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Volume 6• Number 2 • July - December 2013

DOI: http://dx.doi.org/10.12660/joscmv6n2p74-93

Quantitative Modeling in Practice: Applying
Optimization Techniques to a Brazilian Consumer
Packaged Goods (CPG) Company Distribution Network
Design (Technical Note)
Gustavo Corrêa Mirapalheta
Fundação Getulio Vargas - EAESP
[email protected]

Flavia Junqueira de Freitas
Fundação Getulio Vargas - EAESP
[email protected]

ABSTRACT: This article aims presenting an example of quantitative modeling and optimization techniques application to the design of the distribution network of a consumer packaged goods company in São Paulo, Minas Gerais and Paraná states, Brazil. This study shows that economies of 5% to 10% (which represent in absolute terms, approximately R$10 million) can be quickly achieved by the application of linear optimization technics showing a vast area of improvement for Brazilian economy, with minimal investments, on a macroeconomic scale. First, it is made a brief review of quantitative modeling techniques as they are applied in the modeling and optimization of network problems. In the second section it is depicted the company’s distribution problem.. The model is then optimized through a series of software so the methodologies and results can be compared. The article finishes with the results that the company got from the model deployment, presenting a clear case of optimization techniques in a real world application, showing the viability of easily using such techniques in a broad range of distribution and logistics problems.

Keywords: logistics, network design, optimization, quantitative modeling

74

75

1. INTRODUCTION

Mirapalheta, G. C., Freitas, F. J.: Quantitative Modeling in Practice: Applying Optimization Techniques...

ISSN: 1984-3046 • Journal of Operations and Supply Chain Management Volume 6 Number 2 pp 74 – 93

Empresa Júnior). EAESP/FGV is the leading business school in Brazil. From now on the CPG company which is the study object of this article will be just called “company”. The objective is to minimize

the overall distribution costs through the adequate
choice of distribution centers, DCs (“centros de distribuição” as they are called in Portuguese), transport routes from factories to DCs and the appropriate
assignment of customers (mainly wholesale companies and supermarkets) to each DC, based on demand and costs levels.

The usage of quantitative modeling to describe
problems in the area of supply chain management
is an intense research subject (McGarvey & Hannon, 2004). Several linear (and nonlinear as well) optimization techniques have been specifically tailored to them, allowing managers and researchers to have them applied in a variety of different situations (Geunes & Panos, 2005); (Winston, 2003). The usage of these techniques by a broad, non-technical

audience have been much increased through the
dissemination of spreadsheet software, like MicroAt first the company decided to choose the DCs only soft Excel, and Excel’s Add-In package Solver from
by the criterion of proximity from its customers.
Frontline Systems (Ragsdale, 2008). Full scale, inDue to volume increase, coupled with stiff competidustrial models have been studied and solved in tion, the logistics costs started representing a conmicrocomputers, through the usage of numerical siderable percentage of the company profits. This

simulation and optimization software like Mathprompted the upper management to try alternatives works Matlab (Radhakrishnan, Prasad, & Gopalan,
to the selection process, which would be based not
2009), (Huang, 2012), (Huang & Kao, 2012), (Eshonly in one but in several factors. It was hoped that laghy & Razavi, 2011), Opti Optimization Toolbox
this way, besides getting an optimal solution for the
(Wilson, Young, Currie, & Prince-Pike, 2008-2013)
problem at hand, the model could let managers think
and IBM CPLEX (Ding, Wang, Dong, Qiu, & Ren,
their
decisions allowing a
Another
factor
that runs
parallel about
with the
theimplications
analysis is ofthe
environmental
2007), (Goetschalckx,
Vidal,
& Dogan,
2002).inMore
continuous improvement process to be deployed,
recently, the limitations of Frontline Solver Standard
and letting the spread of this quantitative based dethis redesign. Since Exthe model aims a total cost reduction and the
package implications
that is shippedoftogether
with Microsoft
cision process to be spread over other regions.
cel have been overcome with the release of freeware
add-ins like
OpenSolver
2012),the
(Aeschbachproblem
at hand(Perry,
deals with
movement of Another
goods byfactor
carretas,
trucks,
and other
kinds
that runs
in parallel
with
the analysis
er, 2012) which are capable of solving linear models
is the environmental implications of this redesign.
of almostofunlimited
size. there’s a carbon dioxide emission
Since the
model aims
a totalalso
cost have
reduction
diesel vehicles,
reduction
that could
a net and the
problem at hand deals with the movement of goods
The problem that is analyzed and solved, through
by carretas, trucks, and other kinds of diesel veimpact
in the in
company’s
results.
a series positive
of different
methods
this paper,
is the
hicles, there’s a carbon dioxide emission reduction
redesign of the logistic network of a Brazilian comthat could also have a net positive impact in the pany, from the consumer packaged goods sector
company’s results.
When youand
face
the redesigning
(CPG), with headquarters
factory
located in Sãoproblem of a logistics network there are five Paulo city and a customer and distribution network
When you face the redesigning problem of a logistics
elements
their
thatpart
must be
considered: suppliers, factories, DCs,
spreading
over Sãoand
Paulo
state.relationships
Its solution was
network there are five elements and their relationof a consulting project engaged by the undergraduships that must be considered: suppliers, factories, wholesalers
customers
2003), asDCs,
can be
seen in Figure
1.
ate students
companyand
from
Escola de(Chopra,
Adminstração
wholesalers
and customers
(Chopra, 2003), as
de Empresas de São Paulo (namely EAESP/FGV’s
can be seen in Figure 1.

Figure 1 - Logistics Network Elements
Figure 1 - Logistics Network Elements

76

Mirapalheta, G. C., Freitas, F. J.: Quantitative Modeling in Practice: Applying Optimization Techniques...

ISSN: 1984-3046 • Journal of Operations and Supply Chain Management Volume 6 Number 2 pp 74 – 93

Since there´s just one factory in the company´s structure and the company itself doesn´t sell directly to consumers, the model from Figure 1 was simplified

from four levels and five different elements to two
levels and three different elements (as can be seen in
Figure 2) when applying it to this specific problem.

Figure 2 - Company’s Model Logistic Network Elements
Figure 2 - Company's Model Logistic Network Elements

In order to minimize the total operational cost of a
relationship between transportation cost, distance
network, the relationships among the elements and
and transported weight, around the problem of mintheir constraints are modeled with linear functions. imizing the cost of moving products from factories
This is done in order to guarantee the existence of
to distribution centers and there to customers have
only one optimalInsolution
no solution
all. The
evolved
a whole
class of different
solutions, each taiorder toor minimize
theat total
operational
cost
of a network,
the relationships
decision variables are the DCs location, the customlored to a specific piece of the logistic network (Berers that will be assigned
to each
DCtheir
and constraints
the trans- are
wick
& Mohammad,
2003),
(Kropf &
Sauré,
among
the elements
and
modeled
with linear
functions.
This
is 2011),
portation routes that will be chosen to fulfill the
(Nagourney, 2007).
customer´s demands. The last cost factor is the fixed
done in order to guarantee the existence of only
optimal solution
no solution
at system
On aone
theoretical
point of or
view,
a network
cost to operate a DC, which due to its nonlinear relaconsists of a series of nodes interconnected by arcs tionship with the amount that will be moved (since
representing
the transportation
routes to
available
all.
The
decision
variables
are
the
DCs
location,
the customers
that will be assigned
it can be either zero or a fixed amount) requires a
(Nagourney,
2010).
As
in
a
real
distribution
network
linearization procedure in the modeling (Sitek & Withere
are
nodes
which
supply
products
to
each DC and the transportation routes that will be chosen to fulfill the customer´sthe netkarek, 2012). work and there are nodes which demand them. The
In the next
section
it
will
be
presented
a
brief
review
is to move
the products
from
demands. The last cost factor is the fixed challenge
cost to operate
a DC,
which due
to the
its supply
of network modeling and optimization procedures
nodes to the demand nodes in the least costly posas they relate to the process of optimizing and redesible way (Tsao & Lu, 2012) . Most of these probnonlinear relationship with the amount that will be moved (since it can be either zero or

signing a logistic network.
lems can be solved by assigning a different variable
cost to each arc in the network, supposing that the
a fixed amount) requires a linearization procedure
& Wikarek,
amountintothe
be modeling
moved in (Sitek
each route
are the decision
2. LITERARY REVIEW
variables and trying to minimize the linear combination of amounts to be moved and variable costs The area2012).
of logistics optimization through linear
in each arc. This solution must satisfy a series of
programming methods, have undergone a strong
more or less standard constraints . The amount to
development, especially after the 80’s (Sitek & WiIn
the
next
section
it
will
be
presented
brief review
network
modeling
beamoved
out of aofsupply
node
must notand
exceed the
karek, 2012). From an historical perspective the opamount
available
to
be
moved
and
the
amount
to be
timization of goods transportation had been studied
moved
into
a
demand
node
should
at
least
satisfy
optimization
they network
relate to the process of optimizing and redesigning a
as early as
1930, as partprocedures
of the USSR as
railway
it (Hockey & Zhou, 2002). The flux of products in
management (Schrijver, 2002). Its development had
each intermediary node must be kept smooth, in
a major boost
in
the
late
40’s,
with
the
development
logistic network.
other words, the amount coming to the node must
of the Simplex Method by Dantzig and its applicaequal the amount that leaves it minus the amount tion to various problems either in specific engineerof products that will remain in the node, besides ing application or in the solution of broad classes of

that, the arcs can be submitted to a maximum flux
managerial problems (Dantzig, 1963) and another
constraint (Cui, Ouyang, & Shen, 2010). Finally to
one with the development of combinatorial optimisimplify things when the problem is being deployed zation (i.e. integer programming methods) in the bein a spreadsheet, the supplies are considered to be ginning of the 60’s (Schrijver, 2005). Due to the linear

Literary Review

77

Mirapalheta, G. C., Freitas, F. J.: Quantitative Modeling in Practice: Applying Optimization Techniques...

ISSN: 1984-3046 • Journal of Operations and Supply Chain Management Volume 6 Number 2 pp 74 – 93

negative values (as opposed to the demands, which
will be considered positive). This allows all flux constraints in the nodes to be thought of having the following structure: Arrivals – Departures >= Supply(-) or Demand(+)
If the optimization problem under development requires also decisions regarding the availability of a specific network structure (like having available or
not a distribution center or a specific route), binary
variables can be used to model this kind of decision.
As long as these binaries variables are kept adding
or subtracting their values within each other, the
problem will be kept linear and so, entitled to have
an unique solution which will be able to be found by
the simplex method (Altiparmak, Gen, Lin, & Paksoy, 2006).
Besides the Simplex Method...

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