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MASTER OF BUSINESS ADMINISTRATION - MBA SEMESTER 4

ASSIGNMENT SET 1

SUBJECT CODE: PM0006

QUANTITATIVE METHODS IN PROJECT MANAGEMENT

1. Explain the importance of business forecasting. List & explain the steps in the PERT

planning process.

Answer :

Importance of Business Forecasting

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 ishighly 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.

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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 thedata 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

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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 andduration.

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 thr 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.

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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 ach 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

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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 activitys 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.

2. Write a short note on MS projects and explain in brief some of the important

terminologies used in MS Project.

Answer:

MS Project is a tool to help you to plan projects, manage and update project information, and

communicate the status once the project is under way.

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The details of the project tasks and associated resources are entered into the system as a new

project. The system will then display the data in such a way that the relationships of the tasks and

their time scales can clearly be seen and potential problem areas identified.

Project data can be entered and/or viewed in a number of ways; the three principal formatsare charts , forms , and sheets .

Charts can be either Gantt Charts or Network Diagram Charts both of which are a diagrammatic

representation of the project data

Forms contain the data relevant to a single specific task or resource.

Sheets are a table of all the Tasks or all the Resources that are part of the Project.

The above can be displayed separately or in any combination of two, for example,

You can combine any two single-pane views on the screen to create a combination view. In a

combination view, the information in the bottom relates only to the task or resources in the top

view. The reason for having combination views is to make the job of entering and analysing

information easier.

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At the heart of every project management system is a scheduling algorithm . An algorithm is a

mathematical or logical equation that solves a complex problem by breaking down the problem

into simple steps. When scheduling resources and parameters are entered into it, the scheduling

algorithm produces a project schedule that would be impossible for you to produce manually.

This Input/Output model is displayed below.

The Input/Output Model

In Microsoft Project, however complex your project may be, you can vary only information

regarding tasks or resources. The information you provide is fed into the Black Box or

algorithm, to provide you with a schedule in the form of a Gantt chart, Network Diagram Chart,

or Resource Graph. In summary, the seven or eight parameters that you enter result in output that

is a schedule displayed on various views and forms.

The project management industry uses specific language and terminology. Some of these terms

are illustrated below.

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Clarification of Project Management Terminologies

In the illustration above, two tasks have a relationship. Task A is the predecessor task, and Task

B is the successor task . Both of these tasks are considered to be non-critical because they both

have flexibility. Lets focus on Task A. EA marks the earliest possible time Task A can start. SS

marks the scheduled start time for Task A. By default, all tasks are scheduled to start at the

earliest possible time, unless you specify otherwise. In the example above, Task A is scheduled to

start later and therefore has been delayed. SE marks the scheduled end time for Task A, and LE

marks the latest possible time Task A can end. Both of these tasks have slack, the amount of time

a task can slip before it affects another tasks dates or the project finish date. Free slack is theamount of time Task A can be delayed before affecting the start time of Task B, and total slack is

the amount of time that Task A can be delayed before affecting the finish date of the project.

The summary task summarizes Tasks A and B.

Critical tasks, not shown above, have no slack; therefore, delaying this type of task would mean

delaying the project. A critical path is a series of critical tasks. All tasks on a critical path must be

completed on time for the project to finish on time. If one task on a critical path is delayed, then

the project is delayed. In Microsoft Project, a critical path is shown on the Gantt chart and the

Network Diagram Chart in red.

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Some important terminologies in MS Projects

Actual Usage A measure of the resource expended in completing or partially completing a task.

ALAP

Refers to a task that should be started As Late As Possible, using all the free-float time

available.

ASAPUsed to indicate a task that should be started As Soon As Possible, taking into accountthe start date of the project and its predecessor tasks.

Baseline

The original project plan, including the time schedule and resource and cost allocations.The baseline is used for comparing projected values to actuals, and facilitates the trackingand analysing of a projects progress.

Cost Variance

A project tracking function recording the difference between the budgeted cost of thework performed and the actual cost. Values below the baseline show an overspend and

positive values denote cost savings.

Critical PathThe sequence of tasks or activities whose schedules and durations directly affect the dateof overall project completion.

Earned ValueThis is a measure of a projects performance, and is calculated by multiplying a tasks

planned cost by the percentage of work completed.

Float (slack)The amount of time by which a non-critical task can be delayed before it affects another tasks schedule.

Gantt chart

A graphical representation of a project schedule showing each task as a bar, the length of which is proportional to its duration. Many project management packages use aspreadsheet section to the left of the Gantt chart to display additional information.

Hammock Task A task whose duration is calculated based on the time span between its predecessor andsuccessor activities.

Histogram A bar chart that shows resource workloads over a time period.

LagThe amount of time between the finish of a predecessor task and the start of a successor task.

Lead The amount of time that a task is permitted to start before its predecessor is finished.

Loading

A measurement of resource usage on a task per unit of time. Different methods of loadingmay be used depending on whats available in your project management application andwhats applicable for your particular project.

Loading(back) A loading pattern that allocates resource usage as late in the task as possible.

Loading (contour)The contour-loading pattern assesses which resources are left over after allocation to thecritical tasks and spreads these resources among the remainder.

Loading(fixed) When using fixed-loading algorithms, you specify the actual amount of resource allocated

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to the encompassing tasks.

Loading(front) Front loading systems will attempt to allocate resources as early in the task as possible.

Loading(uniform)This loading pattern allocates the resource usage on a by day basis in a task. This willusually be done without causing any one task to be over committed.

MilestoneA project event that represents a checkpoint, a major accomplishment or a measurablegoal.

Negative floatRefers to an unscheduled delay before an actual task start time that must be recovered if the project is not to be delayed.

OBS codes

Organisational Breakdown Structure codes are used to identify tasks by resource groupsin a hierarchical format. OBS codes are often used to reflect departmental structure in acompany or code of accounts, and can also be used for filtering tasks.

Network Diagram

Project Evaluation and Resource Tracking charts, also called network diagrams. Network Diagrams are a graphical depiction of task dependencies, and resemble flow charts.Dependencies are shown by connecting lines or arrows indicating the work flow.

PredecessorIn dependency relationships, the predecessor is the task that must be started or completedfirst.

Project ManagementBest defined as a body of knowledge, a set of principles, or techniques dealing with the

planning and control of projects.

ResourceAny person, group of people, item or equipment, service or material used inaccomplishing a project task.

Resource Levelling

The process of resolving resource conflicts. Most project management programs offer anautomated resource levelling routine that delays tasks until the resources assigned to themare available.

Resource Driven

Task durations determined by the program and based on the number of an allocation of resources, rather than the time available. Both individual tasks and entire projects can beresource-driven.

Sub-project

A group of activities which are treated as a single task in a master project schedule.Subprojects are a way of working with multiple projects that keep all the data in one filerather than in independent files.

Successor

In a dependency relationship between two tasks, the successor is the task that must await

the start or completion of the other.

WBS codes

Work Breakdown Structure codes are used to identify tasks in a hierarchy. Many projectmanagement applications associate these codes with an outline structure. WBS codes can

be used to filter the project schedule for tracking and reporting purposes.

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The key to managing cash flow is to ensure that cash comes in faster than it goes out. If sufficient

cash isnt available to meet expenses, money must be borrowed. Borrowing increases project cost

because any money borrowed must be paid back to the lender, along with a charge for borrowing

the money the interest. The flow of cash coming in from the customer can be controlled by the

terms of payment in the contract. From the contractors point of view, its desirable to receive

payments from the customer early in the project rather than later. The contractor might try to

negotiate payment terms that require the customer to do one or more of the following:

Provide a down payment at the start of the project.This requirement is reasonable when the

contractor needs to purchase a significant amount of materials and supplies during the early

stages of the project.

Make equal monthly payments based on the expected duration of the project. Cash outflow

usually is smaller in the early stages of a project. If more cash is coming in than is going out

during the early part of the project, the contractor may be able to invest some of the excess cash

and earn interest. The saved funds can then be withdrawn to meet the greater cash outflow

requirements later in the project.

Provide frequent payments, such as weekly or monthly payments rather than quarterly

payments.

The worst scenario from the contractors point of view is to have the customer make only one

payment at the end of the project. In this situation, the contractor will need to borrow money to

have cash available to meet expenses throughout the project.

MASTER OF BUSINESS ADMINISTRATION - MBA SEMESTER 4

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ASSIGNMENT SET 2

SUBJECT CODE: PM0006

QUANTITATIVE METHODS IN PROJECT MANAGEMENT

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

required for PERT & CPM.

Answer :

Relationship between PERT and CPM

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 plannedshutdown 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

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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.

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2. Describe Time-Cost optimization Algorithm.

Answer :

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.

What do you understand by a decision tree. Write a short note on project crashing

using network analysis.

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Decision Tree on choosing between two products

Figure 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.

Network Analysis

Network Analysis is a core technique available to the Project Managers for planning and

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controlling their projects. It has wide application in the architectural projects, transportations

projects etc. Network analysis is a mathematical model of analyzing complex problems, as

in transportation or project scheduling, by representing the problem as a network of lines

and nodes. It can also be described as an analytic technique used during project planning to

determine the sequence of activities and their interrelationship within the network of

activities that will be required by the project. It involves breaking down a complex projects

data into its component parts (activities, events, durations, etc.) and plotting them to show

their interdependencies and interrelationships. It real-life scenario, it can be used as a data

processing method using topologically linked data such as street maps or river networks

with the purpose of determining the routes between geographic locations, and other analyses

requiring the consideration of path and direction.

Networks

A network is a set of points, called nodes, and a set of curves, called branches (or arcs or

links), that connect certain pairs of nodes. In network analysis, only those networks are

considered in which a given pair of nodes is joined by at most one branch. Nodes are usually

denoted by the uppercase letters and branches are denoted by the nodes they use to connect.

The following figure shows a network with 5 nodes.

Network

Figure is a network consisting of five nodes, labeled A through E, and the six branches are

defined by the curves AB, AC, AD, BC, CD and DE.

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A branch is oriented if it has a direction associated with it. Schematically, directions are

indicated by the arrows. The arrow of the branch AB in Figure signifies that this branch is

directed from A to B. Any movement along this branch must originate at A and it must end

at B. Any movement in the direction B to A will not be permitted.

If the two branches have a common node, then these two branches are said to be connected.

In figure, branches AB and AC are connected, but branches AB and CD are not connected.

A path is a sequence of connected branches such that in the alternation of nodes and

branches, no node is repeated. A network is said to be connected if for each pair of node in

the network there exists at least one path joining the pair. If the path is unique for each pair

of nodes, the connected network is called a tree. Equivalently, a tree is a connected network

having one more node than branch.

In figure, {ED, DA, AB} is a path, but the sequence of connected branches {CA, AD, DC,

CB} is not a path, as node C occurs in it twice. The network is connected, and remains

connected even if branches DA and AB are deleted. However, in case of the deletion of the

DE, the network would not remain connected, since there would not be a path linking D

with E. Since D and C are joined by the three paths, the network is not a tree.

Minimum-Span Problems

A minimum-span problem involves a set of nodes and a set of proposed branches, none of

them oriented. Each proposed branch has a nonnegative cost associated with it. The

objective is to construct a connected network that contains all the nodes and is such that the

sum of the costs associated with those branches actually used is minimum. It is to be

assumed that there are enough proposed branches to ensure the existence of a solution. The

minimum-span problem can be solved by a tree. If two nodes in a connected network are

joined by two paths, one of these paths must contain a branch whose removal does notdisconnect the network. Removing such a branch leads to the lowering of the total cost. A

minimal spanning tree may be found by initially selecting any one node and determining

which branch incident on the selected node has the smallest cost. This branch is accepted as

part of the final network. The network is to be then completed iteratively. At each stage of

the iterative process, the attention is to be focused on the nodes which are already linked

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together. All branches linking these nodes to the unconnected nodes are considered, and the

cheapest such branch is identified. In case of the ties, the branches are to be chosen

arbitrarily in order to break the tie. The branch is accepted as part of the final network. The

iterative process is to be terminated when all the nodes have been linked. In case that all the

costs are distinct, it can be proved that the minimal spanning tree is unique and is produced

by the above algorithm for any choice of the starting node.