Mechanicas Lectures

LECTURE 10 LECTURER ENGR

ALI [email protected]

DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST

DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST

PLANNING ENGINEERING AND

PROJECT MANAGEMENT

Topics Covered

Program Evaluation and Review Technique (Pert)

Project Crashing

Sample Problems

Pert calculates the expected durations for all activities and then does an ordinary CPM calculation of the network using these expected values as durations. The expected value and variance can be calculated as:

TE=(a + b + 4m)/6 (already discussed)

Var=V= 1/36 (b - a)

The variance is a measure of uncertainty of the duration. The larger variance, the larger is the uncertainty.

Program Evaluation and Review Technique

2

Standard deviation = = = = ( V )

ProbabilityPr = Φ (D – T) /

D= deadline / desired completion time

T= project completion time

Φ= normal distribution (from table)

Program Evaluation and Review Technique

1/2

Problem 09Problem 09

Activity Preceding Activity

Duration (weeks)

A - 10

B - 07

C - 12

D A 18

E B 14

F B 13

G C 16

H D, E 12

I F, G 06

(Use Pert Technique on P-04)

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

Activity

m a b

AA 1010 99 1717

BB 77 55 99

CC 1212 1010 2020

DD 1818 1616 3232

EE 1414 1313 2121

FF 1313 1010 1616

GG 1616 1515 2323

HH 1212 1111 1919

II 66 55 77

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

Activity

m a b TE

AA 1010 99 1717 1111

BB 77 55 99 77

CC 1212 1010 2020 1313

DD 1818 1616 3232 2020

EE 1414 1313 2121 1515

FF 1313 1010 1616 1313

GG 1616 1515 2323 1717

HH 1212 1111 1919 1313

II 66 55 77 66

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

Activity

m a b TE Var

AA 1010 99 1717 1111 1.781.78

BB 77 55 99 77 .44.44

CC 1212 1010 2020 1313 2.782.78

DD 1818 1616 3232 2020 7.117.11

EE 1414 1313 2121 1515 1.781.78

FF 1313 1010 1616 1313 11

GG 1616 1515 2323 1717 1.781.78

HH 1212 1111 1919 1313 1.781.78

II 66 55 77 66 .11.11

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

The network is calculated using the expected

values (TE). The critical path is A-D-H.

Project completion time T= Ta+Td+Th

= 11+20+13 = 44

Variance V= Va + Vd + Vh

= 1.78+7.11+1.78= 10.67

The variance as such does not provide much practically useful information about uncertainty. It is used to calculate probability, which can then be used as a decision parameter.

For example, project manager would like to know what is the probability of reaching the 40-days deadline calculated by CPM method.

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

Standard deviation= = (V) = (10.67) =

3.266

ProbabilityPr = Φ (D – T) /

D= deadline / desired completion time=40

T= project completion time=44

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

1/2 1/2

Pr = Φ (40 – 44) / 3.266

= Φ (-1.23) = 0.11

The chance of meeting the

deadline is 11 percent only.

What deadline project manager should give if he/she wants 90 percent probability of finishing on or before the deadline?

If this deadline is D, using the formula

Problem 09 (Pert Solution)Problem 09 (Pert Solution)

0.90 = 0.90 = ΦΦ (D – 44) / 3.266 (D – 44) / 3.266

ΦΦ(1.28)= (1.28)= ΦΦ (D – 44) / 3.266 (D – 44) / 3.266

D= 48.2D= 48.2In order to have 90 percentguarantee against a delay, the deadline should be 49 days.

R

E

S

U

L

T

Program evaluation and review technique (PERT) allows activity duration with uncertainty. It assumes that there is no underlying connection leading to simultaneous duration variation of two or more activities.

If activity X is delayed, this does not lead to a similar delay of activity Y. This is, of course, a questionable assumption. Quite often there are activities that are connected.

For example, a delay of an activity may be caused by a shortage of labor. In this case it is reasonable to believe that this is the case for other activities performed in the same region.

Comments on Pert

Crashing means reducing project time (total project completion time)

The objective of crashing is to reduce the entire project completion time by a certain amount at the least cost.

Crashing is achieved by reducing the activity (s) times in a network.

Activity time can be reduced by utilizing additional resources i-e additional labor, more equipment and so on.

Project CrashingProject Crashing

Although shortening or crashing activity times can be expensive; doing so might be worthwhile. This is also referred as cost-time trade-offs.

Project CrashingProject Crashing

Project CrashingProject Crashing

Crash Cost and Crash Duration

Crash cost is defined as the cost associated with the fastest way of doing something and results in what we call the crash duration.

Normal Cost and Normal Duration:

Normal cost is defined as the cost associated with the most economical way of doing something and results in what we call the normal duration.

Project CrashingProject Crashing

Rules:

Crash the activities on the critical path. As a result of crashing, a parallel non-critical path may become new critical path.

Start crashing with least cost of crashing per unit time, crash the most costly activity if required, last of all.

Project CrashingProject Crashing

16

4

2

3

3 4

32

Total Project

Time 07 days

Reduce it

to 06 days

Project CrashingProject Crashing

Act- Act- ivityivity

NormNormalal

TimeTime

(days)(days)

NormNormalal

CostCost

($)($)

CrasCrashh

TimeTime

(days(days))

CrasCrashh

CostCost

($)($)

CostCost

TimeTime

1-21-2 33 4040 11 8080 (80-40)/(3-1)(80-40)/(3-1)

=20=20

1-31-3 22 5050 11 120120

1-41-4 66 100100 44 140140

2-42-4 44 8080 22 130130 (130-80)/(4-2)(130-80)/(4-2)

=25=25

3-43-4 33 6060 11 140140

crash cost per unit timecrash cost per unit time

Project CrashingProject CrashingActivity 1-2 and Activity 2-4; both are on critical path. The project completion time can be reduced to six days by crashing either 1-2 or 2-4 by one day.

It costs $20 per day to crash activity 1-2

and $25 per day to crash activity 2-4.

Therefore it is less costly to crash activity 1-2 by one day in order to achieve an over all project completion time of six days.

Problem 10The data of activities, activity precedence, activity normal and crash times and costs for a pipe line renewal is given in the table on next slides.

a) Develop a network for the project.

b) Determine the project completion time with normal time of activities.

c) Crash the project to reduce the project completion time with least incremental cost.

Note: Time is given in days and cost in rupees.

Problem 10Problem 10

Activity

Prece-dence

Normal

time

Normal cost

Crash time

Crash cost

A - 3 - 1 -

B - 4 - 4 -

C A 2 900 1 1000

D C 1 300 1 300

E D 5 2500 3 3000

F D 9 900 5 1200

G E 5 3500 2 5000

H B, D 1 300 1 300

I B, D 2 900 1 1200

Go on next slide for remaining data of Problem 10

Remaining Problem 10

Activity

Prece-dence

Normal

time

Normal cost

Crash time

Crash cost

j H, I 4 1200 2 2000

K G, J 6 4200 3 5400

L K 2 800 1 1000

M F, H, I 2 500 1 800

N L, M 2 500 1 800

O N 2 400 1 600

P L, M 4 1200 2 1600

Q N, P 2 400 1 600

R O, Q 2 400 1 500

Remaining Problem 10

Discussion