Essays /

14105 30226 1 Pb Essay

Essay preview

Volume 6• Number 2 • July - December 2013


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




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,
decisions allowing a
that runs
parallel about
with the
analysis is ofthe
2007), (Goetschalckx,
& Dogan,
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
at hand(Perry,
deals with
movement of Another
goods byfactor
and other
that runs
in parallel
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
diesel vehicles,
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
a series positive
of different
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
the redesigning
(CPG), with headquarters
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
must be
considered: suppliers, factories, DCs,
over Sãoand
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
2003), asDCs,
can be
seen in Figure
ate students
Escola de(Chopra,
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


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
a whole
class of different
solutions, each taiorder toor minimize
theat total
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
and constraints
the trans- are
& Mohammad,
(Kropf &
the elements
with linear
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
point of or
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
the transportation
routes to
the customers
that will be assigned
it can be either zero or a fixed amount) requires a
linearization procedure in the modeling (Sitek & Withere
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
is to move
the products
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,
be modeling
moved in (Sitek
each route
are the decision
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
brief review
out of aofsupply
must notand
exceed the
karek, 2012). From an historical perspective the opamount
to be
timization of goods transportation had been studied
they network
relate to the process of optimizing and redesigning a
as early as
1930, as partprocedures
of the USSR as
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
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


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...

Read more


+1 -1 -140 -18 -2013 -3046 -40 -5 -6 -797 -828 .. /10.12660/joscmv6n2p74-93 /articles/eolss.pdf /bitstream/handle/10156/3746/perrythesis. /ibm/university/academic/pub/page/ban_ilog_programming. /personal/jmf/philipsaure/kropfsaure_2011_12_16.pdf /project/opensolver/ /wiki/opti/index. 0 00 04 07 08 1 10 11 12 123 13 14 14105 15 16 17 17m 18 19 1930 19401946 1960 1963 1984 2 2.1 20 2002 2003 2004 2005 2006 2007 2008 20082013 2009 2010 2011 2012 2013 20a 20integer 20large 20masters 20program.pdf 20scale 20thesis 21 22 23 24 25 26 26.133.512 26.133.716 26.139.605 26.150.744 26.162.250 26.176.833 26.194.947 26.212.528 26.235.984 26.260.671 26.284.127 26.312.369 26.341.173 26.374.946 26.414.672 26.456.825 26.508.863 26.566.322 26.633.644 26.710.367 26.787.013 26.871.384 26.971.041 27 27.115.694 27.291.289 27.480.289 27.752.740 28 28.045.175 28.565.673 29 29.180.240 290.000 3 3/4 30 30.016.453 30226 31 31.070.534 32 33 39 3gb 3rd 4 4.000.000 40 45m 497 4x2 5 50mb 520 520.000 557 5th 6 60 7 714 74 75 76 77 78 79 792 8 80 81 810 817 82 83 84 85 851 86 865 87 88 89 9 90 91 92 93 a.t abil abl absolut abstract academ access accomplish achiev ad add add-in addin address adequ adher administr adminstração advantag advic aeschbach aeschbachproblem affect agreement ahost aiftransport aim albright algebra algorithm allow almost almostofunlimit alreadi also alt altern although altiparmak alway amin among amount amountconstraint amountintoth analysi analysisitsa analyz anddevelop andguarante andwa anomali anoth ansp1 ansp2 aofsuppli aon appdata appear appendix appli applic applicaequ approach appropri approxim arbitrari arc area area2012 argu argument around arriv art articl artifici asdc ask assign assum ate ation attent auckland audienc author autom automat avail averag avoid b back base basi basic beamov becam becom behub bein berer berwick besid besimplifi best better beyond big bigger biggest billion binari binat bintprog blank blum boost bound branch branch-and-bound brasil brazil brazilian brief broad broke bug bundl busi bution button byfactor c ca calcul california call cambridg candid cannot capabl capac captur carbon care carreta case catarina cel cell cengag center centr centrino centro chain challeng chang char choic choos chopra chosen chunk cij cision citi citytj class classroom clear click code coeffici column com combin combinatori come command commonwealth compani companyand compar competidustri competit competitor complet complex compos comput comthat conclus conduct confer confus conmicrocomput connector consequ consid consider constraint consult consum context continu control convert cooper copado copado-mendez copi core corpor correct corrêa cost costhub could counterpart coupl cours cpg cplex cplex.xls cplex125.xll creat criterion cross csv ctrl cui cumbersom current curri custom customlor d daili dakota dantzig data dc dcs dctheir de deal decemb decid decis default degre dell demand demonstr depart departur depend depict deploy desatisfysom describ design detail determin deth dethi develit develop di diesel differ difficult ding dioxid direct director directori diretor discret dissemin distanc distribuição distribut distributor distrikeep divid divis dock document doesn dogan doi doig done dong doubt download downsid drawback dsc due duxburi dynam eaesp eaesp/fgv earli earlier easi easili econometrica economi ed edit effect effici effort eight eighti either ej ej-fgv electr element eleven embed emerg emiss employ empresa encapsul engag engin engineerof enough entir entitl environ environment equal er error esc escola eshlaghi eshon especi establish etc european evalu even everi everyth evolv exact exampl example01.m exceed excel exchang execut exist exitflag experi explain express extens extern exth extra f face fact factor factori faculti fair far featur feder felt fgv fgveaesp fie field fifti figur file final find finish first five fix flag flanneri flavia [email protected] flexibl flux flávia focus follow forchosen forlinear form format fortran found four fourteen framework free freeli freewar freita frontlin fulfil full fulli function fundação futur fval g gen general generat genet gerai get getulio geun ghz gin give global go godfrey goe goetschalckx good gopalan got grand great greater group grove guarante guess gustavo [email protected] h half hand handl hannon happen he/she headquart hernandez hicl hide high high-level higher hind histor hj hockey home hope hors host howev huang hub hubsha hubstransp1 huge human hundr i.e i.e.moved i2c2 ibm ieee ignor ili illustr ilog imiz impact implic import impress improv in includ increas incred indic individu indock indu industri inform infrastructur ing initializequicksolv inmor input instal instanc instead institut integ integr intel intens interconnect interest interfac intermedi intermediari intern inthat introduct introductori invent inventori invest involv issn isspreadsheet issu j jan job journal jr juli junior junqueira júnior k kao karek kearney keep keepestablish kept key keyword kilomet kind km know knowledg ko kropf l lack laghi land languag laptop larg last late later lay lb lead learn least leav lem less let level like limit lin lindo line linear link linprog list literari load locat logic logist long look loop lower lp lpsolv lu m macroeconom made main major make manag manageri mand maneuv manika manipul manner manufactur march margin mark market mason master mathemat mathprompt mathwork matlab matlababov matric matrix matter maximum mazon mcgarvey mean meet mehnen member memori mendez mention menu method methodolog microat microcomput microsoft microsystem mid mid-level middl middle-level million milp min.volume mina minim minimum minor mintheir minus minut mirapalheta mix mj modal mode model modest modiand modifi modl mohammad moment monica month mov move movement much multimod multipli must mustdu n n.dcs nagourney name nation natur need negat neglig neighborhood net netkarek network neural never new next nice nineti no.1 no.17 no.3 node non non-academ non-linear non-neglig non-techn nonetheless nonewrit nonlinear normal north notand note notploy nov null number numer ny o object obtain obvious offer ofgood ofth oftot oh ok one onset opamount ope open open-source-softwar opensolv opensolver.xla opensolver21 oper oppos opti optim optimalinsolut optimisimplifi option opwer order org origin otherresources/aeschbacher otherwis output outth ouyang ov overal overcom p pacif packag pag page pags.775-779 pair paksoy pani pano paper paradigm parallel paramet paraná park part parti partial particular partprocedur pass past paulo pb pdf per percentag percept perform perri person personnel perspect php/dl/downloadopti pictur piec pike place plain plan plus point portat portfolio portugues posa pose posit possibl possibles poswher potenti power pp pp.1111-1118 practic prasad precis prefer prein prepar present press pretti previous princ prince-pik problem probnonlinear procedur proceed process processd produc product prof.andrew prof.of profession profit program project proper provid proxim pure purpos put qiu quadrat qualit quant quantit quantiti quarter quick quir r radhakrishnan ragsdal railway ram rand rang ravindran raw razavi re read reai real realiz realli reason reassur receiv recent recip recognit record redes redesign reduc reduct refer reflect regard region relaconsist relat relationof relationship releas remain ren repeat repetit replic report report.m report.xls repres reproduc requir reread research resourc restrict result retail retriev revenu review revis ribbon rio roam rout routin run runquicksolv sale santa satisfi sauré save scale scenario schedul school schrijver scienc scientif scope search second section sector secur see seem seen select sell senior sent separ sequenc seri set seven sever share sheet shen shipment shippedoftogeth show showloc shown shut side sider sign similar simpl simplex simplifi simul sinc sitek situat six sixteen sixti size small smaller smooth social soft softwar solid solut solv solver somehow someon someth sometim somewhat soni sophist sourc south south-western southern spars special specif speed spread spreadsheet springer springerverlag stabil staff standalon standard start state state.relationships statist stay step sthe stiff still stop straighforward strateg streamlin string strong structur student studi studio125 stuff subdirectori subject submit subset subtract sudden suggest suit suitabl sul sum sun supermarket suplemento suppli supplier supply-chain support suppos surpass surpris system são sãoand sãoproblem tabl tactic tailor taiorder take taken talk tamount task tation taught team technic techniqu technolog ten term test teukolski thanhub thatpart thatstructur theat thecross thegood thei theimplic theless themodel theoret theori therefor thesi theto thetoproblem thing think third third-parti thirteen thirti thomson thought thousand three throughdepict ti time timiz tion tionship tipic tiwari tj tmax tmin toco togeth ton took tool toolbox toor total totalalso totalmov totalt toth tough tran transfer transit translat transp transp1 transp2 transpor2 transport transporta transportahub transportaov tri trio truck true tsao two two-year twofold type ufrg unbound undergo undergon undergradu undergraduship understand understood uniqu unit univers unlimit unpack unstabl upon upper urban usa usag use user ussr usual v vaio valid valu van varga variabl varieti varifor various vast vba vector vehicl veimpact vendor version versus vetterl viabil vidal view virginia vol.143 vol.5 vol.7 vol.9 volum w wang want wars way websit weight well western whoever whole wholesal wick widespread wiin wikarek willing wilson window winston winter wither within without word work workbench workshop world would wrapper write written wrong x x1 x2 x3 xij xlsread xlswrite xtype y year york youand young yuan zation zealand zero zhou zip zurich