56050499 pm0011 project planning scheduling

Project Planning & Scheduling – PM0011 of 12

Master of Business Administration-MBA Semester 3

Project Planning & Scheduling – PM0011

Assignment Set-

Q.1 Explain the following

a. Rolling wave planning b. Decomposition

c. Precedence diagramming method d. Dependency determination

Ans:

a. Rolling wave planning: this is a technique which plans as and when the project unfolds. In this

technique the plans are made with the upcoming events.

It is not often possible to foresee the future activities in a project with consistent detail over the

entire period of the project. Therefore, planning is often done in "waves" or stages, with the

activities in the near term planned in detail and the activities in the longer distance of time left

for future detail planning. There may in fact be several planning waves, particularly if the precise

approach or resource requirement is dependent or conditioned on the near-term activities. Such

a planning approach is commonly called rolling wave planning.

Rolling Wave Characteristics

The fact is that the distinguishing characteristic of the planning done now for a future wave is

that both cost accounts and network tasks are "long" (or "large") compared to their near-term

counterparts. We have already discussed the long task in this discussion. Project managers can

substitute the words "large cost account" for "long task" and all of the statistical discussions apply,

except that the principles and techniques are applied to the cost accounts on the WBS and not

to the network schedule.

Monte Carlo Effects in the Rolling Wave

Whether you are doing a Monte Carlo analysis on the WBS cost or on the network schedule, the

longer tasks and larger work packages have greater variances. The summation of the schedule

at its outcome milestone or the summation of the WBS cost at the top of the WBS will be a normal

distributed outcome regardless of the rolling waves. However, the Monte Carlo simulation will

show you what you intuitively know: the longer task and larger cost accounts, with their

comparatively larger variances, will increase the standard deviation of the Normal distribution,

flatten its curve, and stretch its tails.

As the subsequent waves come and more details are added, the overall variances will decrease

and the Normal distribution of the outcome variable, whether cost or schedule, will become

more sharply defined, the tails will be less extreme, and the standard deviation (which provides

the project manager entrée to the confidence tables) will be more meaningful.

The Critical Chain

There is a body of knowledge in schedule and resource planning that has grown since 1997

when Eliyahu M. Goldratt wrote Critical Chain,* arguably one of the most significant books in

project management. In this book, written like a novel rather than a textbook, Goldratt applies to

project management some business theories he developed earlier for managing in a production

operation or manufacturing environment. Those theories are collectively called the Theory of

Constraints. As applied to project management, Goldratt asserts that the problem in modern

project management is ineffective management of the critical path, because the resources

necessary to ensure a successful critical path are unwittingly or deliberately scattered and

hidden in the project.

The Theory of Constraints

In the Theory of Constraints, described in another Goldratt business novel, The Goal,** the idea

put forward is that in any systemic chain of operations, there is always one operation that

constrains or limits the throughput of the entire chain. Throughput is generally thought of as the

value-add product produced by the operation that has value to the customer. If the chain of

operations is stable and not subject to too many random errors, then the constraint is stable and

identifiable; in other words, the constraint is not situational and does not move around from one

job session, batch, or run to the next.

1


To optimise the operation, Goldratt recommends that if the capacity of the constraint cannot be

increased, or the constraint cannot be removed by process redesign, then all activities ahead of

the constraint should be operated in such a manner that the constraint is never starved. Also,

activities ahead of the constraint should never work harder, faster, or more productively than the

minimum necessary to keep the constraint from being starved. Some may recognise this latter

point as a plank from the "just-in-time" supply chain mantra, and in fact that is not a bad way to

look at it, but Goldratt's main point was to identify and manage the constraint optimally.

From Theory of Constraints to Critical Chain

When Goldratt carried his ideas to project management, he identified the project constraint as

the critical path. By this association, what Goldratt means is that the project is constrained to a

certain duration, and that constrained duration cannot be made shorter. The consequence of

the critical path is that constrained throughput (valuable deliverables to the project sponsor)

cannot be increased, and indeed throughput is endangered if the critical path cannot be

properly managed.

Goldratt made several recommendations in his book Critical Chain, but the most prominent are:

The tasks on the critical path do indeed require statistical distributions to estimate the range

of pessimism to optimism. But, unlike PERT or CPM, Goldratt insists that the median value, the

50% confidence level, be used. Using the median value, the so-called 50-50 point, means

that there is equal likelihood that the task will underrun as overrun. (PERT uses the BETA

distribution and requires that the expected value be used. CPM traditionally uses a single-

point estimate and, more often than not, the single estimate used is the "most likely" outcome

and not the expected value.)

All task activity in the project schedule network that is not on the critical path should be

made subordinate to the demands of the critical path.

There should be "buffers" built into any path that joins the critical path. A buffer is a task of

nonzero duration but has no performance requirement. In effect, buffer is another word for

reserve. However, Goldratt recommends that these buffers be deliberately planned into the

project.

By using the median figure for each task on the critical path, Goldratt recognises that the

median figure is generally more optimistic than the CPM most likely estimate and is often

more optimistic than the expected value. Goldratt recommends that the project manager

"gather up" the excess pessimism and put it all into a "project buffer" at the end of the

network schedule to protect the critical path.

We have already discussed Goldratt's point about a project buffer in our earlier discussion

about how to represent the project schedule risk as calculated on the network with the

project sponsor's business value dates as set in the programme milestones. We did not call it

a buffer in that discussion, but for all intents and purposes, that is what it is. Figure 7-15

illustrates the placement of buffers in critical chain planning.

The critical chain ideas are somewhat controversial in the project management community,

though there is no lack of derivative texts, papers, projects with lessons learned, and

practitioners that are critical chain promoters. The controversy arises out of the following

points:

Can project teams really be trained to estimate with the median value? If so, then the critical

chain by Goldratt's description can be established.

Can team leaders set up schedule buffers by taking away schedule "pad" from cost account

managers, or does the concept of buffers simply lead to "pad" on top of "pad?" To the extent

that all cost account managers and team leaders will manage to the same set of principles,

the critical chain can be established.


b. Decomposition: this technique is about breaking project work packages into smaller more easily

manageable units.

Most projects important enough to have a significant impact on quality are too large to tackle

all at once. Instead, large projects must be broken down into smaller projects and, in turn, into

specific work elements and tasks. The process of going from project objectives to tasks is called

decomposition. Project decomposition begins with the preparation of a preliminary plan. A

preliminary project plan will identify, in broad high-level terms, the objectives of the project and

constraints in term of time and resources. The work to be performed should be described and

precedence relationships should be sketched out. Preliminary budgets and schedules will be

developed. Finally, subplans will be developed for each subproject for the following:

Control plans.

Quality control plans.

Cost control plans.

Schedule control plans.

Staffing plans.

Material plans.

Reporting plans.

Other plans as deemed necessary.

These subplans are developed in parallel for the various subprojects.

Improvement happens one project at a time, but without proper planning these project may

well fail to deliver their objectives.

c. Precedence Diagramming Method (PDM): is a method for constructing project schedule network

diagram that has rectangular boxes, depicting nodes and arrows connecting the boxes,

depicting the logical relationship between the activities. this technique is also called Activity on

Node (AON).

Fig. 1: Activity on Node

d. Dependency determination: this technique is used to define the sequence based on the types of

dependencies between the activities.

Q.2 State and describe process of estimating resource & duration for the activity

Ans: As we are already aware that for every step we take has a time frame and every move needs

some resource and both these parameters need to be considered before each action. Thus even

though the activity is identified and sequenced, we get only partial schedule, to get further clarity

on the schedule it is very important to understand the resource requirement and time required to

complete each activity. The importance of the two parameters can be understood from the fact,

that project management has two separate processes for find the two requirements. The two

processes are:

· Determining resource requirement for each activity

· Calculating the time required for each activity

Determining resource requirement for each activity

There are various resources used on a project. Some of which are people, machinery, money. And

for each activity, to be accomplished we have a particular resource requirement. The reason for

calculating this requirement is, that there is a cost factor attached to each resource and to execute

the project successfully, it is very important that we are aware of the cost component.

The information or input to this process may be similar or different from the previous processes. The

basic inputs to this process are:

· List of activity

· Activity Characteristics

· Resource Calendar: this document gives us an idea of the resource availability for the project

activities. It also gives information about the resource skillset.

http://resources.smude.edu.in/slm/wp-content/uploads/2010/10/clip-image0025.jpg


· Enterprise Environmental Factor

· Organization Asset

To use this information and determine the resources for each activity, we require the methodologies

and tools listed below:

· Expert Judgment

· Alternative analysis: There may be two or more ways to doing a particular task. Through this

scrutiny, we try finding an alternative mode of accomplishing a task. And this may require a

different set of skills, which can help incase of unavailability of the resource for the first set of

activity and may save cost as well.

· Pre-stated estimating information: This includes production or resource rates pre-stated by the

organization.

· Bottom-up Estimating: Incase the activity is complicated enough for determining the resource

requirement; it can be further decomposed into the detail of the work to be performed. And

resource requirement for the detailed work is determined. This way of calculating resource

requirement for an activity by deriving the resource requirement for its sub-parts is called bottom-

up estimating.

· Project Management Software: several soft wares for project management are available which

assist in planning and managing resource requirements for the various tasks in a project.

The outcomes of this process are:

· Activity Resource Requirement: This document lists the types and quantity of resource required

for project activities. It also list the skillset required and quality of material required and other

characteristics of the resources.

· Resource Breakdown Structure: It is the hierarchical structure of the resources required for the

project activities, further categorizing it on the basis of their types. It help project manager in

maximum utilization of the resources and make sure no resources are wasted.

· Project document updated

Calculating the time required for each activity

Once we have the calculated the resource requirement based on their availability, we can get

idea about the time it would take to complete the activity. In this process we use outcomes from

previous processes and organizational documents to calculate the time taken for each activity. The

major inputs required for this process are:

· List of activities


· Activity Resource requirement

· Resource Calendar

· Scope Statement

· Enterprise environmental factors

· Organizational Asset

The tools and techniques used for calculating the time duration of each activity ion a project are:

· Expert Judgment

· Analogous estimating: this estimating technique uses information from previous similar projects to

calculate the duration. This methodology is cost effective and time saving but the result may not

be very accurate.

· Parametric estimating: this technique uses historical data, i.e. information from similar previous

projects and relationships between variables. This technique is more accurate then the

analogous estimating.

· PERT (Program evaluation and Review Technique) Estimate: also known as three-point estimate, is

more accurate then the estimating techniques mentioned before. This estimate is calculated

using the following formula:

Expected activity Duration (tE) = (tO + 4tM + tP)/6

Activity standard deviation tD = (tP – tO)/6

Activity Variance = tV = (tP- tO)2/6

The range of duration can be calculated :

tE +or – tD

Where

tO = Optimistic or activity duration in best scenario.

tM = Most likely or activity duration resource availability and dependencies are as assumed

tP = Pessimistic or activity duration in worst scenario.


· Reserve Analysis: contingency reserves or buffer may also be included in the schedule

accounting for uncertain schedule.

The major outcomes of this process are:

· Activity Duration estimate: This gives an approx. figure of the duration of activity. It may be a

rough figure or a range, between which the duration may be present.


Q.3 Describe the basic elements of a project plan.

Ans: The basic elements of the project plan are:

· Project Requirements: The project plan lists the basic requirements of the project and the

objective of undertaking the project.

· General Approach: In this section the both the managerial and technical approach for the

project is listed. It describes the project guidelines. This part of the plan describes the various

approaches which need to be followed all through the project. These approaches may include

the design document, the instructional designing approach etc.

· List of stakeholders: stakeholders can impact a project both positively or negatively. Thus it is very

important to identify all the project stakeholders at the starting of the project. Project plan should

contain the list of stakeholders and their relation to the project and the mode of communication

to be followed for managing the same.

· Contractual aspects: This important section describes the reporting requirements, customer

related information, list of resources supplied by client, liaison agreements, project review and

abortion process, list of deliverables and project specifications, schedules.

· Resources: This section lists the resources required for the project, their availability, their cost.

· Risk: The risk management plan of the project plan talks about the various risks identified in the

project. The alternative choices, mitigation and contingency plans. Steps to monitor and control

the risks.

· Communication: The communication management plan talks about the communication

methodology

· Quality: Every project should be evaluated against standards and by methods established at the

project inception. This section describes these quality standards.

Q.4 Complete the below mentioned chart:

Ans: Expected Activity Duration (tE) = (tO + 4 tM + tP)/6

Activity Variance = tV = (tP - tO)2/6

Activity Pessimist

tP

Most

likely

tM

Optimist

tO

PERT

tE

Variance

tV

A 20 12 10 13.00 16.67

B 30 25 18 24.67 24.00

C 105 80 56 80.17 400.17

D 200 145 85 144.17 2204.17

E 145 112 89 113.67 522.67

Q.5 Describe inputs and outputs for the following processes

a. Determining resource requirement for each activity

b. Calculating time requirement for each activity.

Ans:

The basic inputs to this process are:

· List of activity


· Resource Calendar: this document gives us an idea of the resource availability for the

project activities. It also gives information about the resource skillset.

· Enterprise Environmental Factor

· Organization Asset

The outcomes of this process are:

· Activity Resource Requirement: This document lists the types and quantity of resource

required for project activities. It also list the skillset required and quality of material

required and other characteristics of the resources.


· Resource Breakdown Structure: It is the hierarchical structure of the resources required for

the project activities, further categorizing it on the basis of their types. It help project

manager in maximum utilization of the resources and make sure no resources are

wasted.


The major inputs required for this process are:

· List of activities


· Activity Resource requirement

· Resource Calendar

· Scope Statement

· Enterprise environmental factors

· Organizational Asset

The major outcomes of this process are:

· Activity Duration estimate: This gives an approx. figure of the duration of activity. It may

be a rough figure or a range, between which the duration may be present.



Master of Business Administration-MBA Semester 3

Project Planning & Scheduling – PM0011

(Book ID: 1237)

Assignment Set- 2 (60 Marks)

Q.1 Describe the five process groups and 9 knowledge areas of project management.

Ans: Mapping of planning process with Knowledge areas

Most of the experienced project managers believe that project management can be dichotomized

in two major ways; firstly as process groups and secondly as Knowledge areas. As per the project

management fraternity, project management can be dissected into 9 knowledge area and 5

process groups. The authority and responsibility of decisions for all the project management

processes lies with the project manager. The five process groups are based on Deming’s cycle,

considering a project as a solution to a given problem. As per the cycle, these are four steps to a

problem solving process. These four steps are Plan-Do-Check-Act.

Project process group include processes which are linked by their inputs or results, where the output

of one process may be the input for the other. These five process groups are as listed below:

· Initiation: Processes in this group launch a project or project phase. The key activities in this group

include, but are not limited to, creating a feasibility study. Identifying a business needs, creating

project charter, product description and selecting project manager.

· Planning: The process in this group collect information from various constituent processes unto

the degree of completion and confidence. Project managers should include stakeholders in the

planning process group. Project management plan integrates scope, cost, schedule, risk etc. to

produce a realistic plan which is acceptable to the stakeholders.

· Execution: Process groups consist of processes to complete the work in each of the phases.

These processes help the project manager coordinate and direct project resources to meet the

objectives of the project plan. The key activities in this group are acquire project team, perform

quality assurance, develop project team, vendor solicitation and selection, distributing project

information and direct and manage project execution.

· Monitoring and Controlling: Processes in this process group ensure that the project goes

according to plan. Activities in this process group are actions to be implemented when project is

not going as per plans. In this process group variances from the project baseline are identified

and necessary corrective measures are undertaken. Key activities in this process group are

ensuring quality control, providing scope verification, implementation change control, and

configuration management, controlling key parameters like cost, schedule and scope and

monitoring risk response.

· Closing: This process group included all processes to close all activities in a project or project

phase. The activities in this process group are to be performed even for the projects which have

been terminated in the middle or aborted projects. Key activities which are a part of this process

group include, but are not limited to auditing procurement documents, scope verification,

closing procurements, document lessons learned, submitting final reports, and archiving project

records

The 42 processes are also grouped into various knowledge areas. The nine knowledge areas are:

· Project Integration Management: The processes in this knowledge area amalgamate all the forty

two processes of project management. Integration includes characteristics of confederacy,

consolidation, enunciation and integrative events that are important for project management.

The processes in this knowledge area are used for balancing processes in all the other

knowledge areas. The major activities in this knowledge area include but are not limited to

creating the project management plan, monitoring the plan, performing change control and

closing the project.



· Project Scope Management: is required to define the work required in a project. The processes in

this knowledge area define the boundary of the project, control and manage change in scope,

verify that the work required is completed and manage customer and stakeholder’s satisfaction.

· Project Time Management: relates to the processes which need to be accomplished to

complete the project within the defined schedule. Effective time management helps saving

project cost and quality. In the processes in this knowledge area project schedules are drawn

up, without relation to the estimates for size, cost and development resources.

· Project Cost Management: Cost estimation is difficult since there are many factors that influence

the cost of a project and not on all of them are under the project’s direct control. The processes

in this knowledge area handle project cost that goes into planning, executing, monitoring and

closing a project.

· Project Quality Management: PMI defines quality as the degree to which a set of inherent

characteristics fulfil requirements. Quality of the product impacts customer satisfaction and

interns impact business growth and also team morale. Project quality management deals with

quality processes, roles and responsibilities and quality goals of the organization.

· Project Human Resource Management: One of the most important tasks in project management

is resource management and the most tedious managed resource, which impacts all other

project parameters, is human resource. The processes in this knowledge area help project

manager in planning for team acquisition to team reliving.

· Project Communication Management: Communication is essentially the interpersonal process of

sending and receiving messages. It is believed that about 85-90% of a project manager’s profile

requires communication. Miscommunication or absence of communication can impact a

projects performance. The processes in this knowledge area helps project manager to identify

what to communicate, whom to communicate, how to communicate and when to

communicate.

· Project Risk Management: Project risk is an uncertain event that can have a negative or positive

impact on the project. An appropriate contingency or mitigation plan is required to face risks.

The processes in this knowledge area help identify risks, plan for them, and monitor them.

· Project procurement management: Frequently project teams or sub-products need to be

outsourced. The decision to outsource or create a product in-house is made in the procurement

management processes. Procurement is a set of processes to evaluate, purchase, and

administer an agreement with vendors for such products/goods, service or result, as required by

the project but not available within the project organization.

Planning process group collects information from various constituent processes upto the degree of

completion and confidence. As per PMI, there are 21 processes in the planning process group,

which is half of the total project management processes. This very fact, emphasis on the importance

of planning process in project management. These twenty one processes are spread across nine

knowledge areas. The distribution can be well understood from the table given below:

Table 1.0: mapping processes to knowledge area



Q.2 List the inputs, outputs, tools and techniques for the vendor management process.

Ans: For vendor management the basic requirements the existence of a vendor, which would only

happen if product, good or service is acquired at the best cost to meet the need of the project This

process is about documentation of purchasing decisions and policies and approaches for product

outsourcing. The major inputs required for this process are:

· Scope baseline: this is the component of project plan which gives information about the project

scope, listed in the scope statement, lists the work breakdown structure and description of the

WBS elements.

· Requirement documentation: This document would have information about the project

requirements both technical and legal along with the legal implications.

· Teaming agreement: They are contractual agreements made between two or more parties as a

result of partnership or joint venture.

· Risk register: is document which lists the identified risks, risks which have already occurred in

similar projects in the past, and cost involved in risk mitigation.

· Activity resource requirements: This document lists the types and quantity of resource required

for project activities. It also lists the skillset required and quality of material required and other

characteristics of the resources.

· Project schedule: this structured document gives us the start and end date of each activity. It

gives a detailed description of the activities to be performed in the project, their dependencies

and requirements. They can be represented in the following format:

- Milestone chart

- Bar charts

- Project schedule network diagrams

· Activity cost estimates: They are measurable calculation of the feasible cost required to

complete project work.

· Cost performance baseline: is an approved budget at competition, which is used for monitoring

and controlling cost and cost variances.

· Enterprise environmental factors: Information about organizational culture, processes,

infrastructure, government standards, human resource data, PMIS, stakeholder information etc.

· Organizational Assets: this includes all process related assets, which an organization captures,

which can impact project success. This can range from organization policies, procedure,

processes to knowledge base created from previous project experiences.

The tools and techniques used for this process are:

· Make-or-Buy analysis: This analysis helps take a call whether it is beneficial to buy a product from

third party or make it. Even making should happen in-house or should be outsourced. Depending

on what gives the maximum profit, choice is made.

· Expert judgment: this is about taking opinion from an experienced about whether the product

should be made or bought, or its production should be outsourced.

· Contract types: whenever the product is to be created and procurement form third-party is

done, it is assumed that the failure of the product risk i8s shared with the third party. Contract

type defines how the risk shared. The various types of contract are Fixed = price, cost

reimbursable, time material contact.

The major outputs of this process are:

· Procurement documents: the procurement documents are procurement management plan,

which consists of the contract type, issues management, type of estimates, how to manage the

multiple vendors, procurement statement of work, which defines the work to be accomplished

as a part of the procurement contract, the proposal sent to the vendor, list of vendors who bid

for the proposal, terms and conditions of the contract, RFP (request for proposal) etc.

· Make-or-buy decisions: this document mentions whether the product is to be bought or made, if

any risk sharing policy used etc.

Q.3 The below example depicts the preparation of cake. Here, some of the interdependent

activities where some follow a particular order, whereas others are performed independently.

Activity Preceding

Activity

Estimate

in minutes

Start Start 0

D Start 4

Activity D,A 6

F D,A 7


E F,E 8

G F,E 5

B G 5

H H 7

C C,B 8

END 0

In the above mentioned example, a sequence of events is maintained. Each of the Activity is

interdependent with the other. Using CPA determines the critical path for the above and draw the

CP diagram.

Q.4 Write a paragraph on each:

a. Non-linear programming formulation b. Integer programming formulation

c. Dynamic programming formulation d. Disjunction programming formulation

e. Linear programming formulation

Ans:

a. Non Linear Programming Formulations

A non linear program (NLP) is a generalization of a linear program that allows the objective

function and the constraints to be non linear in x1……..xn.

Under certain convexity assumptions on the objective function and the constraints there are

necessary and sufficiency conditions for a solution to be optimal. If the objective function and

constraints satisfy the required convexity assumptions, then the optimality of a solution can be

verified easily via these conditions.

There are a number of methods for solving non linear programming problems. These methods

tend to be different from the methods used for linear programming problems. (However, they

may use linear programming methods as subroutines in their overall framework). The most

commonly used methods for non linear programming are:

1) Gradient methods

2) Penalty and barrier function methods

In both applications, the objective functions are non linear and the constraints linear.

Consider a non linear programming problem with multiple equality constraints. Such a problem

can be transformed into an unconstrained problem using so-called lagrangian multipliers. For

example, consider the non linear programming problem

Minimize of (x1……..xn)

Subject to

f1 (x1……….xn) = O

fm (x1………xn ) = O

This problem can be transformed into the following unconstrained optimization problem with the

objective function.

Minimize of (x1………xn) + λ1 f1 (x1……xn) + λ3 fm (x1………xn )

If the original objective function of (x1………xn ) satisfies certain convexity conditions, then the

optimal solution can be obtained by taking the partial derivative of the un constrained problem

with respective to xj and set that equal to zero. This yields n equation with n + m unknowns

(x1………xn + λ1………… λm) .These n equations together with the original set of m constraints result in

a system of n + m equations with n + m unknowns.

b. Integer Programming Formulations

An integer program (IP) is a linear program with the additional requirement that the variables

x1………xn have to be integers. If only a subset of the variables are required to be integer and the

remaining ones are allowed to be real, the problem is referred to as a mixed integer program

(MIP). In contrast with the LP an efficient algorithm for the IP or MIP does not exist. Many

scheduling formulations can be presented as integer programs.

c. Dynamic Programming

There are various classes of methods that are useful for obtaining optimal solutions for such NP-

Hard problems. One class of methods is referred to us Dynamic programming. Dynamic

programming is one of the more widely used techniques for dealing with combinational

optimization problems. It is a procedure that is based on a divide and conquers approach.

Dynamic programming can be applied to problems that are solvable in polynomial time, as well

as problems that are NP – Hard.


d. Disjunctive Programming Formulations:

There is a large class of mathematical programs in which the constraints can be divided into a

set of conjunctive constraints and one or more sets of disjunctive constraints. A set of constraints

is called conjunctive if each one of the constraints has to be satisfied. A set of constraints is

called disjunctive if at least one of the constraints has to be satisfied but not necessarily all.

In the standard linear program all constraints are conjunctive. A mixed integer program contains

paires of disjunctive constraints. The fact that the integer variable x jk has to be either 0 or 1 can

be enforced by a pair of disjunctive linear constraints, either x jk = 0 or x jk = 1. This implies that the

single machine problem with precedence constraints and the total weighted completion time

objective can be formulated as a disjunctive program as well.

e. Linear Programming Formulation

The most basic mathematical program is the linear program (LP). An LP prefers to an optimization

problem in which the objective and the constraints are linear in the variables to be determined.

An LP can be expressed as follows:

The objective is the minimization of costs.

The c1……….cn vector is referred to as the cost vector. The variables

x1 …xn have to be determined so that the objective function c1 x1 +……

cn xn is minimized. The column rector refers to the level at which this activity j is performed. The b1

…..bm is referred to as the resource vector. The fact that in linear programming n denotes the

number of activities and in scheduling theory n refers to the number of jobs is a more

coincidence that in liner programming m denotes the number of resources and in scheduling

theory m refers to the number of machines in a coincidence as well. The representation above

can write in matrix form:

There are several algorithms or classes of algorithms for solving an LP. The two most important

over are

i) The simplex methods and

ii) The interior point methods

Although simplex methods work very well in practice, it is not known if there is any version of the

simplex method that solves the LP problem in polynomial time. The best known example of an

interior point method is the Karmakar algorithm, which is known to solve the LP problem in

polynomial time.

Q.5 What is a business case? List the business related questions answered using a business case.

Ans: What is a Business Case?

The Business Case is a one-off, start-up document used by senior management to assess the

justification of a proposed project, or to assess the options for a project that has already received

funding. If approved, it confirms senior management support and/or resourcing for a recommended

course of action (option).

The business case answers the following business related questions

– How did the initiative come about?

– What is the opportunity / treat / issue improvement being addressed?

– Why in clear and concise terms, is the initiative necessary?

– What is the desired product, service or result?

– What are the benefits to the enterprise and its customers?


– What are the qualitative benefits, such as customer satisfaction, strategic value cycle time

improvements?

– What are the linkages to the enterprise’s vision, mission and value drivers ( that is mental , quality,

efficiency)

– Why will the initiative succeed?

– What must be invested to get the desired product, service, result or benefit?

– What are the expected incremental productions or operational costs for the new or modified

product, service, or production process?

– What are the proposed spending reductions, revenue improvements or profit improvements

related to justify the initiative?

– What is the enterprises capital to successfully implement the initiative while meeting financial

objectives?

– What other factors materially impact the potential success of the initiative such as additional

services, required efficiencies, minimum or maximum quantities required product quality and

development objectives?

– What are the concerns, issues and risks?

– What are the parameters and criteria used for prioritizing the initiative with respect to other

business strategic initiatives?

– What is the exit strategy if the strategic initiative is not delivering the desired return or investment?

Q.6 What is delay analysis? Explain the various types of delay analysis methodology.

Ans: What is a ‘delay analysis’?

Delay analysis is a forensic investigation into the events or issues that caused a project to run late

resulting in Schedule Variances. Delay analysts refer to `critical' and `non-critical' delays; the first are

events causing delay to the project's completion date and the second type affect progress on the

project but do not directly impact the project completion date.

During the past decade developments in computer technology and the availability of more

advanced planning software packages changed the way in which delay claims and the results of a

delay analysis are presented.

Delay analysis methodology

There are two types. The first type of delay analysis methodology is prospective; which demonstrates

the theoretical or likely impact of the consequences of delaying events rather than showing what in

fact occurred. The basis of this methodology is to establish a programming model of the project,

usually the contractor's as planned programme, then impact the model by the application of

delaying events. This type of methodology is commonly used to demonstrate what extension of time

a contractor is due, as a result of the application of employer responsible delaying events. This is said

to be the contractor's entitlement. Entitlement in this context is derived from the results of a delay

analysis and is not to be confused with contractual entitlement. In summary the prospective type of

methodology is a theoretical calculation of the likely delay a delaying event(s) would cause to

project completion. In other words, it focuses firstly on the delaying event and then demonstrates

the likely delay to progress and ultimately project completion that is likely to flow from the event.

The second type of delay analysis methodology is retrospective. The retrospective analysis tries to

show what actually occurred on a project; where the delays were; and what caused the delay to

project completion. The analysis shows how actual progress differed from what was planned. By

focusing on how the works actually progressed, the analysis will show when work activities were

delayed, and from the results of the analysis, investigation of what caused the actual delays can be

carried out. In summation, this type of methodology looks at what actually happened, what

activities were actually delayed and only thereafter what caused the delay. Both types of delay

analysis methodology are to some degree subjective. The prospective analysis relies heavily on a

programming model of the project and the delay analyst's opinion on how the delay event was

likely to influence the model. The retrospective analysis is less subjective as it relies on actual

progress. However, interpretation of the results as to what caused delay is subjective. This is because

the delay analyst will usually have to consider a number of related issues as to what caused delay

and apply his own experience and judgment.

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