AN APPLICATION FOR EFFICIENT
TELECOMMUNICATION NETWORKS PROVISIONING USING LINEAR PROGRAMMING
Maria Augusta Soares Machado,
IBMEC-RJ, Brazil
E-mail: mmachado@ibmecrj.br
Walter Gassenferth
IBMEC-RJ, Brazil
E-mail: walterg@quantiac.com
Submission: 17/06/2014
Revision: 02/07/2014
Accept: 07/07/2014
ABSTRACT
This paper presents a practical
proposition for the application of the Linear Programming quantitative method
in order to assist planning and control of customer circuit delivery activities
in telecommunications companies working with the corporative 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 company’s
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.
Keywords: Linear Programming Method, Telecommunication Networks, Provisioning.
1. INTRODUCTION
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 customer’s 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 customer’s needs before their competitors do. A data
communication network provisioning, for instance, which in 1999 was activated
in 45 days by Europe’s biggest players, BTI, and by U.S.A.’s 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 customer’s network and
this prioritization of delivery brings about some loss to the service
provider’s cash.
This paper, which is based on data
provided by one telecom provider in Brazil, presents an essay that aims to
propose a simple alternative, yet with a solid mathematical basis, in order to
ensure there is a marker in the prioritization of customers’ circuit
provisioning that aims at the main goal of sales and the business: its profitability.
2. CIRCUIT ACTIVATIONS 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 customer’s
application, simulating the day-to-day of the business as shown in Figure 2.
Figure 1 – Diagram
representing a Customer Network Provisioning set up from the backbone of a
large telecom operator.
In Figure 2, it can also be noticed
that within the assembly of the backbone’s physical part the local access
granting activities (2), also known as ‘last mile’; equipment acquisition
activities for installation at customers’ sites (4); facility allocation
activities (communication channels to be used in the customer’s network) within
the operator’s large backbone (1); and customer’s network configuration (3) are
all capital availability activities of fundamental importance in order to
ensure activation of all the circuits making up the customer’s network
provisioning.
Figure 2 – Simplified
representation of the Customer Network Provisioning Process of a large telecom
operator in Brazil.
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 – 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.
3. THE LINEAR PROGRAMMING MODEL PROPOSED
The operational research is a
mathematical method developed to solve problems related to tactical and
strategic operations. Its origins show its application in the decision-making
process of business analysis, mainly regarding the best use for short funds.
This shortage of funds is a characteristic of hyper-competitive environments.
Although the practical application of a mathematical model is wide and complex,
it will provide a set of results that enable the elimination of a part of the
subjectivism that exists in the decision-making process as to the choice of
action alternatives (BIERMAN and BONINI, 1973).
One important feature of the
operational research that greatly benefits analysis and decision is the use of
models. The models allow for experiments to be conducted and this means that
the decision may be further tested and evaluated before final decision and,
therefore, before preparation and implementation of any solution through
planning and action (ACKOFF, 1976).
It is clear that the study of a real
system has a certain degree of complexity since it is influenced by a number of
elements or variables and also by both internal and external social, political
and economic matters. The characteristics of the decision-making process will
have great influence on determining and utilizing models. One model consists of
the representation of reality through variables that allow for solving a given
problem. Ackoff and Sasieni (1971) classify problems in three kinds:
a)
Iconical:
those models dealing with the representation of images in a different scale
from the actual object of study like, for example, aircraft, ships and
automobiles models;
b)
Analogical:
these make use of a set of properties in order to represent another set of
properties like, for example, the graphs that make use of geometrical greatness
and positions in order to represent many types of variables and their
relationships;
c)
Symbolical:
these represent the variables and their relationship through letters, numbers
and other types of symbols; they are general and abstract models, normally
presented like mathematical relations and reflect the structure of what they
reproduce.
Therefore, the complexity of the
decision-making process applied to business, in some cases, can be studied
through operational research by means of symbolic models (CARASTAN, 1993).
The operational research can assist
the decision-making process through the Linear Programming Model. This model is
suitable for solving such problems as, for example, allocation of short funds
in order to achieve a certain goal. Linear Programming deals with special
mathematical problems by developing rules and relationships that aim at the
distribution of limited funds under the restrictions imposed by either
technological or practical aspects when an attribution decision has to be made
(ANDRADE, 1990).
One type of problem for which the
Linear Programming provides a solution could be summarized as: to maximize or
to minimize any dependent variable which is a linear function of several
independent variables which are subject to many restrictions (CARLSON, 1988).
Example: profit maximization, return
on investment, sales, cost reduction, machine-hour, size of material
inventories etc.
In order to solve problems through
the proposed model, structuring of a general formulation is required.
The problems dealt with here refer
to the optimization of resources of a given object function “f”, which is
subject to system and/or environment restrictions. When the problem involves
“n” decision-making variables and “m” restrictions, the model can be
represented mathematically in the form of either maximization or minimization
of the object function (CORRAR and TEÓPHILO, 2003; ZUMA V.,
CALDEIRA, A. M., PACHECO, G. L., MACHADO, M. A.S., GASSENFERTH, W., 2008). For
instance, for a maximization problem:
MAXIMIZE
Z = C 1X 1 + C 2X 2 + ... + C nX n
Subject
to restrictions:
a
11X 1 + a 12X 2 + ... + a1nXn ≤ b1
a21X1
+ a22X2 + ... + a2nXn ≤ b2
am1X1
+ am2X2 + ... + amnXn ≤ bm
Being
compulsory that:
X1,
X2, ... ,Xn ≥ 0 (note: non-negative figures)
4. THE HYPER-COMPETITION CONCEPT
The application of linear
programming models is recommended in production environments, especially in
companies that are faced with a scenario of hyper-competition supporting the
decision-making process. Hyper-competition consists of an environment marked by
fast and intense competitive movements in which aggressive, innovative flexible
competitors invade the market to build up advantages and destroy their
opponents’ position. The approach focused in the hyper-competitive environment
is made up of the rupture of the "status quo", thus creating a number
of temporary advantages (D'AYENI, 1995).
The hyper-competitive behavior
creates, continuously, new competitive advantages that render obsolete or
neutralize the opponent’s competitive advantage, create inequality and destroy
perfect competition, thus breaking market equilibrium. Hyper-competition takes
place in a world of complex dynamics, where players interact at world level,
where competitive advantages are ephemeral and the life cycle of products is
short, unstable and, in many cases, unpredictable. In this context of permanent
instability, survival becomes a function of the ability to interact
associatively with suppliers, customers and competitors. And so arises the need
for organizational networks that aim to reduce uncertainties and risks and to
organize economical activities through the coordination and cooperation among
companies.
As for the internal plan,
organizations need to work in a more optimized fashion by reducing their costs
and maximizing their earnings by means of revenue anticipation, for instance.
The mathematical models become of utmost importance in supporting productive
activities and aiming at a higher efficiency of the operating processes and
greater support to the tactical, immediate decisions, causing this type of
organization to have a continuous evolution, which is fundamental in a
hyper-competition market. The telecommunications market, especially in
5. THE CASE OF THE BRAZILIAN TELECOM COMPANY
The customer network provisioning
division of a big telecommunications company in the Brazilian market activates
on a monthly basis 3,000 circuits of different products (types of network),
which are offered to the market in the following categories: Private Telephone
Network, Internet Network, Intranet Network, Low Speed Data Network, and High
Speed Data Network. Its limited capital and output capacity allow it to
activate only 35% out of the 8,500 circuit’s 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 company’s higher
management can be followed.
So, in a typical month of 2004, a
survey was conducted as to the situation of the company’s circuit delivery and
the following results were attained:
Table 1: Table that
summarizes Circuit Backlog (Circuit Delivery) per Service Backlog of a
Brazilian Telecom Company in a typical month.
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$ 2,66; 1R$ = US$ 0,375 on Dec/30/2004);
·
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 3,000 circuits per
month without any additional work shift or engagement of temporary labor. Five
main limiters were attained as well as their quantities that are required per
month per type of product, as shown in Table 2 below.
Table 2: Table that summarizes the required
amount of each component that make up customer’s circuits per type of service
backlog.
Where:
Type of Resource: Part required for
making up a customer’s circuit: Access or Last Mile is the linking point
between the customer’s site and the operator’s backbone; Equipment for the
customers’ sites are modems, routers or other equipment required for customer
communication on each of his sites; Network Facilities are communications
channels within the operator’s backbone that carry customers’ 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 operator’s backbone to allow traffic of the customer’s
network circuits through its facilities; Other Resources are a set of minor
factors that have been grouped into a single item.
·
PT:
Private Telephone Networks;
·
INTER:
Internet networks;
·
INTRA:
Intranet Networks;
·
LSD:
Low Speed Data Networks;
·
HSD:
High Speed Data Networks.
Finally, the available amount of
each limiting resource in a month was attained, from the physical viewpoint, as
shown in Table 3 below.
Table 3: 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 company’s revenue
formation, resulting from the greater amount of earnings as possible and
considering the existing limitations.
6. THE SOLUTION PROPOSED THROUGH A LINEAR PROGRAMMING
MODEL
What the company’s 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 model’s automation is guaranteed
through Microsoft Office’s Excel application available in any of the telecom
companies’ PCs in
In addition to the information made
available by the company, only a calculation of the 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 1,200, as shown in Table 1, the maximum number of activated
circuits would be 1,200, equivalent in financial values to: 1200 x 1406,57 = R$
1.687.884,00.
Where:
1406,57 is the weighted average of a
circuit’s price, considered the prices in the fourth column of the Table in Table
1 against the weighting figures of the second line of the Table in Table 2, the
line referring to access. By doing the same with the other limiting resources,
the limits of the table in Table 4 are attained.
Table 4: Table for the
monthly physical and financial limit of each resource required for the
activations.
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 à 1545,65 x 1 + 1856,36 x 2 + 445,01 x 3
+ 1081,22 x 4 + 1492,51 x 5
Once what is intended is to maximize
the revenue from the prices of the circuits of each product (see Figure 1).
Restrictions
to the Model:
R1)
998 x 1 + 162 x 2 + 132 x 3 + 289 x 4 +
108 x 5 ≤ 1.687.884,00;
R2)
1276 x 1 + 206 x 2 +169 x 3 + 369 x 4 + 137 x 5
≤ 2.157.202,84;
R3)
333 x 1 + 54 x 2 + 44 x 3 + 96 x4 + 36 x 5
≤ 562.736,00;
R4)
1477 x 1 + 239 x 2 + 196 x 3 + 428 x 4 + 159 x 5 ≤ 2.497.269,12;
R5)
958 x 1 + 155 x 2 + 127 x 3 + 277 x 4 + 103 x 5 ≤ 1.620.057,60;
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 Table 2).
R6)
x 1 + x 2 + x 3 + x 4 + x 5 ≤ 3000; maximum output capacity considered.
R7)
x 1 ≤
5042;
R8)
x 2 ≤
816;
R9)
x 3 ≤
668;
R10)
x 4 ≤
1459;
R11)
x 5 ≤
543;
Once there is a finite set of
circuits to be activated per month per type of network (product).
R12
a R16) x 1, x 2, x 3, x 4, x 5 ≥ 0. Since there are no negative activations
(deliveries).
By submitting the Model to the
SOLVER function in Microsoft’s Excel application, the results shown in Figure 3
are attained.
Figure 3: Output of
Excel’s SOLVER function.
The most outstanding points shown
through the Excel’s results are: the optimum outputs for the topic month would
be the activation of 1,441 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 3,000 activations monthly, amounting to a revenue of R$
4.768.888,31 for the company in the month of study.
If the same model is calculated,
bringing production up to 4,000 circuits a month, the distribution would be:
Telephone networks 1,062, Internet 816, Intranet 120, Low Speed Data 1,459,
High Speed Data 543, for a revenue of R$ 5.597.053,12, leaving only the
Telephone and Intranet circuits to be solved in over 30 days, as Figure 4 below
shows.
Figure
4: Output of Excel’s SOLVER function.
7. 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 pre-defined by the company’s 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$ 1.406,39 = R$ 4.219.170,00, which is R$ 549.718,31 lower than the
revenue made available, by following the linear programming model. This means
some revenue anticipation of roughly 2.5 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
4,000 circuits per month, the revenue anticipation is increased by (R$
5.597.053,12 – 4.768.888,31) R$ 828.164,81 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 an
activation, such as a customer’s urgent need or its category in a segmentation
by size or importance. The same method used in this paper can guide the
acquisition of resources for circuit activation, rental of third parties’
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.
REFERENCES
ACKOFF, R. L.; SASIENI, M. W. (1971) Pesquisa Operacional. Tradução de José L.M.Marques e Cláudio G.
Reis. LTC, Rio de Janeiro.
ACKOFF, R. L. (1976) Planejamento
Empresarial. Tradução de Marco Túlio de Freitas. LTC, Rio de Janeiro.
ANDRADE, E. L. (1990). Introdução
à Pesquisa Operacional. LTC, Rio de Janeiro.
BIERMAN Jr., H.; BONINI, C. P. (1973) Quantitative Analysis for Business
Decisions. 4th edition, Richard D. Irwin, Illinois.
CARASTAN , J. T. (1993). Uma
Análise da Utilidade da Programação Linear sob o Enfoque Contábil-Gerencial.
Tese de Doutoramento defendida e aprovada na Faculdade de Economia,
Administração e Contabilidade - USP, São Paulo.
CARLSON, C. K. (1988) “Information Management Approach and Support to Decision-Making”.
Information & Management, North-Holland, Vol.15, Number 3, Oct, 88.
CORRAR, L. J.; TEÓPHILO, C. R. (2003). Pesquisa Operacional para Decisão
em Contabilidade e Administração. Editora Atlas, Rio de Janeiro.
D’AVENI, R. (1995). Hipercompetição.
Editora Campus, Rio de Janeiro.
YANKEE GROUP. [My Yankee Home Page]. Available for members in: http://www.yankeegroup.com/custom/search/search_results.jsp#search_results ,
ZUMA, V.; CALDEIRA, A. M.;
PACHECO, G. L.; MACHADO, M. A. S., GASSENFERTH, W. (2008), Métodos Quantitativos com EXCEL, Thomson Learning.