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Mehrdad

Mehrdad MUniversity Alireza RasUniversity Amir H. Sar KEYWORClosed loopBinary progvehicle rousimultaneoand deliver

In today's windustrial

Correspondin*

Email: rashidi@Received 13 D20 December 2

Internationa

ational Jour

Loop Su

d Mirzaba

Mirzabaghi, M

shidi Komijan

rfaraz, Assista

RDS p supply chagramming,

uting, us pick-up ry

1. Introworld, the chspheres are

ng author: Alire

i@azad.ac.ir December 2015; r2016

al Journal of Ind

nal of Indus

upply Ch

aghi, Alirez

M.Eng. studen

n, Associate P

ant Prof., Col

Aain,

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oduction1 hanges in the

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eza Rashidi Komij

revised 10 Febru

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za Rashid

nt, College o

Prof., Departm

llege of Indust

ABSTRACT

In the recento economicwell as envihand, manyforward antransport aca logistic symixed integeforward / renetwork use/reverse logcommon facdisposal facand multi-peach level. Vsuch as muwith simultaand split dbetween thethroughout total cost. Nshows that reasonable t

© 2016 IUReserved

e economic amore quick

ijan

uary 2016; accep

ring & Producti

eering & Pr

ber 2016, Volumpp. 287- 3

tp://IJIEPR.

anning W

i Komijan

of Industrial

ment of Indust

trial Engineer

T

nt decade, spc benefits ofironmental ly studies cnd reverse ctivities are ystem, and iter linear preverse suppled in this p

gistic networcilities of procilities and cproduct withVarious typeulti-period raneous delivdelivery. The various fthe planninNumerical ethe proposetime for sma

UST Public

nd kly

pted

thhagorecoinanpa

ion Research, Se

roduction Re

me 27, Numbe303

.iust.ac.ir/

With Veh

n*& Amir

Engineering,

trial Engineer

ring, Tehran S

pecial attentf recovery alegislation alaim that s

logistic calso one of t needs an a

rogrammingly chain as paper is a rk, which is oduction/rec

customers. Th the abilityes of vehiclerouting, muvery and pi

he model rfacilities in ng horizon wexample fored model coall and medi

ation, IJIE

han in the paas increasedoods at a lowespond to ompetitive ncreasingly end integratedarallel to th

eptember 2016, V

esearch (201

er 3

hicle Rou

H. Sarfara

Tehran Sou

ring, Firoozko

South Branch,

tion is paid and recyclinand social cseparate, secauses sub

f the most impaccurate pla

g model is pwell as vehmulti-echelocomprised

covery and The proposedy to considee routing moulti-depot, mick-up, flexiresults pres

forward awith the objr solving thould reach tium real-wo

EPR. Vol.

ast. Competd, and costumwer price and

this requadvantage

established d logistics. Oese developm

Vol. 27, No. 3

16)

uting

az

uth Branch, I

ooh Branch, I

Islamic Azad

to reverse lng of used pconcerns. Oequential pb-optimality.

mportant comanning. In throposed for

hicles routinon integrateof capacitatdistributiond model is mer several fodels are alsmulti-producible depot aent the pro

and reverse jective minimhe model usthe optimal orld problem

27, No.3, A

ition amongmers want hd low delive

uest and m, compansupply chaiOn the othements in the

Islamic Azad

Islamic Azad

d University

logistic due products as n the other

planning of . Effective

mponents of his study, a r integrated ng. Logistic ed forward ted facility, /collection,

multi-period facilities in so included cts, routing assignment, oduct flow

directions mization of sing GAMS solution in

ms.

All Rights

g companies high quality ery time. To maintaining

nies have n networks

er hand and e economic

f

f

f

288 M. H. S

sphere, becproducts, inof customattention tohas increaslegislationsresponsibillife cycle point of vproducts isproducts, service resway, it incompany. been done used produimportant Kodak, Xerefurbishin In the litreverse loglogistics, in(i.e., consuproducts) manage endecisions sto secondcustomers)materials), markets throf some haMany studseparate orreverse lAccording forward anconsiderablthe integrreverses losupply chasignificant loop suppSupply of raw materiadistributioncostumers CLSC in returned premanufactway that isform of CL

Mirzabaghi, Sarfaraz

Internationa

cause of envncreasing en

mers and eno the reverssed. In somes force ity for theirof the prod

view, recoves profitable f

establishmesults in custndirectly leIn recent yon the econ

ucts [1]. In thcompanies, erox, have

ng and repairi

terature, difgistics’ procen general foumers) wherare collecte

nd of life puch as reman

d markets , recycling

repairing rough repairi

azardous matdies in ther sequential ogistics reto these stu

nd reverse le savings in

rated systemogistics, whain (CLSC)

importance ly chain inraw materiaals into finisn of finishethrough thereverse flow

products froturing, recycs appropriateLSC.

A. Rashidi K

al Journal of Ind

vironmental invironmental nvironmentae logistics (e countries,

companiesr products oducts. From ry and recy

for the compnt of aftetomer satisfaads to moryears, manynomic benefithe past three

such as Gepaid speciaing of the ret

fferent clasesses are presorms, start frre used proded and thenproducts thronufacturing (or if poss(to convert (to sell in

ing), and finerials. e literature

planning ofesult in sudies, integralogistics co

n costs [2]. Inm includes hich is calle

that has re[3]. Typica

n forward als from suphed productsed products e distributionw includes om final coling or dispo

e. Fig. 1 show

Komijan*& A

dustrial Engineer

impact of usconsciousne

al legislation(RL) networenvironment

s to taover the enti

an economycling of usanies. In som

er-sales repafaction; in thre profits f studies hats of recyclidecades, maneneral Motoal attention turn products

ssifications sented. rever

from end useducts (returnn attempts ough differe(to resale thesible to fir

them to ran the secoally, disposi

showed thf forward asub-optimalitated design

ourses lead n the literatur

forward aed closed-loecently gainally, a closeflow includpliers, conves in plants, a

to the finn centers. Tcollecting t

onsumers aosing them inws the gener

A. C

ring & Producti

sed ess ns, rks tal

ake ire

mic sed me air his for ave ng ny rs, to

s.

of rse ers

ned to

ent em rst aw nd ng

hat nd ty. of to re, nd op

ned ed-des ert nd nal

The the nd n a ric

OsuinW20coacadefmsyreacprprroandiinTrinCcoDfoAbedisuinacreHcotrefmdiInopm

Closed Loop Su

ion Research, SE

Fig. 1. T

One of the upply chain nventory

Wajszczuk [40%-30% of ompanies. Tctivities candvantage forffective tran

most importaystem, and everse logisctivities limroducts recroducts shououte with thnd distributirection is on the supply cransportation

nto two typesCollection oostumers and

Distribution oorward flow.

An important etween twoirections. Inuitable approntegration ctivities resueturned prod

Hence, an oncerns finansfer the fficiently by

models such aistribution plnventory mperational de

main tools to

upply Chain P

Eptember 2016, V

The generi

most imporis logistic

and tran4] showed th

the total cherefore, ann create sur companies.sportation acant componit needs anstics, non-e

mit the econcovery. Co

uld be done ahe lowest cotion of prone of the mchain managn activities s: of returned d move in theof refurbishe

issue in CLSo different

n this case, oach to costof distribuults in the

ducts on the important

nding optimproducts

y implementas vehicle rolanning.

management ecision that o improve r

Planning Wit

Vol. 27, No. 3

c form of C

rtant activitiactivities thsportation

hat the logistcosts of ma

ny optimizatiustainable . As mentioctivities are

nents of ean accurate peffective tranomic succollection ofat the right tiost. Also, traoducts in th

most importangement.

in CLSC a

products e reverse flowed and new

SC is creatinflows in

integrating t savings. Foution and

vehicles wway back to

operationalmal vehicle

through thtation of mouting mode

is another is known asesponsivenes

th Vehicle …

CLSC

es of each hat includes

activities. tic costs are anufacturing ion in these competitive

oned earlier, one of the

ach logistic planning. In ansportation ess of the f returned me and in a ansportation he forward nt problems

are divided

from final w. products in

ng synergies n different

flow is a or example,

collection with full of o the depot. l decision

routes to he network mathematical els in CLSC

important s one of the ss at lower

Closed Loop

cost, reduccustomer seThis paper brief discupresented; mathematicSection 3. computatioIn Sectionoffered.

2-1. ClosedAccording Executive C‘‘The proccontrollingraw matergoods and consumptioof recapturA review literature shin the fieldfrom suppsmaller pareverse loglogistics litespecially objective innumber acollection disposal ccapacity aPishvaee etto design areverse logcollection ccenters wiearlier, sepand reversThe configincluding lbetween componentintegrated reverse logcosts ([2],[of many onumber, loas plants, recovery, dthe optimaland reversproposed a

p Supply Cha

Internationa

cing inventoervice. is organized

ussion about the probl

cal formulaThe generat

onal results an 5, some

2. Literad-loop suppl

to the AmCouncil, revcess of plan the efficierials, in-prorelated info

on to the poinring value or

of the suhows that a d of forward

plier to finaart of the litgistics [3]. terature showafter 2005, n RL netwo

and locationcenters, rem

centers, as and the optt al. [8] propa single pro

gistics networcenters, recoith limited

parate or sequse logistics guration of location of f

them, ints. Some studplanning an

gistics reduc[9],[10],[11])of these pa

ocation, and distribution

disposal centl products flose directiona MILP mod

ain Planning W

al Journal of Ind

ory costs, a

d as follows: previous re

em descripation are tion of data are presented

concluding

ature reviewly chain ma

merican Revverse logisticnning, implent, cost-effe

ocess inventormation fromnt of origin fr proper dispupply chainlarge part of

d logistics nal costumersterature is inA review o

ws that studieare increas

ork design isn of facilimanufacturin

well as detimal flow posed a MILduct and murk consisting

overy centerscapacities. A

uential plannresults in sreverse logi

facilities andnfluences dies in this fnd design ofces the total). In genera

apers is to capacity of

n centers alters, as well aow among thn. Jayarmandel to design

With Vehicle

dustrial Enginee

and improvi

in Section 2lated works

ption and comprised instances a

d in Section remarks a

w nagement erse Logistis is defined ementing, aective flow tory, finishm the point for the purpoposal’’([5],[6n managemef the studies

network desis; a relativen the field of the reveres in this fielsing [7]. Mas to define tities such ng centers aetermine theamong them

LP formulatiultiple-echelg of costumes, and disposAs mention

ning of forwasub-optimalitistics networ

d material floall netwo

field show thf forward al supply chaal, the purpodetermine tfacilities, sulso collectioas determini

hem in forwan et al. [1n an integrat

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, a is

its in nd 4.

are

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ose 6]). ent

is gn ely of

rse ld, ain the as nd eir m. on on rs, sal

ned ard ty. rk, ow ork hat nd ain ose the uch on, ng

ard 12] ted

focuSeCondeneinecreAfocofaorcocompoinMelcotaarsianonreWinmisneofthnedeco(eprrea fomcoinpapranhoco2.Aro

M. MirzabaH. Sarfaraz

ion Research, Se

orward/reverustomer demelma et al.

CLSC with can demand eveloped a etwork. Beamnteger linear chelon CLSCemanufacture

Another issorward/reveronsiderable acilities suchr manufacturommon facilomplexity,

maintenance oint of view,nfrastructure.

MILP model lectronic proommon faciabu search mrticle has imple assumpnd location only one plaemanufacturi

Wang [16] pntegrated forw

manufacturings one of theetwork desigf remanufacthe same. Thuew productemands. Hoonsider somee.g., capacroduction, aneturned produ

mathematiorward/ re

manufacturingollection comn two modesarameters. Oroduct flow nd reverse orizon with ost. .2. Vehicle ro

As mentionedoutes is one

aghi, A. Rashz

eptember 2016, V

se logisticsmand for rem

[13] consiapacitated fa

and returMILP form

mon et al. [programing

C, in which ed products isue in dse logistics attention is

h as distriburing/ recoverlities not onl

but alsocosts are re, duo to using. Lee and D

to design oducts withlities and smeta-heuristisome weakptions such aof common fant. Also, ing process ipresented a ward/reverseg/recovery coe most popugn. It also atured producus, remanufacts, come towever, the real-worldcity constnd the unceucts). Pishvacal model verse logig/ recovermmon facilits with stochOutputs of among variodirection ththe objectiv

outing probled earlier, fiof the mos

hidi Komijan

Vol. 27, No. 3

s system manufactureidered a macilities and rned produ

mulation to [14] develop

formulationthe quality

is the same. design of

networks ths the use oution/ collectry centers. Cly reduces tho construceduced fromg common fa

Dong [15] dthe CLSC

h distributioolved this mic algorithm

knesses. Foras the speciffacilities andin reverse s considered

model on e logistics neommon facilular models

assumes that cts and new ctured produto market

heir model d important atraints, mertainty in daee et al. [10

to design istics netwry and dies and dispo

hastic and dtheir model

ous facilitieshroughout thve of minim

ems finding optimst important

289*& A.

based on d products.

multi-product uncertainty

ucts. They design this

ped a mixed n for a four-of new and

integrated hat received of common tion centers Considering he planning ction and

m economic facilities and developed a network of n/collection model with

m. But, this r example, fied number d the use of flow, only

d. Zhou and design of

etwork with lities, which

for CLSC the quality products is

ucts, such as to satisfy does not

assumptions multi-product demand and 0] proposed

integrated work with distribution/ osal centers

deterministic l were the

s in forward he planning mizing total

mal vehicle operational

290 M. H. S

decisions significantlservice. MamanagemenoperationalProblem (Ramser [1operations sciences. Bso-called C(CVRP), costumers for a homserved by capacity badetermine total cost oroute startcustomer istotal demanvehicle caextensions optimizatiomajority ofof effectivereview papcomprehenet al. [19]. Since the Ramser in in many wworld aspevariants of is Multi-destudied byassumes thscattered amis visited bthese depota same deMDVRP problem. Smodel for echelon sumethod to model to a[22] propoheuristic apthat minimIn another time horizobe made inproblem iseach periodover the p

Mirzabaghi, Sarfaraz

Internationa

in CLSC ly reduce coany of the stnt did not l decision. (VRP), intro17], is a

research aBasic formulaCapacitated in which around a ce

mogeneous phomogeneou

ased at the da set of del

over a singlets and endss served by nd on each

apacity. Thisare N

on problems f articles foce solution prpers in this nsive review first article 1959, this p

ways by intects, resultinf the VRP. Oepot VRP (My Sumichrashat multiple mong the cuby a vehicle ts (i.e., each epot). Wu e

to multiplSepehri et a

multi-produupply chainsolve the pro

a single prodosed a matpproach for mizes total trakind of VRP

on, and delivn different d to find a fed, such that planning ho

A. Rashidi K

al Journal of Ind

managemeosts and imptudies in the

consider tThe Veh

oduced by well-known

applied to ation of this Vehicle Rougeographica

entral depot product. Theus vehicles wdepot. The Clivery routes period, such

s at the deponly one veroute does ns problem aNP-hard [18]. For th

cused on therocedures. Tfiled in thecan be foun

of VRP byproblem has troducing adng in a larg

One of the vaMDVRP), wh

st et al. [depots are gstomers and that is assigroute must s

et al. [21] le-depot lo

al. [22] propuct MDVRPn. They uoblem by deduct model. Mthematical multiple prodveled distancP, planning iveries to thedays. The obfeasible routithe total cosrizon is mi

Komijan*& A

dustrial Engineer

ent that cprove custom

area of CLSthis importahicle Routi

Dantzig an problem

transportatiproblem is tuting Proble

ally dispershave deman

ey have to with a limitCVRP aims s of minimuh that: (i) eapot; (ii) eaehicle; (iii) tnot exceed tand all of

combinatorhis reason, te developme

There are some literature. nd in Eksiog

y Dantzig abeen extenddditional reage number ariants of VRhich was first20]. MDVRgeographicaleach custom

gned to one start and end developed t

ocation-routiposed a MILP in a mulsed Lagrancomposing tMahdavi et model and ducts MDVRce. is made overe customer cbjective of thing solution st of the routinimized. Th

A. C

ring & Producti

can mer SC ant ng nd in on the em sed nds be

ted to

um ach ach the the its ial the ent me A

glu

nd ded al-of

RP tly RP lly

mer of at

the ng LP lti-

nge the al.

a RP

r a can his in

tes his

prRBfoCprwFrprcuA(MreburesualInsttheaenisvevesethbeflroKcoflgeOdevepicopr[3alalDsia loVdigrfrouRapin

Closed Loop Su

ion Research, SE

roblem is Routing Probl

eltrami et aormulation o

Christofides eresented an

with pre-defirancis et aroblem, in wustomer was

An extensionMDPVRP). eceived a greut the MDPelatively fewuch as Kanglgorithm to sn the basic Mtart and end he number ofach vehicle nds in the sas developed ehicles to reehicle startservicing to suhat servicing e performedexibility in

oute as "flexKek et al. onsidered a exible assignenetic algorit

One of the vaeal with theehicle routiickup and dostumer requroblem has b31]. A generall deliveries ll pickups mu

Deliveries imultaneousl

vehicle andoading at ea

VRPSPD is istribution syrocery storeresh food outdated item

Reverse logispplication antegration of

upply Chain P

Eptember 2016, V

known as lem (PVRP) al. [24] and of this proet al. [26]. extension o

ned days toal. [27] devwhich the nu

a decision vn of PVRP The MDVR

eat deal of atPVRP has b

w studies haveg et al. [28

solve this proMDPVRP, ev

in the samef vehicles of starts its tra

ame depot. Ain which no

eturn to the s from an iub-set of cosof the custo

d at lower determining ible assignm[29]. Eydi MILP modenment and sthm. riants of VR

e issues in ring problem

delivery (VRuires both debeen introdual assumptiomust be origust be transpand pickuy when eachd unloadingach custome

frequently ystem of groe may have or soft drin

ms or emptystics and Carea for VRf forward a

Planning Wit

Vol. 27, No. 3

the Periodwhich is intthe first m

oblem is prFoster and

of PVRP to o visit eachveloped PVumber of vivariable of th

is Multi-deRP and the Pttention in th

been rarely se been done 8], that useoblem. very vehicle e depot. In of each depot avel from its

A new type oo obligation

initial depoinitial depotstumers, endomers in the cost. The ithe last dep

ment" was intand Abdor

el for the MDsolved this

RP that is widreverse logim with si

RPSPD), in welivery and puced first byn in this proginated from

ported back tups must h customer ig is carried er. The app

encountereocery store c

both a delnk) and pi

y bottles) deCLSC are alRPSPD. In and reverse

th Vehicle …

dic Vehicle troduced by

mathematical roposed by

Ryan [25] a problem

h costumer. VRP for a isiting each he problem. epot PVRP PVRP have he literature, studied and in this area. d an exact

route has to other words, is fixed and s depot and f MDPVRP is made to

ot and each t and after

ds to a depot next period

idea of the pot of each troduced by rahimi [30] DVRP with model with

dely used to istics is the imultaneous which each

pickup. This y Min et al. blem is that

m the depot, o the depot.

be met s visited by out before

plication of ed in the

chains. Each livery (e.g., ckup (e.g.,

emand [32]. lso another

this case, flows (for

Closed Loop

instance, collection) Dethloff [VRPSPD idepot. Thissubsequentmultiple deand deliverIn the majocustomer ionly oncealways reademand excase, the pocustomer Deliveries that allowicosts up to As said earthe majoritmainly focapproachesheuristic efficient mproblem haresearchersformulationmoderate-scommerciaand/or malgorithms motivation according ton vehicle Therefore, is proposedrouting proechelon clo 3. Proble

In this papeperiod, anchain netwThis chaincenters, discenters andsaid in theforward asimultaneomodel, we Moreover, common acsaves morethe opedistribution

p Supply Cha

Internationa

integration is a suitable

[33] developin a reverse ls model hast studies. Salepots VRP ry. ority of vehis served by . However,

alistic becausxceeds the ossibility of characterize(SDVRP) A

ing split serv50%.

rlier, VRP isty of studies cused on hes. Despite tapproaches

mathematicaas received s. Howeverns may allosized problemal package omathematical

for the prof our pa

to the literatrouting in in this pape

d to combineoblems and imosed-loop sup

em Descriper, we consid

nd multi-prowork considn consists stribution/ cod customers’e literature and reverseusly and aim to prevemploying

ctivities (e.g.e money, timerational cn/collection

ain Planning W

al Journal of Ind

of distre approach toped a MILlogistics netw

s been devellhi and Nagi with simulta

cle routing ponly one vthis assum

se sometimesvehicle capmultiple vis

es the VRPArchetti et alvicing can r

s an NP-hardon this prob

euristic and the increasin

for VRPal formulati

much less r, efficient ow us to som instance or to develo

model-basroblem. Thisaper. On theture, there isclosed-loop

er, a comprehe different tymplement thpply chain.

ption and Fder a multi-eoduct closeddering comm

of productollection faci nodes (see review sect

e features proposing

vent sub-optig common ., production

me and energycost. Eac

(productio

With Vehicle

dustrial Enginee

ribution ao cost saving

LP model fwork with oloped in man[34] propos

aneous picku

problems, eavehicle exactmption is ns the custom

pacity. In thits to the samP with Spl. [35] showreduce routi

d problem, thblem have be

meta-heuristng interest

P, developiions for thattention fro

mathematicolve small by using anop new exased heurists is the mae other hans a few studi

supply chaihensive mod

ypes of vehichem in a mul

Formulationechelon, muld-loop suppmon facilitietion/ recoveilities, disposFig. 2). As wtion, with t

of netwoan integratimal solution

facilities fn and recovery and decreach common/ recover

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one ny

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hus een tic in ng his om cal or ny act tic ain nd, ies in. del cle lti-

n lti-ply es. ery sal we the ork ted ns. for ry) ase on ry)

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Inprdiprtothdi[1thpranfoththdilimflMpltrinecprannoIntrceasitspeth(cfr

M. MirzabaH. Sarfaraz

ion Research, Se

enter plays aorward flowrecovery) ronsidered at

Fig. 2.

n this networroducts fromistribution/coroducts, whio the producthat are notisposal cente16], demandhrough the roducts. Thend recovereorward flow,he productionhe end istribution/comitation for eet.

Moreover, thlanning at ansportation

ndependent chelons are roblem) and n initial cenodes, go to an each perioavel at a ceenters are nssignment). s travel fromeriod. In the he products tcostumers) arom it simult

aghi, A. Rashz

eptember 2016, V

a distributorw on the net

ole in thePishvaee et a

. The consi

rk and in them customers ollection ceich are recovtion/recoveryt recoverablers. Accordid of custom

recovered ey assumed ted products the new andn/recovery ce

customeollection cen

all facilities

e model deeach ech

n vehicles of other ecindirect (toueach vehicl

nter and aftea final center.od, each vehenter, so thnot the samIn each perim the final echelon 1 (2o the distribu

and picks uptaneously (V

hidi Komijan

Vol. 27, No. 3

r (producer) twork, and e reverse al. [10]).

dered netw

e reverse floare transpo

nters. Someverable, are y centers andle are traning to Zhou mers can b

products that the qua

is the samd recovered penters are tra

ers throunters. There is and the tra

eals with trahelon. The

in each echelons. Traur; such as le starts its

er servicing .

hicle starts aat the initia

me necessariliod, each vecenter in th

2), each vehiution/ collecp the returnRPSPD). In

291*& A.

role in the a collector one (e.g.,

work

ow, returned orted to the e of these transported

d the others nsported to

and Wang be satisfied

and new ality of new me. In the products by ansported to ugh the s a capacity ansportation

ansportation employed

chelon are avels in all

the routing travel from a subset of

and ends its al and final ly (flexible ehicle starts he previous icle delivers ction centers ned product the echelon

292 M. H. S

1 (2), in distributionsatisfied by(i.e., split echelon distributionone vehicleIn the firsproducts ineach periodcapacity), anext perioregarding required prrecovery cproducts tocenters (sreturned pproduction/returned distributionto the custocollected production/the next pproducts arcustomers. the produplausible flIn the secvehicle (reup requiredistributionsubset of collect the one of thecollected deliveries Mixed inte Sets: A B C D T P K1 K2 K3

Parameterst1p,i Tt2p,i T

Mirzabaghi, Sarfaraz

Internationa

each perion/ collection y multiple vservicing is3 in

n/collection e exactly onlst echelon, n each prodd can be stocand after thaod. In each

its capacitroducts fromenter and stao a subset simultaneousproducts) an/ recovery products.

n/collection omers in the

returned /recovery ceperiod). On re produced In each of pcts can beluctuation in cond echeloegarding its ed productsn/ collection

customers returned pro

e distributionreturned

to customer

ger linear pr

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A. Rashidi K

al Journal of Ind

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Komijan*& A

dustrial Engineer

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from customno possibili

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Vol. 27, No. 3

mers are noity to stock tn/ collectionrecoverable

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M. MirzabaH. Sarfaraz

ion Research, Se

n/recovery con/recovery coduction/reco

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f product typ

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aghi, A. Rashz

eptember 2016, V

enter i (hourcenter i overy center

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t (hour) period t (hout (Independ

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( , i j B ); o

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very center i

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od t

d t

fter loading t

enter i after

hidi Komijan

Vol. 27, No. 3

r)

i

d at producti

d at distributi

ur)dent of prod

dent of prod

otherwise 0

); otherwise

); otherwise

therwise 0

C ); otherwise

B ); otherwise

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Mirzabaghi, Sarfaraz

Internationa

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A. Rashidi K

al Journal of Ind

level of proding of periodlevel of proproducts fromroduct p of vof period t roduct p of

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11

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Komijan*& A

dustrial Engineer

duct p in distd t oduct p in dim production

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Closed Loop Su

ion Research, SE

lection cente

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Eptember 2016, V

er i after load

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bution/collect

as follows:

,i jc t T k

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, , , ,.3i j k t i jz c

Planning Wit

Vol. 27, No. 3

ding the vehi

receiving newod t very center i

llection cent

y center

tion center

y vehicle k

riod t; otherw

nning of per

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riod t

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ion Research, Se

i

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aghi, A. Rashz

eptember 2016, V

, ,.1 1p i th hh

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hidi Komijan

Vol. 27, No. 3

), 1,k k t

A

A

p

,A j B

,A j B

, ,B j B i

, ,B j B i

j B

295*& A.

(2)

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Mirzabaghi, Sarfaraz

Internationa

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A. Rashidi K

al Journal of Ind

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Komijan*& A

dustrial Engineer

M

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Planning Wit

Vol. 27, No. 3

t

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Vol. 27, No. 3

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[7]. Pokharereverse Conserv(4), (200

[8]. Pishvae“Reverssimulateof advaVol. 47,

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[11]. Pishvaerobust loop suuncertaiModelli

[12]. JayaramSrivastamodel fOperatio(1999),

[13]. Salema AQ. “A

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،Karimi b esign using onal journal echnology ،

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[14]. Beam

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[15]. Lee

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[23]. MahdavHosseinmodel Multi-prrouting vehicles(2012),

[24]. BeltramVehiclecollectio1,(1974

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[26]. Christof

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