HospitalA F

I

C G Finish

D

E

HB J

K

Start

Probabilities

Critical Path = B - D - H - J - K

T = 72 days TE = 69 days


I

C G Finish

D

E

HB J

K

Start

2 = (variances of activities) z = T - TE

2

Probabilities




I

C G Finish

D

E

HB J

K

Start


2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

Probabilities




I

C G Finish

D

E

HB J

K

Start


2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z =72 - 69

11.89

Probabilities




I

C G Finish

D

E

HB J

K

Start


2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z = = 0.8772 - 69

11.89

Probabilities




I

C G Finish

D

E

HB J

K

Start


2

2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89

z = = 0.8772 - 69

11.89

Probabilities



From Appendix 2Pz = .8078 .81


I

C G Finish

D

E

HB J

K

Start

Project duration (weeks)

69 72

Probability of meeting the schedule is 0.8078

Length of critical path

Normal distribution: Mean = 69 weeks; = 3.45 weeks

Probability of exceeding 72 weeks is 0.1922


I

C G Finish

D

E

HB J

K

Start


2

2 = 0.11 + 2.78 + 7.11 + 5.44 + 0.11 = 15.55

z = = 1.2772 - 67

15.55

Probabilities

Path = A - C - G - J - K


From Appendix 2Pz = .8980 .90


I

C G Finish

D

E

HB J

K

Start

Project duration (weeks)

67 69

Probability path B-D-H-J-K is less than 67 weeks

Normal distribution for path B-D-H-J-K: Mean = 69 weeks; = 3.45 weeks

Probability path A-C-G-J-K is more than 69 weeks

Normal distribution for path A-C-G-J-K: Mean = 67 weeks; = 3.94 weeks


I

C G Finish

D

E

HB J

K

Start

8000 —

7000 —

6000 —

5000 —

4000 —

3000 —

0 —

Dir

ect

cost

(d

oll

ars)

| | | | | |5 6 7 8 9 10 11


I

C G Finish

D

E

HB J

K

Start

8000 —

7000 —

6000 —

5000 —

4000 —

3000 —

0 —

Dir

ect

cost

(d

oll

ars)

Crash cost (CC)

Normal cost (NC)

| | | | | |5 6 7 8 9 10 11

Time (weeks)(Crash time) (Normal time)


I

C G Finish

D

E

HB J

K

Start

8000 —

7000 —

6000 —

5000 —

4000 —

3000 —

0 —

Dir

ect

cost

(d

oll

ars)

Crash cost (CC)

Linear cost assumption

Normal cost (NC)

| | | | | |5 6 7 8 9 10 11



I

C G Finish

D

E

HB J

K

Start

8000 —

7000 —

6000 —

5000 —

4000 —

3000 —

0 —

Dir

ect

cost

(d

oll

ars)

5200

Crash cost (CC)

Linear cost assumption

Normal cost (NC)

Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks

| | | | | |5 6 7 8 9 10 11



I

C G Finish

D

E

HB J

K

Start

Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks

Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65


I

C G Finish

D

E

HB J

K

Start



Critical Path B-D-H-J-K: 69 weeks

Crash Activity J by 3 weeks @ $1,000/week


I

C G Finish

D

E

HB J

K

Start





3($28,000) - 3($1,000) = $81,000


I

C G Finish

D

E

HB J

K

Start





3($28,000) - 3($1,000) = $81,000$2,624,000 - $81,000 = $2,543,000


I

C G Finish

D

E

HB J

K

Start


Total cost = $2,624,000 $2,543,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65



3($28,000) - 3($1,000) = $81,000$2,624,000 - $81,000 = $2,543,000


I

C G Finish

D

E

HB J

K

Start

FinishStart

A

12

C

10

G

35

E

24

0 12

I

15

F

10

12 27

12 22

22 57

9 33

12 22

48 63

2 14 53 63

14 24 24 59

35 59

0000 00 00

22

22

2626

4141

3636

0

22

B

9

0 9

0 9

D

10

9 19

9 19

H

40

19 5919 59

J

4

59 6359 63

K

6

63 6963 69

Precedence for Playground activitiesPrecedence for Playground activities

CodeCode Activity Activity DescriptionDescription TimeTime Immediate Immediate Name Name (days) (days) PredecessorsPredecessors

AA PlanningPlanning Find location,Find location,determine resourcedetermine resourcerequirementsrequirements 2020 NoneNone

BB PurchasingPurchasing Requisition lumberRequisition lumberand sandand sand 6060 Planning (A)Planning (A)

CC ExcavationExcavation Dig and gradeDig and grade 100100 Planning (A)Planning (A)DD SawingSawing Saw lumber intoSaw lumber into

appropriate sizesappropriate sizes 3030 Purchasing (B)Purchasing (B)EE PlacementPlacement Position lumber inPosition lumber in

correct locationscorrect locations 2020 Sawing, excavation (D,C)Sawing, excavation (D,C)FF AssemblyAssembly Nail lumber together`Nail lumber together` 1010 Placement (E)Placement (E)GG InfillInfill Put sand in and underPut sand in and under

equipmentequipment 2020 Assembly (F)Assembly (F)HH OutfillOutfill Put dirt aroundPut dirt around

equipmentequipment 1010 Assembly( F)Assembly( F)II DecorationDecoration Landscape, paintLandscape, paint 3030 Infill, outfill (G,H)Infill, outfill (G,H)

Playground ProjectPlayground Project

AAPlanningPlanning

BBPurchasingPurchasing

DDSawingSawing

EEPlacementPlacement

CCExcavationExcavation

FFAssemblyAssembly

HHOutfillOutfill

IIDecorationDecoration

GGInfillInfill


APlanning

BPurchasing

DSawing

EPlacement

CExcavation

FAssembly

HOutfill

IDecoration

GInfill

ES=20ES=20EF=80EF=80

ES=80ES=80EF=110EF=110

ES=120ES=120EF=140EF=140

ES=20ES=20EF=120EF=120

ES=140ES=140EF=150EF=150

ES=170ES=170EF=200EF=200

ES=150ES=150EF=160EF=160

ES=150ES=150EF=170EF=170

ES=0ES=0EF=20EF=20

Two passTwo passapproachapproach

Forward PassForward Pass


APlanning

BPurchasing

DSawing

EPlacement

CExcavation

FAssembly

HOutfill

IDecoration

GInfill

ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30










Backward PassBackward Pass


APlanning

BPurchasing

DSawing

EPlacement

CExcavation

FAssembly

HOutfill

IDecoration

GInfill

ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30SSBB=10=10

ES=80ES=80EF=110EF=110LF=120LF=120LS=90LS=90SSDD=10=10

ES=120ES=120EF=140EF=140LF=140LF=140LS=120LS=120SSEE=0=0ES=20ES=20

EF=120EF=120LF=120LF=120LS=20LS=20SSCC=0=0

ES=140ES=140EF=150EF=150LF=150LF=150LS=140LS=140SSFF=0=0

ES=170ES=170EF=200EF=200LF=200LF=200LS=170LS=170SSII=0=0

ES=150ES=150EF=160EF=160LF=170LF=170LS=160LS=160SSHH=10=10

ES=150ES=150EF=170EF=170LF=170LF=170LS=150LS=150SSGG=0=0

ES=0ES=0EF=20EF=20LF=20LF=20LS=0LS=0SSAA=0=0



APlanning

BPurchasing

DSawing

EPlacement

CExcavation

FAssembly

HOutfill

IDecoration

GInfill

ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30SSBB=10=10

ES=80ES=80EF=110EF=110LF=120LF=120LS=90LS=90SSDD=10=10

ES=120ES=120EF=140EF=140LF=140LF=140LS=120LS=120SSEE=0=0ES=20ES=20

EF=120EF=120LF=120LF=120LS=20LS=20SSCC=0=0

ES=140ES=140EF=150EF=150LF=150LF=150LS=140LS=140SSFF=0=0

ES=170ES=170EF=200EF=200LF=200LF=200LS=170LS=170SSII=0=0

ES=150ES=150EF=160EF=160LF=170LF=170LS=160LS=160SSHH=10=10

ES=150ES=150EF=170EF=170LF=170LF=170LS=150LS=150SSGG=0=0

ES=0ES=0EF=20EF=20LF=20LF=20LS=0LS=0SSAA=0=0

Critical PathCritical Path

Cost-time relationships analysisCost-time relationships analysis

55 66 77 88 99 1010 1111

Activity time duration (weeks)Activity time duration (weeks)

To

tal d

irec

t ac

tivi

ty c

ost

($)

To

tal d

irec

t ac

tivi

ty c

ost

($) 8,0008,000

7,0007,000

6,0006,000

5,0005,000

4,0004,000

3,0003,000

Crash time, costCrash time, cost

Linear cost assumptionLinear cost assumption

Estimated costs forEstimated costs fora 2-week reductiona 2-week reduction

Normal time, costNormal time, costHypotheticalHypotheticalactual cost curveactual cost curve NTNT NCNC

CTCT CCCC Cost to crash perCost to crash perweek = week = CC - NCCC - NC

NT - CTNT - CT

Limitations of PERT / CPMLimitations of PERT / CPM

project activities must be clearly defined, project activities must be clearly defined, independent, and stable in their relationshipsindependent, and stable in their relationships

precedence relationships must be specified precedence relationships must be specified and networked togetherand networked together

time activities in PERT are assumed to follow time activities in PERT are assumed to follow the beta probability distribution this may be the beta probability distribution this may be difficult to verifydifficult to verify

time estimates tend to be subjective, and are time estimates tend to be subjective, and are subject to fudging by managerssubject to fudging by managers

there is inherent danger in too much there is inherent danger in too much emphasis being placed on the critical pathemphasis being placed on the critical path

Resource LimitationsResource Limitations

2

B

5

4

C

2

5

A

1

6

D

3

Activity time in days

Workers required per day

FinishStart

3

E

3

1 2 3 4 5 6 7 8 9 10 11 12

Day

Activity

A

B

C

D

E

Resource Requirements

Resource LimitationsResource LimitationsGantt ChartsGantt Charts

project scheduling a. a. elimam

Documents

project completion time

project planvi

project manager

project planschedule

project schedulinga

activity ccannot

preceeding activity

time estimatesiv