Final hrm project 2003

Operation Research Techniques

Project Report On

Application of

Subject Operation Research

Submitted to Prof PM Bhole

Prepared by Mohd Adil (45)

Date 1732011

1

ACKNOWLEDGEMENT

First and foremost let I sincerely thank ALMIGHTY for the

great opportunity and blessings that he has showered up on

us for the successful and timely completion of our project

work

I extent my sincere gratitude to Dr Vidya Hatangadi

Director of AIAIMS for her kind support and guidance for

making our project great success

I extent my sincere gratitude to guide Mr PM Bhole

lecturer Allana Institute of Management Studies for the

kind support and proper guidance without which the project

would not have been efficiently completed

I render my whole hearted thanks to librarian for their

assistance and co-operation given to me in regard to this

work

Once again I take this opportunity to convey me sincere

thanks to each and every person who helped me directly

and indirectly in the successful completion of this project

2

CONTENTS

SRNO TOPICS PAGE NO

1 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

04----05

2 Structure of Linear Programminghelliphelliphelliphelliphelliphelliphellip

06----08

3 Assumptions of Linear Programming helliphelliphelliphellip

09----11

4 Limitations of Linear Programminghelliphelliphelliphelliphellip

12----12

5 Applications of Linear Programminghelliphelliphelliphelliphellip

13----15

6 Case Studyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

16----26

7 Conclusionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

27---27

3

8 Bibliographyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

28---28

4

INTRODUCTIONIn a decision-making embroilment model formulation is important

because it represents the essence of business decision problem The

term formulation is used to mean the process of converting the

verbal description and numerical data into mathematical expressions

which represents the relevant relationship among decision factors

objectives and restrictions on the use of resources Linear

Programming (LP) is a particular type of technique used for economic

allocation of scarce or limited resources such as labour material

machine time warehouse space capital energy etc to several

competing activities such as products services jobs new equipment

projects etc on the basis of a given criterion of optimally The phrase

scarce resources mean resources that are not in unlimited in

availability during the planning period The criterion of optimality

generally is either performance return on investment profit cost

utilily time distance etc

George B Dantzing while working with US Air Force during World War

II developed this technique primarily for solving military logistics

problems But now it is being used extensively in all functional areas

of management hospitals airlines agriculture military operations oil

refining education energy planning pollution control transportation

planning and scheduling research and development etc Even

though these applications are diverse all IP models consist of certain

common properties and assumptions Before applying linear

programming to a real-life decision problem the decision-maker must

be aware of all these properties and assumptions which are

discussed later in this chapter

5

Before discussing in detail the basic concepts and applications of

linear programming let us be clear about the two words linear and

programming The word linear refers to linear relationship among

variables in a model Thus a given change in one variable will always

cause a resulting proportional change in another variable For

example doubling the investment on a certain project will exactly

double the rate of return The word programming refers to modelling

and solving a problem mathematically that involves the economic

allocation of limited resources by choosing a particular course of

action or strategy among various alternative strategies to achieve

the desired objective

A large number of computer packages are available for solving a

mathematical LP model but there is no general package for building a

model Model building is an art that improves with practice To

illustrate how to build IP models a variety of examples are given in

this chapter

6

STRUCTURE OF LINEAR PROGRAMMING

General Structure of LP Model

The general structure of LP model consists of three components

Decision variables (activities)

We need to evaluate various alternatives (courses of action) for

arriving at the optimal value of objective function Obviously if there

are no alternatives to select from we would not need LP The

evaluation of various alternatives is guided by the nature of objective

function and availability of resources For this we pursue certain

activities usually denoted by x1 x2hellipxn The value of these activities

represents the extent to which each of these is performed For

example in a product-mix manufacturing the management may use

LP to decide how many units of each of the product to manufacture

by using its limited resources such as personnel machinery money

material etc

These activities are also known as decision variables because they

arc under the decision-makers control These decision variables

usually interrelated in terms of consumption of limited resources

require simultaneous solutions All decision variables are

continuous controllable and non-negative That is x1gt0

x2gt0 xngt0

The objective function

The objective function of each LP problem is a mathematical

representation of the objective in terms of a measurable quantity

7

such as profit cost revenue distance etc In its general form it is

represented as

Optimise (Maximise or Minimise) Z = c1x1 + c2X2 hellip cnxn

where Z is the mcasure-of-performance variable which is a function

of x1 x2 xn Quantities c1 c2hellipcn are parameters that represent the

contribution of a unit of the respective variable x1 x2 xn to the

measure-of-performance Z The optimal value of the given objective

function is obtained by the graphical method or simplex method

The constraints

There are always certain limitations (or constraints) on the use of

resources eg labour machine raw material space money etc that

limit the degree to which objective can be achieved Such constraints

must be expressed as linear equalities or inequalities in terms of

decision variables The solution of an LP model must satisfy these

constraints

The linear programming method is a technique for choosing the best

alternative from a set of feasible alternatives in situations in which

the objective function as well as the constraints can be expressed as

linear mathematical functions In order to apply linear programming

there are certain requirements to me met

There should be an objective which should be clearly

identifiable and measurable in quantitative terms It could be

for example maximisation of sales of profit minimisation of

cost and so on

8

The activities to be included should be distinctly identifiable and

measurable in quantitative terms for instance the products

included in a production planning problem

The resources of the system which arc to be allocated for the

attainment of the goal should also be identifiable and

measurable quantitatively They must be in limited supply The

technique would involve allocation of these resources in a

manner that would trade off the returns on the investment of

the resources for the attainment of the objective

The relationships representing the objective as also the

resource limitation considerations represented by the objective

function and the constraint equations or inequalities

respectively must be linear in nature

There should be a series of feasible alternative courses of action

available to the decision makers which are determined by the

resource constraints

When these stated conditions are satisfied in a given situation the

problem can be expressed in algebraic form called the Linear

Programming Problem (LPP) and then solved for optimal decision

We shall first illustrate the formulation of linear programming

problems and then consider the method of their solution

9

ASSUMPTIONS OF LINEAR PROGRAMMING

The following four basic assumptions are necessary for all linear

programming models

Certainty

In all LP models it is assumed that all model parameters such as

availability of resources profit (or cost) contribution of a unit of

decision variable and consumption of resources by a unit of decision

variable must be known and is constant In some cases these may be

either random variables represented by a known distribution (general

or may be statistical) or may tend to change then the given problem

can be solved by a stochastic LP model or parametric programming

The linear programming is obviously deterministic in nature

Divisibility (or continuity)

The solution values of decision variables and resources are assumed

to have either whole numbers (integers) or mixed numbers (integer

and fractional) However if only integer variables are desired eg

machines employees etc the integer programming method may be

applied to get the desired values

It is also an assumption of a linear programming model that the

decision variables are continuous As a consequence combinations of

output with fractional values in the context of production problems

are possible and obtained frequently For example the best solution

to a problem might be to produce 5 23 units of product A and 10 13

units of product B per week

10

Although in many situations we can have only integer values but we

can deal with the fractional values when they appear in the following

ways Firstly when the decision is a one-shot decision that is to say

it is not repetitive in nature and has to be taken only once we may

round the fractional values to the nearest integer values However

when we do so we should evaluate the revised solution to determine

whether the solution represented by the rounded values is a feasible

solution and also whether the solution is the best integer solution

Secondly if the problem relates to a continuum of time and it is

designed to determine optimal solution for a given time period only

then the fractional values may not be rounded For instance in the

context of a production problem a solution like the one given earlier

to make 5 23 units of A and 10 units of B per week can be adopted

without any difficulty The fractional amount of production would be

taken to be the work-in-progress and become a portion of the

production of the following week In this case an output of 17 units

of A and 31 units of B over a three-week period would imply 5 23

units of A and 10 units of B per week Lastly if we must insist on

obtaining only integer values of the decision variables we may

restate the problem as an integer programming problem forcing the

solutions to be in integers only

Additively

The value of the objective function for the given values of decision

variables and the total sum of resources used must be equal to the

sum of the contributions (profit or cost) earned from each decision

variable and the sum of the resources used by each decision variable

respectively For example the total profit earned by the sale of two

11

products A and B must be equal to the sum of the profits earned

separately from A and B Similarly the amount of a resource

consumed by A and B must be equal to the sum of resources used for

A and B individually

This assumption implies that there is no interaction among the

decision variables (interaction is possible when for example some

product is a by-product of another one)

Finite choices

A linear programming model also assumes that a limited number

of choices are available to a decision-maker and the decision

variables do not assume negative values Thus only non-negative

levels of activity are considered feasible This assumption is indeed

a realistic one For instance in the production problems the output

cannot obviously be negative because a negative production implies

that we should be able to reverse the production process and convert

the finished output back into the raw materials

Linearity (or proportionality)

All relationships in the LP model (ie in both objective function and

constraints) must be linear In other words for any decision variable

j the amount of particular resource say i used and its contribution to

the cost one in objective function must be proportional to its amount

For example if production of one unit of a product uses 5 hours of a

particular resource then making 3 units of that product uses 3 x 5 =

15 hours of that resource

12

LIMITATIONS OF LINEAR PROGRAMMINGIn spite of having many advantages and wide areas of applications

there arc some limitations associated with this technique These are

given below Linear programming treats all relationships among

decision variables as linear However generally neither the objective

functions nor the constraints in real-life situations concerning

business and industrial

problems are linearly related to the variables

While solving an LP model there is no guarantee that we will

get integer valued solutions For example in finding out how

many men and machines would be required lo perform a

particular job a non-integer valued solution will be

meaningless Rounding off the solution to the nearest integer

will not yield an optimal solution In such cases integer

programming is used to ensure integer value to the decision

variables

Linear programming model does not take into consideration the

effect of time and uncertainty Thus the LP model should be

defined in such a way that any change due to internal as well as

external factors can be incorporated

Sometimes large-scale problems can be solved with linear

programming techniques even when assistance of computer is

available For it the main problem can be fragmented into

several small problems and solving each one separately

Parameters appearing in the model are assumed to be constant

but in real-life situations they are frequently neither known nor

constant

13

It deals with only single objective whereas in real-life situations we

may come across conflicting multi-objective problems In such cases

instead of the LP model a goal programming model is used to get

satisfactory values of these objectives

14

APPLICATION AREAS OF LINEAR PROGRAMMING

Linear programming is the most widely used technique of decision-

making in business and Industry and in various other fields In this

section we will discuss a few of the broad application areas of linear

programming

Agricultural Applications

These applications fall into categories of farm economics and farm

management The former deals with agricultural economy of a nation

or region while the latter is concerned with the problems of the

individual farm

The study of farm economics deals with inter-regional competition and

optimum allocation of crop production Efficient production patterns

can be specified by a linear programming model under regional land

resources and national demand constraints

Linear programming can be applied in agricultural planning eg

allocation of limited resources such as acreage labour water supply

and working capital etc in a way so as to maximise net revenue

Military Applications

Military applications include the problem of selecting an air weapon

system against enemy so as to keep them pinned down and at the

same time minimising the amount of aviation gasoline used A

variation of the transportation problem that maximises the total

15

tonnage of bombs dropped on a set of targets and the problem of

community defence against disaster the solution of which yields the

number of defence units that should be used in a given attack in

order to provide the required level of protection at the lowest

possible cost

Production Management

Product mix A company can produce several different

products each of which requires the use of limited production

resources In such cases it is essential to determine the

quantity of each product to be produced knowing its marginal

contribution and amount of available resource used by it The

objective is to maximise the total contribution subject to all

constraints

Production planning This deals with the determination of

minimum cost production plan over planning period of an item

with a fluctuating demand considering the initial number of

units in inventory production capacity constraints on

production manpower and all relevant cost factors The

objective is to minimise total operation costs

Assembly-line balancing this problem is likely to arise when

an item can be made by assembling different components The

process of assembling requires some specified sequcnce(s)

The objective is to minimise the total elapse time

16

Blending problems These problems arise when a product can

be made from a variety of available raw materials each of

which has a particular composition and price The objective

here is to determine the minimum cost blend subject to

availability of the raw materials and minimum and maximum

constraints on certain product constituents

Trim loss When an item is made to a standard size (eg

glass paper sheet) the problem that arises is to determine

which combination of requirements should be produced from

standard materials in order to minimise the trim loss

Financial Management

Portfolio selection This deals with the selection of specific

investment activity among several other activities The

objective is to find the allocation which maximises the total

expected return or minimises risk under certain limitations

Profit planning This deals with the maximisation of the profit

margin from investment in plant facilities and equipment cash

in hand and inventory

Marketing Management

Media selection Linear programming technique helps in

determining the advertising media mix so as to maximise the

effective exposure subject to limitation of budget specified

exposure rates to different market segments specified minimum

and maximum number of advertisements in various media

Travelling salesman problem The problem of salesman is to

find the shortest route from a given city visiting each of the

specified cities and then returning to the original point of

17

departure provided no city shall be visited twice during the

tour Such type of problems can be solved with the help of the

modified assignment technique

Physical distribution Linear programming determines the

most economic and efficient manner of locating manufacturing

plants and distribution centres for physical distribution

Personnel Management

Staffing problem Linear programming is used to allocate

optimum manpower to a particular job so as to minimise the

total overtime cost or total manpower

Determination of equitable salaries Linear programming

technique has been used in determining equitable salaries and

sales incentives

Job evaluation and selection Selection of suitable person for

a specified job and evaluation of job in organisations has been

done with the help of linear programming technique

Other applications of linear programming lie in the area of

administration education fleet utilisation awarding contracts

hospital administration and capital budgeting etc

18

Case Study

LINEAR PROGRAMMING APPLICATION FOR EFFICIENT TELECOMMUNICATION

NETWORKS PROVISIONING

Abstract

This paper presents a practical proposition for the application of the

Linear Programming quantitative method in order to assist planning

and control of customercircuit delivery activities in

telecommunications companies working with thecorporative market

Based upon data provided for by a telecom company operating in

Brazil the Linear Programming method was employed for one of the

classical problems of determining the optimum mix of production

quantities for a set of five products of that company Private

Telephone Network Internet Network Intranet Network Low Speed

Data Network and High Speed Data Network in face of several

limitations of the productive resources seeking to maximize the

companyrsquos monthly revenue By fitting the production data available

into a primary model observation was made as to what number of

monthly activations for each product would be mostly optimized in

order to achieve maximum revenues in the company The final

delivery of a complete network was not observed but the delivery of

the circuits that make it up and this was a limiting factor for the

study herein which however brings an innovative proposition for the

planning of private telecommunications network provisioning

Introduction

19

In the past few years telecommunications have become an input of

great business importance especially for large companies The need

for their own telecommunications network provisioning has been a

constant concern of large- and medium-sized enterprises the world

over Even when a large telecommunications company is outsourced

to operate a customerrsquos network the circuits provisioning of that

network is of utmost importance for the continuation of the business

regarding time and quality Upon delivery of circuits to customers the

large telecom network providers seek ways to reduce their costs by

relying on smaller teams and even more reduced delivery schedules in

an attempt to meet the customerrsquos needs before their competitors do

A data communication network provisioning for instance which in

1999 was activated in 45 days by Europersquos biggest players BTI and

by USArsquos MCI nowadays is

Prepared and delivered to the customer in 21 to 25 days (YANKEE

GROUP 2005) However these are average schedules since urgent

activations are special cases that can be delivered in less than a week

In Brazil the telecommunications industry is facing a scenario with an

excessive number of telecom service providers with an overestimated

demand that marks a scenario of hyper competition Thus the

briefness in activating a service overcomes all of the other features of

that service provisioning also putting aside an adequate planning of

delivery of the products that make up the customerrsquos network and this

prioritization of delivery brings about some loss to the service

providerrsquos cash This paper which is based on data provided by one

telecom provider in Brazil presents an essay that aims to propose a

20

simple alternative yet with a solid mathematical basis in order to

ensure there is a marker in the prioritization of customersrsquo circuit

provisioning that aims at the main goal of sales and the business its

profitability

Circuit Activation in Telecom Companies

In order to better understand the proposition of this paper one must

get to know a little about the activation or delivery process of a

telecommunications network provisioning This network presented in

Figure 1 is a set of circuits interlocking through a large telecom

operator backbone several customer environments (sites) from which

he operates his business This process includes all the activities from

the request of a service order by the customer to the provisioning of

the network in operation (the beginning of its commercial running)

going through assembly of every physical part of the network the

configuration of its logical parameters and the running test with

customerrsquos application simulating the day today of the business as

shown in Figure 2

21

In Figure 2 it can also be noticed that within the assembly of the

backbonersquos physical part the local access granting activities (2) also

known as lsquolast milersquo equipment acquisition activities for installation

at customersrsquo sites (4) facility allocation activities (communication

channels to be used in the customerrsquos network) within the operatorrsquos

large backbone (1) and customerrsquos network configuration (3) are all

capital availability activities of fundamental importance in order to

ensure activation of all the circuits making up the customerrsquos network

provisioning

22

The lack or poor distribution of such capital brings about a delay in

the provisioning of the networks resulting in loss of profit to the

telecom operator Moreover the random allocation as in a line-up

system ndash FIFO - First In First Out or simply proportional to the

resources available might bring about an undesired delay effect on

large capital inflow to the operator thus representing a problem that

can be solved in a structured way through a Linear Programming

Model

Brazilian Telecom Company

The customer network provisioning division of a big

telecommunications company in the Brazilian market activates on a

monthly basis 3000 circuits of different products (types of network)

which are offered to the market in the following categories Private

Data Network and High Speed Data Network Its limited capital and

output capacity allow it to activate only 35 out of the 8500 circuits

backlog monthly This does not pose a problem for the customers

since they accept delivery of their networks in up to 60 days

depending upon the complexity of the network and the kind of

business it is intended for

However since the prices charged for the circuits in each kind of

network are different the company expects that priority be given to

the activation of the circuits that represent higher earnings to the

company Nowadays there is no indicator of how many circuits for

each kind of product must be activated on average per month so that

guidance from the companyrsquos higher management can be followed

23

So in a typical month of 2004 a survey was conducted as to the

situation of the companyrsquos circuit delivery and the following results

were attained

Figure 3 ndash Table that summarizes Circuit Backlog (Circuit Delivery)

per Service Backlog of a Brazilian Telecom Company in a typical

month

24

Where

Service Backlog Circuit delivery orders for each product of the

company

Physical Backlog Number of telecommunications circuits to be

delivered

Financial Backlog Total revenue of the company after circuit

activations (deliveries) (in R$ 1US$ = R$ 266 1R$ = US$ 0375 on

Dec302004)

Price per Circuit Average unit price of each circuit in each kind of

network

An attempt was made to understand the existing limitations to carry

out circuit delivery in addition to the monthly production capacity

which is already estimated in 3000 circuits per month without any

additional work shift or engagement of temporary labor Five main

25

limiters were attained as well as their quantities that are required per

month per type of product as shown in Figure 4 below

Figure 4 ndash Table that summarizes the required amount of each component that make up Customerrsquos circuits per type of service backlog

WhereType of Resource Part required for making up a customerrsquos circuit

Access or Last Mile is the linking point between the customerrsquos site

and the operatorrsquos backbone Equipment for the customersrsquo sites are

modems routers or other equipment required for customer

communication on each of his sites Network Facilities are

communications channels within the operatorrsquos backbone that carry

customersrsquo signals from one side of the country or the world to the

other Customer Network Configuration is a set of manual

operations by a technician from the provider company in order to

prepare the operatorrsquos backbone to allow traffic of the customerrsquos

26

network circuits through its facilities Other Resources are a set of

minor factors that have been grouped into a single item

PT Private Telephone NetworksINTER Internet networksINTRA Intranet NetworksLSD Low Speed Data NetworksHSD High Speed Data Networks

Finally the available amount of each limiting resource in a month was

attained from the physical viewpoint as shown in Figure 5 below

Figure 5 ndash Physical Limit Table for each

resource required for Activations

Based upon these data the network

activation division had to come up with a

marker so that the selection of the circuits

to have priority activation was favorable

to the companyrsquos revenue formation

resulting from the greater amount of

earnings as possible and considering the

existing limitations

The Solution Proposed Through a Linear Programming Model

What the companyrsquos higher management requires can be achieved

through a simple linear programming model which unfortunately is

not used by any telecom company in Brazil despite the amount of

engineers making up their staff The modelrsquos automation is

guaranteed through Microsoft Officersquos Excel application available in

any of the telecom companiesrsquo PCs in Brazil In addition to the

information made available by the company only a calculation of the

27

limit of activations in financial values is required for each set of

resource limitations (access equipment network facilities

configurations and others) In order to achieve this we considered

that the maximum amount of activated circuits for each limiting

resource considered separately is the limit figure for each resource

That is for instance if all resources were in abundance and access

was limited to 1200 as shown in Figure 3 the maximum number of

activated circuits would be 1200 equivalent in financial values to

1200 x 140657 = R$ 168788400

Where

140657 is the weighted average of a circuitrsquos price considered the

prices in the fourth column of the Table in Figure 3 against the

weighting figures of the second line of the Table in Figure 4 the line

referring to access By doing the same with the other limiting

resources the limits of the table in Figure 6 are attained

Figure 6 ndash Table for the monthly physical and financial limit of each resource required for the activations

28

By building now the primary linear programming model applied to the

problem proposed and considering that all the data are now

available we get the following elements Object function Max 1048774

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

Once what is intended is to maximize the revenue from the prices of

the circuits of each product (see Figure 1)

29

Restrictions to the ModelR1) 998 x1 + 162 x2 + 132 x3 + 289 x4 + 108 x5 lt= 168788400R2) 1276 x1 + 206 x2 +169 x3 + 369 x4 + 137 x5 lt= 215720284R3) 333 x1 + 54 x2 + 44 x3 + 96 x4 + 36 x5 lt= 56273600R4) 1477 x1 + 239 x2 + 196 x3 + 428 x4 + 159 x5 lt= 249726912R5) 958 x1 + 155 x2 + 127 x3 + 277 x4 + 103 x5 lt=

162005760

Once each type of limiting resource (see Figure 2) leads to a

maximum limit of revenue acquisition resulting from circuit delivery

if analyzed separately from the others (see Figure 4)

R6) x1 + x2 + x3 + x4 + x5 lt= 3000 maximum output capacity consideredR7) x1 lt= 5042R8) x2 lt= 816R9) x3 lt= 668R10) x4 lt= 1459R11) x5 lt= 543Once there is a finite set of circuits to be activated per month per type

of network (product) R12 a R16) x1 x2 x3 x4 x5 x6 gt=0 Since

there are no negative activations (Deliveries)

By submitting the Model to the SOLVER function in Microsoftrsquos Excel

application the results shown in Figure 7 are attained

30

The most outstanding points shown through the Excelrsquos results are

the optimum outputs for the topic month would be the activation of

1441 private telephone network circuit activations 816 Internet

network circuit activations 200 low speed data network circuit

activations 543 high speed data network circuit activations and

postponing for the following period the activations of the Intranet

network circuits coming to a total of 3000 activations monthly

amounting to a revenue of R$ 476888831 for the company in the

month of study If the same model is calculated bringing production

up to 4000 circuits a month the distribution would be Telephone

networks 1062 Internet 816 Intranet 120 Low Speed Data 1459

High Speed Data 543 for a revenue of R$ 559705312 leaving only

the Telephone and Intranet circuits to be solved in over 30 days as

Figure 8 below shows

31

Conclusions and Recommendations

Some conclusions and recommendations can be taken from the

information presented in this paper that help in the day-to-day of a

telecommunications company working with activations (delivery) of

customer corporate network circuits First of all the linear

programming methodology proposes markers for the activations that

further focus on parameters predefined by the companyrsquos

management personnel As for the case presented in this paper if

average figures were to be used by sharing the efforts of the

activations teams per service circuits would be activated that would

add to earnings of 3000 x R$ 140639 = R$ 421917000 which is R$

54971831 lower than the revenue made available by following the

linear programming model This means some revenue anticipation of

roughly 25 million American dollars per year On the other hand

within a hyper-competitive environment an output efficiency increase

becomes urgent for any industry or service provider company

Through a Linear Programming Model it gets easy to verify for

instance that by increasing output capacity to 4000 circuits per

month the revenue anticipation is increased by (R$ 559705312 ndash

476888831) R$ 82816481 monthly and this can be enough reason

for the company to hire further human resources to meet this revenue

anticipation

Finally the utilization of statistics-based methodologies is

recommended for output environments even in service providing

aiming at production maximization or even cost reduction It is worth

reminding that the model proposed here presents guidelines for the

priorities not ignoring other underlying factors in prioritizing

32

activation such as a customerrsquos urgent need or its category in

segmentation by size or importance The same method used in this

paper can guide the acquisition of resources for circuit activation

rental of third partiesrsquo access or vacation scheduling of the personnel

involved in the provisioning aiming at a more compatible distribution

of human resources throughout the year regarding the demand for

networks and services by customers

33

BIBLIOGRAPHY

The information included in this project is taken from the

reference

Books

Operation Research

Websites

httpwwwyankeegroupcomcustomsearch

search_resultsjspsearch_results

httpwwwwikipediaorg

httpwwwgooglecom

httpwwwmydigitalfccomop-edimportance-fun-work-

613wwwanswerscom

34

Project Report On
CONTENTS

ACKNOWLEDGEMENT

First and foremost let I sincerely thank ALMIGHTY for the

great opportunity and blessings that he has showered up on

us for the successful and timely completion of our project

work

I extent my sincere gratitude to Dr Vidya Hatangadi

Director of AIAIMS for her kind support and guidance for

making our project great success

I extent my sincere gratitude to guide Mr PM Bhole

lecturer Allana Institute of Management Studies for the

kind support and proper guidance without which the project

would not have been efficiently completed

I render my whole hearted thanks to librarian for their

assistance and co-operation given to me in regard to this

work

Once again I take this opportunity to convey me sincere

thanks to each and every person who helped me directly

and indirectly in the successful completion of this project

2

CONTENTS

SRNO TOPICS PAGE NO

04----05

06----08

09----11

12----12

13----15

16----26

27---27

3

28---28

4

5

this chapter

6

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

CONTENTS

SRNO TOPICS PAGE NO

04----05

06----08

09----11

12----12

13----15

16----26

27---27

3

28---28

4

5

this chapter

6

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

28---28

4

5

this chapter

6

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

5

this chapter

6

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

this chapter

6

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

material etc

x2gt0 xngt0

7

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

represented as

The constraints

constraints

cost and so on

8

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

9

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

programming models

Certainty

10

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Additively

11

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Finite choices

12

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

variables

constant

13

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

14

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

programming

individual farm

15

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

possible cost

constraints

16

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

17

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

sales incentives

18

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Case Study

Abstract

Introduction

19

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

20

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

profitability

shown in Figure 2

21

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

provisioning

22

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Model

23

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

were attained

month

24

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Where

company

delivered

Dec302004)

network

25

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

26

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

27

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

1200 x 140657 = R$ 168788400

Where

28

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

154565 x1 + 185636 x2 + 44501 x3 + 108122 x4 + 149251

x5

29

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

162005760

30

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

31

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

anticipation

32

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

33

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

BIBLIOGRAPHY

reference

Books

Operation Research

Websites

httpwwwwikipediaorg

httpwwwgooglecom

613wwwanswerscom

34

Project Report On
CONTENTS

Date post:	07-Dec-2014
Category:	Technology
Upload:	-aadil-shaikh
View:	698 times
Download:	1 times

Final hrm project 2003

Technology