### Essay preview

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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*supernet.isenberg.umass.edu/articles/eolss.pdf*

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*www-03.ibm.com*

*www-03.ibm.com/ibm/university/academic/pub/page/ban_ilog_programming.*

*www.eui.eu*

*www.eui.eu/personal/jmf/philipsaure/kropfsaure_2011_12_16.pdf*

*www.i2c2.aut.ac.nz*

*www.i2c2.aut.ac.nz/wiki/opti/index.*

*x*

*x1*

*x2*

*x3*

*xij*

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