CISC 322 Software Architecture

Lecture 18: Project Scheduling 2 Emad Shihab Slides adapted from Ahmed E. Hassan

Program Evaluation and Review Technique (PERT) ■ PERT (Program Evaluation and Review Technique) – Based on the idea that estimates are uncertain – Uses ranges and probability and provides an expected value to determine duration of the project – E.g. • The most likely completion time is 4 weeks but • It could be anywhere between 3 weeks and 8 weeks

Probabilistic Time Estimates ■ Beta distribution – a probability distribution traditionally used in CPM/PERT Mean (expected time): Variance:

a + 4m + b t= 6

 2

b-a = 6

2

where

a = optimistic estimate m = most likely time estimate b = pessimistic time estimate

Project Network with Probabilistic Time Estimates: Example Equipment installation

1

4

6,8,10

2,4,12

System development

Start

Equipment testing and modification

2 3,6,9 Position recruiting

System training

8 Manual testing

3,7,11

5 2,3,4

9 2,4,6

3

6

1,3,5

3,4,5

System testing

7 2,2,2

1,4,7 11

Job Training

Orientation

Final debugging 10

1,10,13 System changeover

Finish

Activity Time Estimates TIME ESTIMATES (WKS)

ACTIVITY

1 2 3 4 5 6 7 8 9 10 11

MEAN TIME

VARIANCE

a

m

b

t

б2

6 3 1 2 2 3 2 3 2 1 1

8 6 3 4 3 4 2 7 4 4 10

10 9 5 12 4 5 2 11 6 7 13

8 6 3 5 3 4 2 7 4 4 9

0.44 1.00 0.44 2.78 0.11 0.11 0.00 1.78 0.44 1.00 4.00

Activity Early, Late Times, and Slack ACTIVITY

1 2 3 4 5 6 7 8 9 10 11

t

б

ES

EF

LS

LF

S

8 6 3 5 3 4 2 7 4 4 9

0.44 1.00 0.44 2.78 0.11 0.11 0.00 1.78 0.44 1.00 4.00

0 0 0 8 6 3 3 9 9 13 16

8 6 3 13 9 7 5 16 13 17 25

1 0 2 16 6 5 14 9 12 21 16

9 6 5 21 9 9 16 16 16 25 25

1 0 2 8 0 2 11 0 3 8 0

Earliest, Latest, and Slack 1 0 8 1

Start

2 0 6 0

3 0 3 2

8

9

4 8 5 16 21

3

5

10 13 17

8 9 7 9

6

6

Critical Path

13

5 6 3 6 6 3 4 5

16

7

9

7 3 5 2 14 16

3 Finish

16

9

9

1 0

9 9 13 4 12 16

11 16 25

9 16 25

Total project variance 2 = б22 + б52 + б82 + б112  = 1.00 + 0.11 + 1.78 + 4.00

= 6.89 weeks

Probabilistic Network Analysis Determine probability that project is completed within specified time Z= where

 

x-



 = tp = project mean time  = project standard deviation x = proposed project time Z = number of standard deviations x is from mean

Probability of Completion Time What is the probability that the project is completed within 30 weeks? P(x  30 weeks)

 = 6.89 weeks 2

 =

6.89

 = 2.62 weeks

Z=

=

x-



30 - 25 2.62

= 1.91  = 25 x = 30

Time (weeks)

From Z scores Table, a Z score of 1.91 corresponds to a probability 0.9719.

Z values

Probability of Completion Time What is the probability that the project is completed within 22 weeks? x- 2 Z=  = 6.89 weeks P(x  22 weeks)



 =

6.89

 = 2.62 weeks

=

22 - 25 2.62

= -1.14 x = 22  = 25

Time (weeks)

From Z scores Table, a Z score of -1.14 corresponds to a probability of

0.1271

Z values

Limitations of PERT/CPM ■ Assumes clearly defined, independent activities

■ Activity times (PERT) follow beta distribution ■ Subjective time estimates ■ Over-emphasis on critical path

Project Crashing ■ Crashing – reducing project time by expending additional resources

■ Crash time – an amount of time an activity is reduced

■ Crash cost – cost of reducing activity time

■ Goal – reduce project duration at minimum cost

Project Crashing: Example

4

2 8

12

7 4

1 12

3 4

5 4

6 4

Project Crashing: Example $7,000 –

$6,000 – Crash cost

$5,000 –

Crashed activity Slope = crash cost per week

$4,000 – $3,000 – $2,000 –

Normal activity Normal cost

$1,000 – Normal time

Crash time

– 0

| 2

| 4

| 6

| 8

| 10

| 12

| 14

Weeks

Normal Activity and Crash Data

ACTIVITY

1 2 3 4 5 6 7

NORMAL TIME (WEEKS)

CRASH TIME (WEEKS)

NORMAL COST

12 8 4 12 4 4 4

7 5 3 9 1 1 3

$3,000 2,000 4,000 50,000 500 500 15,000

$5,000 3,500 7,000 71,000 1,100 1,100 22,000

$75,000

$110,700

CRASH COST

TOTAL ALLOWABLE CRASH TIME (WEEKS)

5 3 1 3 3 3 1

CRASH COST PER WEEK

$400 500 3,000 7,000 200 200 7,000

$7000

$500

Project Duration: 36 weeks

4

2 8

$700

12

7 4

1

FROM …

12

$400

3 4

6 4

5 4

$3000

$200

$200 $7000

$500

4

2 8

TO… Project Duration: 31 weeks Additional Cost: $2000

$700

12

7 4

1 7

$400

3 4 $3000

5 4 $200

6 4 $200

Time-Cost Tradeoff Minimum cost = optimal project time

Total project cost

Cost ($)

Indirect cost

Direct cost Crashing Project duration

Time

Time-Cost Relationship ■ Crashing costs increase as project duration decreases ■ Indirect costs increase as project duration increases ■ Reduce project length as long as crashing costs are less than indirect costs

References ■ Hughes, B., and Cotterell, M. (1999) Software Project Management, 2nd edition, McGraw-Hill. (slides) ■ Pfleeger, S.L. (1998) Software Engineering: Theory and Practice, Prentice Hall. ■ Roberta Russell & Bernard W. Taylor, III (2006) Operations Management - 5th Edition, John Wiley & Sons (slides) ■

http://miha.ef.uni- lj.si/_dokumenti3plus2/195166/norm-tables.pdf

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