PM0015 - Quantitative Methods in Project Management - Set 2

SIKKIM MANIPAL UNIVERSITY

DEPARTMENT OF DISTANCE EDUCATION

ASSIGNMENT

SEMESTER 4

NAME : ABHISHEK JAIN

ROLL NUMBER : 511035358

LEARNING CENTER : 02882

SUBJECT NAME :

QUANTITATIVE METHODS IN

PROJECT MANAGEMENT

MODULE NO : SET 2

DATE OF SUBMISSION AT THE

LEARNING CENTRE

: 31-MAY-11

FACULTY SIGNATURE :

MBA 4th Sem Assignment Quantitative Methods in Project Management – PM0015 - Set 2

2011 Abhishek Jain - 511035358 Page 2 of 7

Master of Business Administration-MBA Semester 4

Project Management – PM0015 Assignment Set - 2

Q.1 Explain Relationship between PERT & CPM. Also describe the framework required for PERT & CPM

Ans: PERT and CPM are the project management techniques created for the need of the Western

and Military Establishments to plan, schedule and control the complex projects. CPM/PERT

developed along two parallel streams – one industrial and the other military.

CPM was first introduced by M. R. Walker and J. E. Kelly. This computation was designed for the

UNIVAC-I computer. The first test was made in 1958, when CPM was applied in the construction of a

new chemical plant. In March 1959, the CPM was applied in the planned shutdown at the Du Pont

works in Louisville, Kentucky. The introduction of CPM greatly reduced the unproductive time from

the 125 hours to the 93 hours.

PERT was introduced first for the POLARIS missile program by the Program Evaluation Branch of the

Special Projects office of the U.S. Navy. The calculations were so arranged so that they could be

performed in the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia. Rather

than giving technical benefits, it is found that PERT/CPM provides a focus around which managers

could brain-storm and can put their ideas. PERT/CPM is a great communication medium by which

thinkers and planners at one level can communicate their ideas, their doubts and fears for another

level. Another important feature of the PERT/CPM is that it is a useful tool for evaluating the

performance of the individuals and the teams. There are many variations of CPM/PERT which have

been useful in planning costs, scheduling manpower and machine time. CPM/PERT can answer

following important questions –

How long will the entire project take to be completed? What are the risks involved in this?

Which are the critical activities or tasks in the project which could delay the entire project if they

were not completed on time?

Is the project on schedule, behind schedule or ahead of schedule?

If the project has to be finished earlier than the planned, what is the best way to do this at the least

cost?

The Framework for PERT and CPM

There are six steps which are common to both the techniques. The procedure is as follows –

1. Define the Project and all of its significant activities or tasks. The project (made up of several

tasks) should have only a single start activity and a single finish activity.

2. Develop the relationships among the activities. Decide which activities must precede and which

must follow others.

3. Draw the ‘Network’ connecting all the activities. Each activity should have unique event

numbers. Dummy arrows are used where required to avoid giving the same numbering to two

activities.

4. Assign time and/or estimates to each activity.

5. Compute the longest time path through the network. This is called the critical path.

6. Use the network to help plan, schedule, monitor and control the project.

The key concept used by both in PERT as well as CPM is that a small set of activities, which make up

the longest path through the activity network control the entire project. If these ‘critical’ activities

could be identified and assigned to the responsible persons, management resources could be

optimally used by concentrating on the few activities which determine the fate of the entire project.

The non-critical activities can be re-planned, rescheduled and resources for them can be

reallocated flexibly, without affecting the whole project. The five important questions that should be

asked before the preparation of an activity network are the following –

Is this a Start Activity?

Is this a Finish Activity?

What activity precedes this?

What activity follows this?

What activity is concurrent with this?

Some activities are serially linked. The second activity can begin only after the first activity is

completed. In the certain cases, the activities are concurrent, because they are independent of

each other and can start simultaneously. This is essentially the case in organizations which have



supervisory resources so that work can be delegated to various departments that will be responsible

for the activities to be performed and their completion as per the planning.

Q.2 Describe Time-Cost optimization Algorithm.

Ans: Time-Cost Optimization Algorithm

The process of shortening a project is called crashing and is usually achieved by adding extra

resources to an activity. The steps involved in the project crashing are the following –

Step 1 – Schedule a project with all its activities at their normal duration as well as identify the critical

path and critical activities

Step 2 – Calculate the cost slope for the different activities and rank the activities in the ascending

order of the cost slope

Step 3 – Crash the activities on the critical path as per the ranking, i.e., activity having lower cost

slope would be crashed first to the maximum extent possible

Step 4 – As the critical path duration is reduced by crashing in Step 3, other paths may also become

critical, i.e., we get parallel critical paths. This means that the project duration can be reduced duly

by simultaneous crashing of activities in the parallel critical paths

Step 5 – Crashing as per Steps 3 and 4, one reaches a point when further crashing is either not

possible or does not result in the reduction of crashing of project duration

Step 6 – Compute the total project cost by adding corresponding fixed cost to the direct cost, which

is obtained by adding the crashing cost cumulatively to the normal cost

Q.3 Explain the importance of business forecasting. List & explain the steps in the PERT planning

process.

Ans: Because of the variation of the economic and business conditions over time, managers must

find ways to keep abreast of the effects that such changes will have on their organizations. One

technique which is very much useful in planning for the future needs is the forecasting. Although

numerous forecasting methods have been devised, they all have one common goal – to make

predictions of the future events so that the projections can then be incorporated into the planning

and strategy process. The need for forecasting encompasses the modern society. Forecasting is

highly essential in our modern society to take necessary precautionary action. For example, officials

in government must be able to forecast such things as unemployment, inflation, industrial

production, and expected revenues from personal and corporate income taxes in order to

formulate policies. Marketing executives of a large retailing corporation must be able to forecast

product demand, sales revenues, consumer preferences, inventory and so on, in order to make

timely decisions regarding current and future operations and to assist in strategic planning activities.

The directors of an airline must be able to fill equipment and personnel needs based on forecasts of

the number of passengers and revenues. Administrators of a college or university must make

forecasts of student enrolments and consider the trends in curricula that are based on technological

developments in order to plan for the construction of dormitories and other academic facilities, plan

for student and faculty recruitment, and make assessments of other needs. There are two common

approaches to forecasting – qualitative and quantitative. Qualitative forecasting methods are

especially important when historical data are unavailable. Qualitative forecasting methods are

considered to be highly subjective and judgmental.

Quantitative forecasting methods make use of historical data. The goal of these methods is to study

what has happened in the past in order to better understand the underlying structure of the data

and thereby provide a way of predicting future values. Quantitative forecasting methods can be

subdivided into two types – time-series and casual. Time-series forecasting methods involve the

projection of future values of a variable based entirely on the past and present observations of that

variable. For example, the daily closing prices of a particular stock on the New York Stock Exchange

constitute a time series. Other examples of economic or business time series are the monthly

publication of the Consumer Price Index, the quarterly statements of gross domestic product (GDP),

and the annually recorded total sales revenues of a particular company.

Casual forecasting methods involve the determination of factors that relate to the variable to be

predicted. These include multiple regression analysis with lagged variables, econometric modelling,

leading indicator analysis, diffusion indexes, and other economic barometers.

Steps in the PERT Planning Process

PERT planning involves the following steps –

1. Identification of the specific activities and the milestones



2. Determination of the proper sequence of the activities

3. Construction of a network diagram

4. Estimation of the time required for each activity

5. Determination of the critical path

6. Updating of the PERT chart as the project progresses

1. Identification of the Specific Activities and Milestones

The activities are the tasks that are required to be completed in the project. The milestones include

the events marking the beginning and the end of one or more activities. It is helpful to list the tasks in

a table that in later steps can be expanded to include information on the sequence and duration.

2. Determination of the Activity Sequence

This step may be combined with the activity in the identification step since the activity sequence is

evident for some tasks. Other tasks may require more analysis in order to determine the exact order

in which they must be performed.

3. Construction of the Network Diagram

Using the activity sequence information, a network diagram can be drawn showing the sequence of

the serial and parallel activities. For the original activity-on-arc model, the activities are depicted by

arrowed lines and milestones are depicted by circles of ‘bubbles’. Manual drawings may require

several drafts for correct portrayal of the relationships among the activities. Software packages

simplify the step by automatically converting the tabular information into a network diagram.

4. Estimation of the Activity Times

Weeks or days are commonly used unit of time for activity completion, but any consistent unit of

time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity

completion times. For each activity, the model usually includes three time estimates –

Optimistic time – Generally optimistic time represents the shortest time in which the activity can be

completed. It is the common practice to specify optimistic times to be three standard deviations

from the mean so that there is approximately a 1% chance that the activity will be completed within

the optimistic time.

Most likely time – Most likely time is the completion time having the highest probability. This time is

different from the expected time.

Pessimistic time – The pessimistic time is the longest time that an activity might require. Three

standard deviations from the mean are commonly used for the pessimistic time.

PERT assumes a beta probability distribution for the time estimates. For the beta distribution, the

expected time for each activity can be approximated using the following weighted average –

Expected time = (Optimistic + 4 X Most likely + Pessimistic) / 6

This expected time may be displayed on the network diagram.

To calculate the variance for each activity completion time, if three standard deviation times were

selected for the optimistic and pessimistic times, then there are six standard deviations between

them, so the variance is given by – [(Pessimistic – Optimistic)/6]2.

5. Determination of the Critical Path

The critical path is determined by adding the times for the activities in each sequence and

determining the longest path in the project. The critical path determines the total calendar time

required for the project. If activities outside the critical path speed up or slow down (within limits), the

total project time does not change. The amount of time that a non-critical path activity can be

delayed without delaying the project is referred to as slack time.

If the critical path is not immediately obvious, it may be helpful to determine the following four

quantities for each activity –

ES – Earliest Start Time

EF – Earliest Finish Time

LS – Latest Start Time

LF – Latest Finish Time

These times are calculated using the expected time for the relevant activities. The earliest start and

finish times of each activity are determined by working forward through the network and

determining the earliest time at which an activity can start and finish considering its predecessor

activities. The latest start and finish times are the latest times that an activity can start and finish

without delaying the project. LS and LF are found by working backward through the network. The

difference in the latest and earliest finish of each activity’s slack. The critical path then is the path

through the network in which none of the activities have slack. The variance in the project

completion time can be calculated by summing the variances in the completion times of the

activities in the critical path. Given this variance, one can calculate the probability that the project



will be completed by a certain date assuming a normal probability distribution for the critical path.

The normal distribution assumption holds if the number of activities in the path is large enough for the

central limit theory to be applied.

Since the critical path determines the completion date of the project, the project can be

accelerated by adding the resources required to decrease the time for the activities in the critical

path. Such a shortening of the project sometimes is referred to as project crashing.

6. Updating of the PERT chart as the Project Progresses

Adjustments in the PERT chart are to be made as the project progresses. As the project unfolds, the

estimated times can be replaced with the actual times. In cases where there are delays, additional

resources may be needed to stay on schedule and the PERT chart may be modified to reflect the

new situation.

Q.4 What do you understand by a decision tree. Write a short note on project crashing using network

analysis.

Ans: A Decision tree (or tree diagram) is a decision support tool that uses a tree-like graph or model

of decisions and their possible consequences, including chance event outcomes, resource costs

and utility. Decision trees have vast applications in operations research and decision analysis for

identifying a strategy most likely to reach a specific goal. It is widely used for project policy decision

making. Another use of decision tree is as a descriptive means for calculating conditional

probabilities.

A decision tree analysis is a specific technique in which a diagram (decision tree) is used for the

purposes of assisting the project leader and the project team in making a difficult decision. The

decision tree is a diagram that presents the decision under consideration and, along different

branches, the implications that may arise from choosing one path or another. The decision tree

analysis is often conducted when a number of future outcomes of scenarios remains uncertain, and

is a form of brainstorming which, when decision making, can help to assure all factors are given

proper consideration.

A decision tree is a logical model represented as a binary (two-way split) tree that shows how the

value of a target variable can be predicted by using the values of a set of predictor variables. It can

be described as an algorithm or a formal step-wise process used in coming to a conclusion or

making a judgment. An example of the decision tree is shown below –

Figure 1: Decision Tree on choosing between two products

Figure 1 describes a decision tree for choosing between two products X and Y. A company has to

decide upon development of two products X and Y. They can develop only one product at a time.

For developing the product X, they have to make an initial investment of INR 2 Lakh, whereas for

developing the product Y, they have to make an initial investment of INR 3 Lakh. Now as per the

decision tree, in case of opting the product X, there is probability of 0.7 that the return in one year

will be INR 1 Lakh and there is probability of 0.3 that the return will be INR 3 Lakh. Now, if the product

Y is opted, there is probability of 0.4 that the return will be INR 2 Lakh after a year and there is

probability of 0.6 that the return will be INR 3 Lakh after a year. Now, after analyzing the decision

tree, it is possible to get an insight of the future prospects (expected returns) of both the products

and accordingly it is possible for the company to choose the most profitable product for

development.

Project Crashing as in question 6 of assignment set 1



Q.5 Describe in brief the various pages of the task information form in the MS Project software.

Ans: Task entry is the main activity in setting up a new project. The tasks which have been identified

at the Design Stage must be entered in this stage. The system will hold task information in a task

database, which we cannot access directly but is used by the system whenever we view task data.

This is one of the two databases the system uses and the other is the resource database. It is

important to understand that the system checks the data that it holds and where the data does not

cross check then the system will generally update the database to make it right. It is important to

keep an eye on this process; this will be discussed in a later section. As each entry is made, the

system will update the appropriate data and views to reflect the entries. The order of entry should be

in the logical progression but this is not essential as it can be changed. Normal Task entry will be by

using the standard Task Sheet. The Gantt View shows the Gantt Chart in the right part of the window

with the Task Sheet in the left part.

Figure 2: Task Information Box / Task Sheet (General Section)

The Task sheet is a view of the selected task with information shown in the columns as follows:

ID: The Task Identification number.

Name: The Name of the Task.

Duration: The time the Task will take including the time units.

Start Date: This is the current Scheduled Start date for the Task. Not the Planned or Actual Start.

Finish Date: The Scheduled Finish date.

Predecessors: The ID numbers for the preceding Tasks that are linked to this Task.

Resources: The names of the resources performing or used in the Task.

Table 1: Information in the Task Sheet

Figure 3: Task Information Sheet (Predecessors Section)



Task Entry Form

One can select the Task Entry view to see the Gantt Chart in the upper pane and the Task Form in

the lower pane. To do this, you have to choose View, More Views, Task Entry.

From the Task Sheet the following entries can be made.

ID: The Task Identification number.

Task Name: The Name of the Task.

Duration: The time the Task will take including the time units.

As the entries are made, the Gantt Chart will automatically be updated to display the tasks.

If someone is using the Task Form, it is possible for him/her to enter and/or view the following:

Name: The name of the task

Duration: The length of time the task will take and the units of time.

Fixed: A check box to specify the start date to be fixed.

Start: The scheduled start date, if this is not entered the system will calculate it from the

data entered and the relationships defined.

Finish: The scheduled finish date, entered or calculated as above.

% Complete: A measure of the completion of the Task if it has been started.

Tables and Descriptions

Resource Table

ID: The identification number of the Resource

Resource Name: The name of the resource.

Units The number of units available for the resource.

Work The amount of work currently assigned to the resource.

Predecessor Table

ID The identification number of the Predecessor.

Predecessor Name: The name of the Predecessor. If this is not entered the system will look it up

using the ID number.

Type: The relationship with the current Task which will be FS, or SS, or FF.

Lag The time delay between the end of the Predecessor the start of the Successor.

Completion of all the fields at entry time is not necessary as more information is added so the system

will update the boxes. It is only necessary to enter the data that has been determined in the design

stage.

In order to enter task descriptions and durations one cell at a time:

In the Task Name column, select the first available cell and type the name of the task.

Press TAB

In the Duration column, type the value of the duration. If the duration is anything other than

days, type m for minutes, h for hours, or w for weeks.

Press ENTER

Press LEFT ARROW to return to the Task Name column and repeat steps 1 through 4 as

required.

Entering task descriptions and durations by selecting a range:

Select the first cell (the numbered cell) of the desired range.

Drag the mouse through the range of cells you want to include.

In the first cell, type the desired information.

Press TAB

In the Duration column, type the appropriate information.

Repeat steps 4 and 5 as required.

It is possible to move to the previous cell without deselecting the range through pressing SHIFT+TAB.

Clicking the mouse inside or outside the range will deselect the range.

Q.6. Describe how you can change the duration of a project task.

Ans: Changing Duration

The default duration is 1day. To change this one can simply overtype with the new value.

Change the durations for each Module to 2d.

When the Wizard appears READ THE INFORMATION then click on the OK button.

Select all the remaining tasks.

Open the Task information box.

Set the duration to 1.5d

Documents

PM0015 - Quantitative Methods in Project Management - Set 2