Project Management - Part 2

Overview

What happens when activity times in a project are:

Not fixed Crashing the project

Not known with certainty PERT (Project Evaluation and Review Technique)

Project Crashing

Estimated time is fixed... no more.

Can reduce the length of time of a project through additional resources manpower, equipment

Direct cost of activity is always increased

Project Crashing: Motivation

Need to reduce time of project because: Requirement to complete in specified time frame Economic advantage

Three kinds of costs Crash costs (activity direct costs) Administration costs (or project indirect costs) Penalty costs

Incur crash costs to avoid administration and penalty costs

Calculating Crash Costs per Unit Time

CrashTime =3

Normal Time =7

Crash Cost = $9,000

Normal Cost = $3,000

Crash Cost / Unit Time = 9000 – 30007 – 3

= $1,500

Project Crashing: Procedure

Always crash one period at a time!

1. Identify critical activities

2. Select least expensive to crash

3. Savings? Implement if so. Update all paths

4. Repeat 1-3 until no cost savings are possible

2 1

5 3

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

ABCD AXYZ

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

NormalDuration:

MinimumDuration:

Path Duration

1615 Which

activity should we

crash?

(per period)

ABCD 16AXYZ 15

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

5 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

ABCD 16AXYZ 15

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

5

2 1

3NormalDuration:

MinimumDuration:

Path Duration

(per period)

ABCD 16AXYZ 15

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

5 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

5 5 3

3

ABCD 16AXYZ 15

Choose B because it is the cheapest of the three alternatives (A, B, or C)

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

5 3

12

NormalDuration:

MinimumDuration:

Path Duration

B

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

100 500 400 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

3

12

NormalDuration:

MinimumDuration:

Path Duration

Cost Save Net Cumul

Which activity(s) should we crash

next?

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

3

2 1

4NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

4

2

3

1

3

25

2

4 5 3

3

ABCD 16 15AXYZ 15 15

Cost 100Save 500Net 400Cumul 400

B

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

4 3

3

25

2

5

3

4 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

BY

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

B BY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

3

2 1

NormalDuration:

MinimumDuration:

Path Duration

Which activity(s) should we crash

next?

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

B BY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

3 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

B BY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

3 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

B BY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

B BY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

3 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

3

25

2

3 5 3

3

ABCD 16 15 14AXYZ 15 15 14

Cost 100 225Save 500 500Net 400 275Cumul 400 675

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

3

25

2

5

3

3 3

2 1

NormalDuration:

MinimumDuration:

Path Duration

B BY A

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

2

25

2

3 5 3

3

ABCD 16 15 14 13AXYZ 15 15 14 13

Cost 100 225 250Save 500 500 500Net 400 275 250Cumul 400 675 925

B BY A

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

2

25

2

5

3

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

3

2

3

1

2

25

2

3 5 3

3

ABCD 16 15 14 13AXYZ 15 15 14 13

Cost 100 225 250Save 500 500 500Net 400 275 250Cumul 400 675 925

B BY A

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

3 3

2

25

2

5

3

NormalDuration:

MinimumDuration:

Path Duration

Which activity(s) should we

crash next?

(per period)

A

B C D

X Y Z

3 2

2

2

3

1

2

25

2

3 4 3

3

ABCD 16 15 14 13 12AXYZ 15 15 14 13 12

Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100

B BY A CY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

2 3

2

25

2

4

3

NormalDuration:

MinimumDuration:

Path Duration

(per period)

A

B C D

X Y Z

3 2

2

2

3

1

2

25

2

3 4 3

3

ABCD 16 15 14 13 12AXYZ 15 15 14 13 12

Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100

B BY A CY

Crash Costs

A -$250

B-$100

C-$200

D-

X-$350

Y-$125

Z-$325

Admin Cost = $500

A

B C D

X Y Z

3 2

2 3

2

25

2

4

3

NormalDuration:

MinimumDuration:

Path Duration

Which activity(s)

should we crash

next?

(per period)

A

B C D

X Y Z

3 2

2

2

2

1

2

25

2

3 3 3

3

ABCD 16 15 14 13 12 11AXYZ 15 15 14 13 12 11

Cost 100 225 250 325 525Save 500 500 500 500 500Net 400 275 250 175 -25Cumul 400 675 925 1100 1075

B BY A CY CZ

We lose $$, so do not crashCZ

Admin Cost = $500

A

B C D

X Y Z

3 2

2 2

2

25

2

3

3

NormalDuration:

MinimumDuration:

Path Duration

A

B C D

X Y Z

3 2

2

2

3

1

2

25

2

3 4 3

3

ABCD 16 15 14 13 12AXYZ 15 15 14 13 12

Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100

B BY A CY

A

B C D

X Y Z

3 2

2 3

2

25

2

4

3

NormalDuration:

MinimumDuration:

Path DurationMost economicalduration

Achievedby crashing

Spent $900 in increased direct costs

Avoided $2000 inadministration costs

Net savings

PERT (CPM With 3 Time Estimates)

In past, time estimate is firm Now… task duration is uncertain

New activity Natural variance

Use 3 time estimates to deal with uncertainty a = most optimistic estimate m = most likely b = most pessimistic

Formulas

et (expected time) = (a + 4m + b)/6

σ (standard dev) = (b - a)/6 σ 2 (variance) = (b - a)2/36 = [(b - a)/6]2

Z = (D - et)/σ

How many standard deviations awayD is from et

Activity List for Example Problem

Activity DescriptionImmediate

PredecessorsRequired Activity

Time (weeks)

ABCDEFGHIJ

Select office siteCreate organization and financial planDetermine personnel requirementsDesign facilityConstruct the interiorSelect personnel to moveHire new employeesMove records, key personnel, etc.Make financial arrangementsTrain new personnel

--B

A,CDCFFB

H,E,G

3534824253

Mean and Variance

Activity a m b ET ó ó2

ABCDEFGHIJ

132241

2.514

1.5

34.5347

1.53.5253

5946165

7.536

4.5

3534824253

2/31

1/32/32

2/35/61/31/31/2

4/91

1/94/94

4/925/361/91/91/4

et = (a + 4m + b)/6σ = (b - a)/6σ 2 = (b - a)2/36 = [(b - a)/6]2

(1+4·3+5)/6

(5-1)/6

[(5-1)/6]2

et =

=

=

For activity A,

et

Path Length

Path length is the sum of expected times of activities on the path not sum of most likely times

Longest expected path length is critical Path length is uncertain, and so is project

duration Path has variance equal to sum of variances of

individual activities on path

A

B

D

C

E

F

G

H

I

J

0 3

0 5 5 8

5 10

8 12

8 10

12 20

10 12

10 14 20 23

20 23

18 23

18 20

16 20

12 20

5 8 14 16

8 12 5 8

0 5

A

B

D

C

E

F

G

H

I

J

0 3

0 5 5 8

5 10

8 12

8 10

12 20

10 12

10 14 20 23

20 23

18 23

18 20

16 20

12 20

5 8 14 16

8 12 5 8

0 5

0

0.1

0.2

0.3

0.4

et = 2322

If we want to know the probability of completing the project in 22 weeks or less:

Calculating probability of different completion time

Calculations

et = 23 weeks

σ2CP =2

BCDEJ

Z = (D - et)/σ CP = (22-23)/2.4095 = -0.42 Take .42 to the Z table => 1-.66 = .34

Beware - never add standard deviations!

= 5.8056= σ 2B + σ 2

C + σ 2D + σ 2

E + σ 2J

22 is 0.42 SD below Mean of 23

0

0.1

0.2

0.3

0.4

et = 2322

34% chance < 22 (table)

50% chance > 23

16% chance between 22 and 23