Imus Institute

College Department

Case Study Number 3

Bautista, Ralph Ephraim I.

Mr. Eulogio T. Catalan

September 10, 2012

Every one of us is fan of different kind of music. Just like the Programs and Arts

Committee of the student Government Association, they love the Bloodless Coup so they will do

anything to get this band no matter what.

This association had tried to invite this group many times. They failed but this time they

already have the Bloodless Coup. The problem is, the band will arrive after 18 days. The group is

starting to plan about the concert that they about to organize.

Just like other events, hindrances occurred in this case. But thank their very good leader.

He keeps on motivating his subordinates so they can generate good decisions. He don’t cram or

panic just like other uneducated leaders.

18 days is not enough to organize a big event like this. They will have a big band in their

own stage. Bloodless Coup is a famous band and they want to bring the band to their fellow

students.

The first problem is the auditorium where the band will perform. Next are the tickets,

hotel arrangements for the accommodation of the band, union negotiations, stage hands, ushers,

press conference, stage set up, advertising and promotions, preliminary act and the sale of the

tickets.

To solve this problem, they need to accomplish all of these in 18 days or shorter. Using

PERT or Project Evaluation and Review Technique method, we are required to show the solution

regarding this case.

What is PERT? PERT is a method to analyze the involved tasks in completing a given

project, especially the time needed to complete each task, and to identify the minimum time

needed to complete the total project.

PERT was developed primarily to simplify the planning and scheduling of large and

complex projects. It was developed for the U.S. Navy Special Projects Office in 1957 to support

the U.S. Navy's Polaris nuclear submarine project. It was able to incorporate uncertainty by

making it possible to schedule a project while not knowing precisely the details and durations of

all the activities. It is more of an event-oriented technique rather than start- and completion-

oriented, and is used more in projects where time, rather than cost, is the major factor. It is

applied to very large-scale, one-time, complex, non-routine infrastructure and Research and

Development projects. An example of this was for the 1968 Winter Olympics in Grenoble which

applied PERT from 1965 until the opening of the 1968 Games.

This project model was the first of its kind, a revival for scientific management, founded

by Frederick Taylor (Taylorism) and later refined by Henry Ford (Fordism). DuPont's critical

path method was invented at roughly the same time as PERT.1

There are Six Steps to PERT.

Define project and prepare work breakdown structure.

Determine relationships and precedence

Draw network diagram of activities

Assign time and/or cost estimates for each activity.

Determine the Critical Path. (Longest path through network)

Use network to plan, schedule, monitor and control.

The chief feature of PERT analysis is a network diagram that provides a visual depiction of

the major project activities and the sequence in which they must be completed. Activities are

defined as distinct steps toward completion of the project that consume either time or resources.

The network diagram consists of arrows and nodes and can be organized using one of two

different conventions. The arrows represent activities in the activity-on-arrow convention, while

the nodes represent activities in the activity-on-node convention. For each activity, managers

provide an estimate of the time required to complete it.

The sequence of activities leading from the starting point of the diagram to the finishing

point of the diagram is called a path. The amount of time required to complete the work involved

in any path can be figured by adding up the estimated times of all activities along that path. The

path with the longest total time is then called the "critical path," hence the term CPM. The

critical path is the most important part of the diagram for managers: it determines the completion

date of the project. Delays in completing activities along the critical path necessitate an extension

of the final deadline for the project. If a manager hopes to shorten the time required to complete

1 http://en.wikipedia.org/wiki/Program_Evaluation_and_Review_Technique

the project, he or she must focus on finding ways to reduce the time involved in activities along

the critical path.

2The time estimates managers provide for the various activities comprising a project involve

different degrees of certainty. When time estimates can be made with a high degree of certainty,

they are called deterministic estimates. When they are subject to variation, they are called

probabilistic estimates. In using the probabilistic approach, managers provide three estimates for

each activity: an optimistic or best case estimate; a pessimistic or worst case estimate; and the

most likely estimate. Statistical methods can be used to describe the extent of variability in these

estimates, and thus the degree of uncertainty in the time provided for each activity. Computing

the standard deviation of each path provides a probabilistic estimate of the time required to

complete the overall project.

Program Evaluation and Review Technique (PERT) Analysis

The first step in solving this problem is to create a chart listing each activity, the

description, the activity's predecessors and the three time estimates.

Optimistic Most Likely Pessimistica m b

A Get an auditorium 2 4 7B Print tickets A 1 2 4C Hotel and Transportation arrangements A 3 5 10D Negotiate with Local Union A 1 3 8E Hire stage hands D 2 4 7F Hire student ushers D 1 3 5G Arrange a press conference C 2 3 4H Set up the stage E 2 3 6I Assign ushers to their jobs F 1 2 3J Advertising and promotion B,K 2 6 12K Hire a preliminary act 4 5 8L Sell the tickets B,K 1 5 12

Activity Description PredecessorsTime (Days)

2 http://www.inc.com/encyclopedia/program-evaluation-and-review-technique-pert.html

The chart shows the activity times for each activity along with the standard deviation

from each time.  From this, one can see that the total project activity time is under the 18 days

that the students need to complete the project in time.  Thus, it seems highly probable that the

activity will be completed in time.  We can also see that activities a, d, e, and h have no slack. 

This indicates that they are part of the critical path.

Activity Time Early Start Early Finish Late Start Late Finish Slack Critical PathProject 15.17

A 4.17 0 4.17 0 4.17 0 YesB 2.17 4.17 6.33 6.67 8.83 2.5C 5.5 4.17 9.67 667 12.17 2.5D 3.5 4.17 7.67 4.17 7.67 0 YesE 4.17 7.67 11.83 7.67 11.83 0 YesF 3 7.67 10.67 10.17 13.17 2.5G 3 9.67 12.67 12.17 15.17 2.5H 3.33 11.83 15.17 11.83 15.17 0 YesI 2 10.67 12.67 13.17 15.17 2.5J 6.33 6.33 12.67 8.83 15.17 2.5K 5.33 0 5.33 4.33 9.67 4.33L 5.5 5.33 10.83 9.67 15.17 4.33

E(t) = tA + tD + tE + tH

= 4.17 + 3.5 + 4.17 + 3.33

E(t) = 15.17

PERT Analysis

Activity Description Immediate Predecessor

Optimistic (a) Most Probable (m)

Pessimistic (b)

A Get an auditorium

------- 2 4 7

B Printing of tickets

A 1 2 4

C Hotel and Transportation Arrangements

A 3 5 10

D Negotiation with local

union

A 1 3 8

E Hiring of stagehands

D 2 4 7

F Hiring of student ushers

D 1 3 5

G Arrange press conference

C 2 3 4

H Set up stage E 2 3 6

I Assign ushers their jobs

F 1 2 3

J Advertising and

promotions

B 2 6 12

K Hiring of preliminary

act

------- 4 5 8

L Selling of tickets

A, K 1 5 12

Computation of Expected Time:

Computation of Variances:

Expected Times and Variances for the Bloodless Coup Concert

Activity a m b t vA 2 4 7 4.17 0.69B 1 2 4 2.17 0.25C 3 5 10 5.5 1.37D 1 3 8 3.5 1.37E 2 4 7 4.17 0.69F 1 3 5 3 0.45G 2 3 4 3 0.11H 2 3 6 3.33 0.45I 1 2 3 2 0.11J 2 6 12 6.33 2.79K 4 5 8 5.33 0.45L 1 5 12 5.5 3.35

Network Diagram:

Start

Finish

A

D

F

Activity Schedule for the Bloodless Coup Concert

Activity Activity Time

Early Start Early Finish

Late Start Late Finish Slack

A 4.17 0 4.17 0 4.17 0B 2.17 4.17 6.34 6.67 8.84 2.5C 5.5 4.17 9.67 6.67 12.17 2.5D 3.5 4.17 7.67 4.17 7.67 0E 4.17 7.67 11.84 7.67 11.84 0F 3 7.67 10.67 10.17 13.17 2.5G 3 9.67 12.67 12.17 15.17 2.5H 3.33 11.84 15.17 11.84 15.17 0I 2 10.67 12.67 13.17 15.17 2.5J 6.33 6.34 12.67 8.84 15.17 2.5K 5.33 0 5.33 4.33 9.67 4.33L 5.5 5.33 10.84 9.66 15.17 4.33

Regardless of the technique you use, the tendency in project estimation is to provide one

number for each estimate. In other words, if you have 100 activities on your schedule, each

B

C

E

I

J

K

G

H

activity would have one estimate associated with it. This is generally viewed as the “most likely”

estimate. In many cases you can be more accurate by applying a simple PERT (Program

Evaluation and Review Technique) model. PERT is an estimating technique that uses a weighted

average of three numbers (see below) to come up with a final estimate.

The most pessimistic (P) case when everything goes wrong

The most optimistic (O) case where everything goes right

The most likely (M) case given normal problems and opportunities

The resulting PERT estimate is calculated as (O + 4M + P)/6. This is called a “weighted

average” since the most likely estimate is weighted four times as much as the other two values.

You’ll notice that the final PERT estimate is moved slightly toward either the optimistic or

pessimistic value - depending on which one is furthest from the most likely. Generally this ends

up moving the final estimate toward the worst case, since the worst case value tends to be further

out from the most likely that the optimistic number.

You can use the PERT estimates two ways. You can provide these three estimates for all

activities in your schedule or you can only use the PERT formula for those activities that are of

high risk. These are the ones where you’re not really sure of the estimate so there’s a wide

variation between the optimistic and pessimistic values.

Speaking of variation - if you subtract your pessimistic value from the optimistic value

and divide the result by six, you would have the standard deviation, which is a measure of the

volatility of the estimate. In our example above, the standard deviation would be 3.34 ((26 - 6) /

6). The larger this standard deviation is, the less confidence you have in your estimate, since it

would mean you have a large range between the optimistic and pessimistic estimates. If the

standard deviation was small, it would mean you were pretty confident in your estimate, since

the optimistic and pessimistic estimates would be close.

Remember the PERT formula and use it to make estimates when you have a high level of

uncertainly.3

3 http://www.techrepublic.com/blog/project-management/use-pert-technique-for-more-accurate-estimates/120

The benefits of using PERT is you can determine the estimated completion date for a

project and help to determine what chance the project has being completed by that date.

The final duration time of 15.17 days is computed from the critical path or activity path

of activity A, D, E, and H. The formula to compute the critical path is E(t) = tA + tD + tE + tH.

You will only get activities with 0 slack values.

This is how you compute or solve problems related to project with specific completion

time.