A Particle Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem.
ISSN1881-5456
Volume3Numberl May,2009
International
Journalof
Logrsticsand
SCIWSystems
ThelnternationalFederationof LOGISI/CSand SCMSysfemr
The AsiaPacificFederationof LOGISI/CSand SCM Sysfemr
Hiroshi Katayama
Foreword
Suebsak Nanthavanij, Prachya
B oonpraswt, Wikrom Jarutphongs a
VehicleRoutingProblemwith ManualMaterialsHandling:FixedDelivery
Crew- VehicleAssignments
Ririn Diar Astanti, Huynh Tnmg Luong
A HeuristicMethodfor SFI Policy with IncreasingPower-FormDemand
Pattern
Bttsaba Phruksaphanrat, P isal
Yenradee,Ario Ohsato
in a Parallel
AggregateProductionPlanningwith LaborReplacement
MachineEnvironment:PossibilisticLinearProgrammingApproach
Duangpun Kritchanchai, I(irachchaya
Chanpuypetch
A Frameworkfor DecisionSupportSystemsin Logistics:A CaseStudyfor
ThailandRubberExports
The Jin Ai, Voratas Kachitvichyanukul
FleetVehicle
A ParticleSwarmOptimizationfor the Heterogeneous
RoutingProblem
Nobunori Aiura, Eiichi Taniguchi
Evaluationof a ReservationSystemfor On-StreetLoading-Unloading
Spaceswith an Emphasison the RelationshipBetweenUtilizationRatio
andBenefits
Thananya Wasusri, Chariyaporn
Rojntchiwit
The Effectsof Rescheduling
Periodsand DispatchingRuleson Supply
ChainPerformance
in an ApparelSupplyChain
Subhash Wadhv,a,Felix T.S. Chan,
Madhawanand Mishra
FlexibilityConstructBasedDesignof Agile SupplyChainsUsinga
NetworkApproach
Wijitra Naowap ad i'tvat, D ah- Chu an
Gong, Voratas Kac h inic hvanu ku I
and
on Collaborative,Planning,Forecasting,
RecentTrendsin Research
Replenishment
Hyunsoo Kim,Daehee Han, Yongjuttg
Choi, Haejune Jeong
of End-of-LifeConsumer
Analysisof RecyclingProcess
Simulation
in Korea
AdoptingRFID Technology
Electronic
Appliances
San Rathviboon, Mario T. Tabucanon,
Mut ttrcumant Sivakumur
SupplyChainManagement
VendorEvaluationSystemfor a Sustainable
Masatoshi Kitaoka, Hirokazu hva.se,Jtm
Usuki. Rui l{zkamura
Capability Measuresand EstimationUsing Control Chart for Distribution
Management Index
lnternationalJournalof Logisffcs and SCM Sysfems
GUESTEDITOR
Dr.VoratasKachitvichyanukul
COEDITORS
Dr.KatsuhisaOhno
IndustrialEngineering& Management,
SchoolofAdvanced Technologies,
Asian Institute of Technology,Thailand
Dept. ofApplied Information Science,
Aichi Instituteof Technology
Toyota,Aichi 470-0392,Japan
Dr. Shusaku Hiraki
Dept. of Economics& Information Science
HiroshimaShudoUniversity,Japan
Hiroshima,Hiroshima 737-2122,Japan
ADVISORY
BOARD
Dr.Cheng-MinFeng
NationalChiaoTungUniversity,Taiwan
Dr. HiroshiKatayama
WasedaUniversity,Japan
Dr.TakahiroFuJimoto
TheUniversityof Tokyo,Japan
Dr.YoungHae Lee
HanyangUniversity,Korea
Dr. Hark Hwang
IfuraAdrurcedlnstofScience&Takrolqry,Korea
Dr. Marlo Tabucanon
Asian Instituteof Technology,
Thailand
Dr.YutakaKarasawa
KanagawaUniversity,Japan
Dt. ChristopherO'Breien
Universityof Nottingham,
Ningbo Campus,China
REGIONAL
EDITORS
Dr. BongiuJeong
YonseiUniversity,Korea
Dr.VoratasKachitvichyanukul
AsianInstituteof Technology,
Thailand
Dr.ZhihongJln
DalianMaritimeUniversity,China
RajeshPoplani
NanyangTech.University,Singapore
Dr.Lle€hien Lln
NationalKaohsiungUniversityof Scienceand
Technology,Taiwan
Dr.ShamsRahman
RMIT University,Australia
PATING
IZATIONS
PARTICI
ORGAN
The Asia t*tcttic Federationof Logistics &
sGM systems
The JapanSociety of Logistics Systems
The Koreansociety of scM
TheTaiwansoctetyof Logisticssystems
ll"riltf,jffii]nal
Federation
of Logistics&
AIMS& SCOPE
Logisticsand SCM Systemsins an internationaljournal for reportingoriginal quality works on Logisticsand Supply
ChainManagement(SCM)systems.It is publishedby the IntemationalFederationsof Logisticsand SCM Systems.The
aims of the joumal are to
O publish original, high-quality researchthat will havea significantimpacton Logisticsand SCM systems.
O develop,Promoteand coordinatethe theory and practiceof Logisticsand SCM systems;
O encouragethe disseminationof new techniquesand applicationsto Logisticsand SCM systems;
O provide a forum for academicsand professionalsto sharethe advancedknowledgeand experiencesof Logisticsand
SCM systems.
Copyrlght @ The InternationalFederationof Logistics and SCM Systems.All right reserved.
andIndividualsubscription:
50US$/year
Subscllption: Institutionalsubscription:l00US$(12,000JP+)lyear
I
InternationalEditorialBoard Members
of rhe lnternational Federation of Logisfics and s.c,n , s
Australia:
Dr. Erhan Kozan
Schoolof Management
Science,
Univ. of Technology,
Queensland
Australia
Dr. ShamsRahman
LogisticsandSupplyChainDiscipline
Schoolof Management
RMIT University,Australia
Ghina:
Dr. Jian Chen
Dept.of Management
ScienceandEngineering
Tsinghua
University,China
Dr. PengTian
Dept.of Management
ScienceandEngineering
ShanghaiJiaotongUniversity,China
Honq Kong:
Dr. Xiande Zhao
Dept.of DecisionSci.& Managerial
Economics
TheChineseUniversityof HongKong,H. K.
India:
Dr. PramondK. Jain
Dept.of Mechanical& IndustrialEngineering
IndianInstituteof Technology
Roorkee,India
Dr. Masanobu Matsumaru
Dept.of Industial& SystemsEngineering
TokaiUniversity,Japan
Dr. Keizou Wakabayashi
D9lt. Management&IndustrialEngineering
Nihon University,Japan
Korea:
Dr. Kap Hwan Kim
Dept.of IndustialEngineering
PusanNationalUniversity,Korea
Dr. Suk-ChulRim
Dept.of Industial& InformationSystems
Engineering
Ajou University,Korea
Taiwan:
Dr. Yon-ChunChou
Instituteof IndustrialEngineering
NationalTaiwanUniversity,Taiwan
Dr. Yen-ChenJim Wu
Dept.of BusinessManagement
NationalSunYat-SenUniversity,Taiwan
Thailand:
Dr. VoratasKachitvichyanukul
Asian Institute of Technology,Thailand
Japan:
Dr. MasatoshiKitaoka
Dept.of InformationSystemCreation,
KanagawaUniversity,Japan
Dr. PaisalYenradee
SirithornInstituteof Technology,
Thailand
Organization
of The lnternationatFederationof Logisfics and S,C.M.Sysfems
Ghairman
KarasawaoYutaka
And Dr. & EmeritusProfessorof
Chairmanof TheJapanSocietyof LogisticsSystems
Kanagawa UniversitY,JaPan
Vice Chairman
Feng, Cheng-Min
Chairman of The TaiwanSociety of LogisticsSystemsAnd Ph.D. & Professorof
National Chiao TungUniversity,Taiwan
Fujimoto, Takahiro
And DBA & Professorof The
WceChairmanof TheJapanSocietyof LogisticsSystems
UniversitYof Tolqto,JaPan
Katayama,Hiroshi
Wce Chairmanof The Japan Societyof LogisticsSystemsAnd Dn & Professorof
JaPan
WasedaUniversitY,
Lee, Young Hae
Chairmanof TheKorea Societyof SCMAnd Dr & Professorof HanyangUniversity,
Korea
PongchaiAthikomrattanakul
ph.D. & Professorof King Mongkut's(Iniversityof TechnologtThonburi,Thoiland
.,:
Journalof Logisficsand scM sysfems
lnternational
NumberlMaY,2009
Volume3
CONTENTS
HircshiKataYaru
Foreword
I
2 StebsakNotthavwti, PrachyaBoonprasart'Ililoom Jaruphongsa
Fixed Delivery crew - vehicle Assignments
vehicle Routing'prouremwitrr rr,ranr"ttvtaterial,itanJting:
8 Ririn Diar Astefi, futynh TnmgLuong
DemandPattem
AHeuristic rur"tfoJ ro, sft rotty with IncreasingPower-Form
l6
BusabaPhrulcsaphanrat,Pisal Yenrqdee'Ario Ohsato
in a ParallelMachine Environment:
AggregateProductio-nPrunningwith Labor Replacement
pJiitititti" Linear ProgrammingApproach
DuangpunKritchanchai, WrachchayaChanpuypetch
A CaseStudy for ThailandRubberExports
A Frameworkfor DecisionSupportSystems"inLogistics:
32 TheJin Ai, VoratasKachitvichyanukul
Fleet VehicleRouting Problem
A ParticleSwarmOpti*iruiion for the Heterogeneous
Nobunori Aiura, Eiichi Taniguchi
Loading-UnloadingSpaceswith an Emphasis
Evaluationof a ReservationSystemfor on-Street
Benefits
on itt" RelationshipBetweenUtilization Ratio and
48
ThananyaWasusri,ChariyapornRoiruchiwit
in an Apparel Supply
Rules on Supply Chain Perfiormance
The Effectsof ReschedulingPeriodsunJ birp"r"fring
Chain
Mishra
SubhashWadhwa,Felix TS' Chan, Madhawanand
ChainsUsing a Network Approach
Supply
Agile
of
O".ign
Flexibility Con.t-"i-gur"J
Kachiwichyanukul
64 Wijitra Naow'apadiwat,Dah-Chuan Gong' Voratas
and Replenishment
in Researchon collaborative, Planning,Forecasting,
RecentTrends
Jeong
Choi' Haejune
"End-of-Liie72 Hyunsoo Kim,DaeheeHan, Yongiung
process
simulation Analysis of Recycling
TechnologYin Korea
of
consumerElectronicAppliancesAdopting RFID
Sivakumar
SanRathviboon,Mario T. Tabucanon,Muttucumaru
chain Management
Supply
sustainable
vendor Evaluation Systemfor a
Rui Nakamura
88 Masatoshi Kitaoka, Hiroknzu lwase, Jun Usuki'
Chart for Distribution ManagementIndex
Control
Using
CapabilityMeasuresanAnstimation
lnternationalJournal of Logistics and SCM Systems
A Particle Swarm Optimization for the Heterogeneous
Fleet Vehicle Routing Problem
*^
The Jin Ai-A and Voratas Kachitvichyanukul*B
UniversitasAtma Jaya Yogyakarta, Indonesia,e-mail:iinai@mail.uaiv.ac.id
*u
Asian I n stitute of Technology, Thailand, e-maittoo."tas@ait-:ac.th
Abstract
1ts fixed cost1[, variable cost per
characterizedby its
This paper presentsan applicationof particle
swarrn optimization (PSO) for solving the
heterogeneous
fleet vehicleroutingproblem(HVRP).
HVRP is a vehicle routing problem (VRP) variant
thattakesdifferenttypesofvehicle into consideration.
Basedon the numberof vehiclesin eachtype, there
are two types of HVRP in the literature:the vehicle
fleet mix problem (VFM) that deals with unlimited
numberof vehicles and the fixed fleet version of
HVRP that dealswith fixed numberof vehicles.This
paper focus only on the latter since normally the
numberavailablevehicle is known in advancein the
actual operations. A PSO algorithm, solution
representations
and decodingmethodsthat have been
successfullyappliedto the basicvariant of VRP are
re-utilizedas the basicsolutiontechnique.In orderto
acquirethe natureof heterogeneous
type of vehicles
into the technique,a specialpreprocessing
methodis
incorporated
to the vehiclelist, so that a vehiclewith
lower relative routing cost is given higher priority
over the biggerone.The proposedalgorithmis tested
using benchmark data set and the computational
resultshowsthat the proposedmethodis competitive
with otherpublishedresultsfor solvingHVRP.
distance unit gp, and capacity Qp. For each vehicle
type k, m7,vehiclesareavailable.With eacharc (v;,vi),
thereis an associateddistanced;i. The HVRP consists
of designinga set of vehicleroutesin suchway that:
(l) eachroute startsand endsat the depot,(2) each
customeris visitedexactlyonce,(3) the total demand
ofa routedoesnot exceedthe capacityofthe vehicle
assignedto it, and (4) the total routing cost is
minimized.
As defined above, the HVRP is dealing with
many typesof vehicles.With regardto the numberof
vehicle type k (mp),thereare two types of problem in
the literature.The first problemdealswith unlimited
number of mp,which is usually called vehicle fleet
mix problem or the VFM, and the secondproblem
dealswith fixed and limited ze, which is called the
fixed fleet version of HVRP [2]. This paper only
focuseson the latter, since normally the number of
availablevehiclesis known in advancein the actual
operations.
Some researchworks that have dealt with the
HVRP mainly proposed solution methodology for
solving it. Taillard [2] proposeda methodfor solving
the HVRP calledheuristiccolumngeneration(HCG),
which is a hybrid techniqueof tabu searchwith linear
programming. Variants of simulated annealing
Problem,
Routing
Keywords'. Vehicle
algorithm which are called list-based threshold
HeterogeneousFleet, Particle Swarm
accepting (LBTA) algorithm [3] and backtracking
Optimization,Meta-heuristics
adaptive threshold accepting (BATA) algorithm [1]
have been proposedfor solving the HVRP. Li et al.
t4l also proposed another variant of simulated
annealing which is called record-to-record travel
1. Introduction
(HRTR) algorithm for solving the HVRP. From the
FleetVehicleRoutingProblem
The Heterogeneous
(HVRP) extends the Capacitated Vehicle Routing
computational results of those methods over the
benchmark data set of Taillard [2), it can be
Problem (CVRP) by relaxing condition on vehicle
concludedthat the HRTR method is able to provide
characteristics.While in CVRP all vehicles are
bettersolution quality amongothers.
identical, in HVRP the vehicles may differ from one
Recently, particle swartn optimization (PSO),
anotheras they may have different capacity,cost, and
is
the
HVRP
which is an emergingevolutionarycomputingmethod,
other characteristics.In the literature,
:
graph
a
A)
be
has been successfullyapplied for solving the CVRP
defined as follows []. Let G
0t
:
and
I
set
where V: {v6,v1,...,v,}is the vertex
[5, 6] and the vehicle routing problem with
v0
represents
Vertex
simultaneouspickup and delivery - VRPSPD [7]. It
{(vi,v.)lvi,viev,i{l is the arc set.
the
remaining
while
is noted that these VRP variants only cope with
a depotwith a fleet of vehicles,
v;
customer
Each
identical type of vehicles. Therefore, this paper
vertices correspondto customers.
are
several
q1.
There
attemptsto extend thesealgorithms to take different
has a non-negative demand
is
k
type
type
of vehicles into consideration,i.e., to solve
vehicle
of
which
vehicle types, in
HVRP. The same PSO framework and solution
as previouslypublishedwill be used;
representation
however, an additional procedure is developed in
ReceivedDate: November 26, 2008
AcceptedDate: February25,2009
fleet of vehicles.
orderto dealwith heterogeneous
oc
uolluluasardouuopnlos z'z
Ir'o]
[eAJAlUrOq1Ur Joqunu ulopusJ rrrJoJrun
uorlrsodlseq .roqq8rau
JeeuJoJluslsuoc uorlEJelsccsaqJ
uorlrsod
lseq lusol JoJluelsuos uorleJalocreor{J
uollrsoo
lseq 1uqo13roJ tu€tsuoc uorleJelecJeeqJ
uorlrsodlseq
leuosradJoJ luelsuoJ uorleJeloooueqJ
uorsueulp ,t/.1atqtle alcrued ,,,7
eqtgo (lsequ) uotltsod lsag roqq8tau reeN
uorsusrurp u,L! egt 1eelcryed
aIilJo
(tseq1;uotltsod lseq Isco'I
{,/
uoISue|.uIp
(1seq8)
uotltsod
a1t
lseq
1e
lpqolD
u,tl
uorsue{urp o,4 e471eelctued
1,/ eW3o Qsaqd)uotltsod lseq leuosrad
uorleJoll ,,-t aq! ur lq8rervruruoul
uorl€Jelr ,t/ at41ur uorsuaurp
elql1e
elctgud ,1rl et{lJo uolllsod
q,Ll
uorlEJelr q/. etll ur uorsueurp
q,t! e1l1u alcqud ,r,/ erllJo ftrco;en
'J
,)
o)
Y!/h
'l/h
,tBh
'11
/h
(')^
\')"'e
(')'',
:eJaq/Y\
k)
(l)
+ (t) "'e= (l + t) "'e
(r * ,; atro
((')-e - ffrh)n"c+
q:/h)ntc+
ftt\''e q'/h)n'c+
((t)''a ((t).e - o'rh)no+ (t)'ttot(t),u = (t + z)'ttco
"
:u
eqt elepdno1pes
oprsodr{ceeJo uollrsodpue ,{1rco1err
n eJesuorlenbeEurnollog'ssecotduorleJalreql uI 'sal
crged11eJoJsJolJeAoJezsr Jolcel ,{1rco1ar
Ieqrureql
'enl€AI'untllrxBr.u
e puB [unrurultu€ uea/$eq peleJaue
3,{luropue;sr uorsueulpelcrpedqcueqcrq/( ur u'1 de
ls ut pozrlerlrureJesolcrgud7'ryorneurergsrr{lul
'Z dels
leodor
osr/$Jeqlo'letu
sr uorJelrj3SurddolseqtSrdolg
Surddo1g't dats
'senl€Apelepdnaql uo peseqalcrged
qc€eJo uorlrsodpue ,Qrco1e,r
eqt atepdn 'p
'senl€A
6aq roqqSreuJeaupu€
'c
lseqIecollseq 1eqo13'1seq
luuos:edalepdn
'elctgedSurpuodsa.uoc
eql Jo anle^ sseulg oql su enlP^
acueuuogredoql los pue salnoJ olcrqal
Jo les qcua Jo acueuuo;radeql et€nl€^g'q
'(7'3 uoqcegaes)salno:elorqe^
'u
Jo las e o1uorlrsoda1cryedqc€eepoceq
ssacolduouaratl '7 dets
'alcrged
q3peJo,frco1e,r
pueuorlrsodIerlru oql las 'q
'r.ruu,lns
eqlJoJeqr.uetu
seselJru€deleraueg'u
'1 dets
uottoztlDtttul
dUA roJ {roaauurd OSd :t ruql.tro8ly
'dU,\H 3ur,r,1os
JoJ{Jo,{rerlre{srr{}esno1alqrssodoslesr 1r'erogareql
'q'Z pue e'7 dalg ur pelscol are sdals cgrcads
rualqordoql l€ql polou sr t1 '1 ruqluoElv ur pa.rer^ar
,{UaFq sr lro,&\eru€{ OSd eql 'ror^eqaqSulureal
aq seprseq'[1 1]
sElseq 1eqo13
IurcosroJ slueuodruoc
'p p
luaueqcellleJaa^,(q pesodordldacuoc Jor^eqoq
SururealluroosE sl qJrq^\'1seqroqq8reuJBeueql pue
'selcrged
Euoureuorlrsod lseq eql
luacuhe l€Je./\es
sI qJlq.ry\'1seq
eqt selurofuocurosle uorsJa^OSd
1eco1
qlr,r
slql '[01] sarntcrulsSurureallurcos e1dr11nru
tuqruoSly OSd e 'OSdN'IC aql uo peseqpesodord
ueaq puq 4an SurnlosroJ lro^1our€gOSd e'[L-g]
lnlnuufqcr4lqce) pue rV Jo $lro.,YrJerlJBoul
'[6] crol3 osl€puu
[g] ueq:eqEpuu
Kpouue;1,{q papl,tordsr uoqecrlddepue 'anbruqcal
'tusrueqcatu
',!rco1a,r
OSd uo uorluuuoJur eJot{
alcrpedEurlepdnJoJpasno;e uorlrsodtsaq1uqo13
pue
'lseq
lseq leuos:adesaql
leuos:ed11uSuoue lsaq oql
sr qcrr.l^r'uorlrsodlsaq 1uqo1E
eql pue 'alcrgedaq ,{q
pollsrl uaoq eleq leql suorlrsodeqt Suoue uorlourg
e,il1cefqolseq eql se,ilEluql uorlrsodaql se paugap
sr qcrr.{^r'alctged qoee Jo uorlsod lseq yeuosrad
aql lnoqe uorleuuoJuraql surelureluosl? rusru€q3er,u
'uuei$s aql
OSd oql
Jo rol^Bqeg lslcos pue
elrlruEoc eql SurtrelnuruI 'urelqordeqt go uoqnlos
arrqcadsord
sr alcrpedu leqlou€
lualeJlrpEurlunlerra
ol uorlrsodauo uro{ Suvrolq ,firco1e,reql uo peseq
lxou eql ol uorltsod auo tuo{ ulre,r\s aql ur alcrped
,{ranago lueluenotu aql Jo slsrsuoJdals uorleralr
'alcrged aqt
OSd qcEA
Jo fitgqu Eurqcruasaql
Surluesarder
sr Jolcen,{1rcolen
€ pu€ uorlnlosuralqo:d
u EurluaserdeJ
sr uorlrsodelcrgud l€uorsuaurp-plnr.u
'luo8e Sutqcreose se
ItB leql seloru€dgo uuerrs
V
e fq :ege lqEnossr ruelqordcgrcedse Jo uorlnloslsaq
oql 'OSd oql uJ 'por{loruSurqcreasB sB rrr€/r\saql
ur sl€nprlrputaql Jo $lueuenou 1ecrs,(qd
eql seleutur
qorq^\poqlaruqcreespes€quorlelndode sl OSd
IuqtlroSlv osd I'z
f8o1opoqlatr^l
uognlos pesodordaql 'z
uo uorlcerrp
requryspuauruocar
or" ,".;I:t;'ll
'tas
polueserdIJo/$ eql sepnlcuoc? uorpes ',(11uurg
Bl€p{Jerrrqcueqeql uo poqleu pasodordeqlJo sllnsar
'paureldxesr
leuoqulnduoc eql sluesardg uorlcag
qly( leapo1a:npacord
solJrqelJolaeg snoaueSoJalog
'po,roner ,{UaFqeru uorluluesardar
Ieuorlrpp€aql pue
uorlnlos eql pus urqluoSlu OSd aql :,{Eolopoqleu
uonnlos pesodordaql saqucsapZ uoqcas :^\olloJ
se pazueS:o sr raded srgl Jo JapururuoJaql
lnternational Journal of Logistics and SCM Systems
-al,;;J;l;i;F,+--
List
Priority
tocustomer
convert
r-t
-t-
VehicleI
Orientation
j--.,-
I
i2,,,
-l
Vehicle ri
Orientation
"TJi:*i" "Til:ji,1"
SR-1
Figure 1: SolutionRepresentation
VehicleI
Radius
Figure2: Solution
Two solution representationshad been proposed
in previous works of Ai and Kachitvichyanukul [5-7],
which are called solution representation SR-l and
SR-2. For representing VRP with /4 customers and m
vehicles, the representation SR-l is using particle
with (n+2m) dimensions and the representationSR-2
is using3m dimensions.
In brief, both representationSR-l and SR-2 are
using real number in each dimension. In the
representationSR-1, the first r dimensions represent
priorities of customers and the other 2m dimensions
representthe orientation point of vehicles (Figure l).
While in the representation SR-2, 2nt dimensions
representthe orientation point ofvehicles and another
rrt dimensions represent the coverage radius of
vehicles(Figure 2).
In the PSO application for VRP, a specific
decoding method must be defined to transform a
particle with specific representation into vehicle
routes.For representationSR-1, the decoding method
startswith creating a priority list of customers based
on the first n dimensions of a particle. The priority
list is constructed by sorting in ascending order the
position values and taking the dimension index as the
list. The priority matrix of vehicle is then created
basedon the last 2lrl dimensions that are used as the
route orientation point of vehicles, in which a
customer is prioritized to be served by vehicle with
closer distance between customer location and the
vehicle route orientation. Finally, the vehicle routes
are constructedbased on the customer priority list and
vehicle priority matrix. One by one, each customer in
the customer priority list is assigned to a vehicle
based on its priority and such problem constraints as
vehicle capacity constraint and service duration
constraint. This newly assigned customer is inserted
to the best position in the existing vehicle route based
on the least additional cost. Another effort to improve
solution quality of the route is to re-optimize the
emerging route using local improvement procedure,
i.e. 2-opt.
The decoding method for solution representation
SR-2 is slightly different with SR-l. It starts by
transforming a particle into the vehicle orientation
points and the vehicle coverage radius. The vehicle
Vehicleni
Orientation
Vehicle nr
Radius
Representation SR-2
routes are then constructed based on these points and
radius. For each vehicle, starting from the first to the
last vehicle, a feasible route is constructed by
including customers that are located within the
coverage radius and are not yet assigned to other
vehicle. Afterward, local improvement procedures,
such as 2-opt, l-l exchange,and l-0 exchange,are
applied to the constructed routes. If there are
remaining customers that have not been assigned to
any vehicle, the customers are inserted one by one to
the existing routes as long as the route feasibility is
improvetlent
local
the
maintained. Finally,
routes.
ofthe
to
all
re-applied
proceduresare
It is noted that the differences among VRP
variants are in the problem constraints. Therefore,
both representationsSR-l and SR-2 can deal with
the HVRP. Slight modification is needed in the route
construction steps to form feasible routes that did not
violate the problem constraints. To be more specific,
the HVRP has the same problem constraints as the
CVRP, however, different vehicles may have different
capacity and duration limit for the HVRP.
2.3 PreprocessingVehicle List
In the HVRP, different vehicles may have differe
nt fixed and variable cost. This characteristic is not pr
esent in the CVRP case where all vehicles are identic
al. To deal with different cost scheme among vehicles
, an additional procedure is proposed here to preproce
ss the vehicle list based on a cost parameter e* that i
s calculated usine following formula:
6*={\+cr
An ideal formula is to use the expectedtravel
distanceof vehicleas the denominatorof fixed cost.
However,it is difficult to estimatethe expectedtravel
distanceso half of the time durationlimit is set as the
denominator.A vehicle with lower cost parameter
will be preferred over one with higher cost, so that
the routing cost will be reduced.In the solution
representationSR-l and SR-2, the result of this
procedureis implementedby settingthe lowest cost
-:4,-
IAI\.u ShtgSZ
zqcl uolqlv
LW
rr't[sI
v0,
,E'OZII
89'fZ8r
96'I90I
998
9tz
88r
I^IVU 8hI8ZI
zqntrO0tII unrlued
s t ' 9 9 Is
9SI
8Zb
IL6
t8'EZtl
9E'9t81
IO'I/OI
t9t
ZqN OE uorlecUtceds
'uollets{Jo1d
credg ung
relnduo3
I,^{VUSI^I8ZI
zqhtrOsgIII urllrlued
SL9
9E'8SS
60t
O I€
,9'9ZI
t I'298
tzz
L 9 ' IL O
zjtt
ttSs
LL'6SS
IS'TII
9L8Z
SVZZ
OEE
6 L ' IL O
6I
8
L
s0'tsI
o
s
OZ
9r ' 0 / 8
n6'?vtl
M
zs'svl
II
991
WI
89E
6t'8fl
6Z'SI0I
89t
L8t
6Z'SI0I
v6
6 € 'rr9
98'910
er8
n6'Lrj
t9'zr9
s€t
IE
SL9
anrlra[q6
96'6t9r
c/t
(s) atur1.
96'6rSr 0l
v9's19
s0'8tsr
(s)aura
an;1ra[q6
ts't09
t8'Lrgr
(s)aura
ltlu.r.us
a,rqca[q6
(s)aur.1. aa;1ra[q6
lelvrsr
II YIvs
oqlJo uos
dUAH uo lJnseupeqsrlqnd
'
v
0'z 00s
L
9
0
C
b
!
V
z
z
00s
6'Z
6
v
v
ut
'llnser
OOZ
I
008
00b
081
b'z
002
0rl
0 0 r 09
0 0 t z 00€
0
z't
h
z
00€
00r
9t
0l
002
00r
00t
092
0sl
00r
0s
0z
0 s€
J
B
V
J
s
V
J
E
C
J
0zt
002
0zl
3
0'l
08
SZ
0s
I
V
t
o
aqAI
.IJqA
Q
o
0sl
0z
C
00r
SL
Z
6I
8I
C
9L
LI
'lsnJ
'oN
'qoJJ
l'7
9'l
h
B
V
R
s
z'
001
0'l
z
€
0'z
v
9'l
0'l
I
b'l
I'I
z
n
0'l
z't
z
!c
+a
L'l
v
7
z'l
0'l
v
ut
JO'ON
ds uJcU irur,uqcueg duAH sqlJo
v
eJuBlsuI
[z]crH
Iuo J : Z e l q B l
00t
002
001
09v
0il
J
08
TI
V
oc
9I
J
g
V
J
I
09
SI
0s
vl
0s
EI
0v
091
0sz 0 0 r
0 0 r 0s
00s€ 00€
009I
091
000r
00v
0zl
0zI
OL
V
002
I
s7,z 0zr
0s
0v
OZ
0€
07.
T
o
st
a
o
gI
3
CI
J
I
V
aqAI
'Icrt
A
s : t alqEl
'lsnJ
JO'ON
'oN
.qOJJ
luauruedxe yeuorlelnduror aql sl\oqs
'selrriled
puu
g
elq€I
t
oql rog Xysnoauellnuls
pasnlou aru sanle^qloq
001 pue 0S qrrrnu.rq1r.ro81y IAtrCA
'1aselup >lJpr.ur.louaq
aql
uo
pelcnpuor
sr luauruadxa eql
OSd
srql ur paugopflreelc aJeslsoc
'Z
lu€lsuocuorleJelacJe
alqerrunpuu poxg q8noqlly .l alqeJ ur paluasardsr
uorlrsodlsaqroqq8reu
Jueupu?'1 luelsuocuorlsJaleoJe
uorlrsodlsaqIBJoI.0
les elep>lJur.ur{cuoq
srqtJo uorlucgrceds
eql .ocuelsrp
.1
luslsuo3uorlzJalacoe
uorlrsodlsaq 1uqo18
upepllcng
paugep
ss
aJe ueql Buouresecuelsrpaql
luelsuoc
uorl€Jalecce
uorlrsodlseq l€uosJad.y.g lq8rarneruaur
pue deuroleurpJooc
u?rsaueJur uelr8 aJ€sJeruolsnJ
lsul '6'0 lq8ra,r.erileur NJg .g roqq8reuJo Jeqr.unu pue lodep3o suorlrsodeqJ .9 ol tuo.r;sauu,rsad,e
E
'0001 uorlurelr
alJrqe^Jorequnu aql pu€ sjeruolsnc
qloq JoJ
Jo requnu :suorleluasarde:
001 ol 0g Luo{
pelerodrocureJ€ sJoleruzJsdOSd oruusaql .asod:nd
serJelslaruolsncJo Jaqunu oql qlr/\t ,sacuelsur
3;o
uosrruduoc rog 'W11U Jo BD I pue rosseco.rd slsrsuorlas el€p
.[ZI] .le uoploC
{rerrrqcueqslqJ
le
zHD V't td letul r{ll^AJd B uo uru puu
uo4 ,{lyeur8uosr qclq/rr ,(6661) p.ru111e1 les
I.l uolsre^
Jo
elBpegl sl duAHJo uorsra^laau pexu pus
{roaeuerC lEN.$osorclhtr uo a8un8uulg3 Bursn
qloq
rtrc^
.4UAH
pelueuraldurrsr uqtuo8lv OSd eqJ
JoJdunH eql JoJles el8p {rerrqJueq uolllurocv
eql roJ
alq?lre^ules el€p secu?lsurg eql JeAosuorluluesardar
.t
lJnseulsuorlBlnduoJ
uorlnlos qloq qlr^\ {ro^\orue{ OSd aql Eur,{1dde
fq palcnpuoJsr luarurJadxaluuoqelndurocaq1
'rusrueqcausrql
uro{ palcadxa
'lJnsaJ sr
aql Jo uorlcnpeg .elJrrla^ anrsuadxa1sua1
lsoJ
paqsrlqndlseq eql selecrpuracugedflploq (elqelstql
aql ol ^llJolJdreq8rqueurrS
sl qclr{/y\.1sr1
passecordard
ul 'Z alqeJ uo pelsrlsl dUAH eql uo rlnsarpeqsrlqnd aql ur alcrqen
eql
roJ
pelrrutsuoc
lsrg
,{11srgsr
eql Jo uosueduoc .uorluru;ogurslql ol uorlrppe
.lsrl alJrqe^eql uo peseq
olnoJ
eql'aJoJaJeqJ
Xlureu
uI 'lsll eql ur sanle^ eql ol sleJeJlsoc elqBrre^
sl z-us roJ poqleu uorl3rulsuocolnoJ oql asurs
'Z-US uon€luesarde:
eql puu selcrqa^ lle roJ (g__!) otaz sr lsor pexg
to; ,{lyercedsalueuodun .(re,r
'4UAH
.salcrqel
aql
Jo uorsJel leag paxg eql JoC
sr arnpacordSursseco:da-td
srqt teqt pe1o.l,, i1
'ut elJrr{s^er{lsBolcrqe^
IIBroJ (t:ta) auo ol slenbelsoc alqerr€Aeql puu lsrl
oqt se atuesaql sr lsoc paxg aql ler1lpeugep{11ensn
lsoc lseqSrqeq1f11eugpue,Z elcrqe^eql s? elcrqe^
sl ll 'ntrg^ eql uI auAH Jo uorsre^laau psxg puu
puooas eql ,l elcrqa^ aql sE olcrr{e^
lsoc lsa^4,o1
InternationalJournal of Logistics and SCM Systems
cornputationaltime for all problems is less than 74
secondsfor 50 particlesand lessthan 172secondsfor
100 particles. It is evident also that the solution
qualitywith 100particlesis insignificantlybetterthan
from the solutionwith 50 particles.
Resultfor solutionrepresentation
SR-2 is better
thansolutionrepresentation
SR-l result,in which the
resultsare very closeto the bestknown solution.For
all instances,
the averagepercentage
deviationis less
comprises of the average, standard deviation, and the
minimum objective function of each instance over 10
iterations, altogether with
its
corresponding
percentagedeviation and the average computational
time (in second) for solution representationSR-l and
SR-2, respectively. The percentage deviation is
calculatedas the ratio between the deviation of the
resultfrom the best published result.
For solution representationSR-1, overall results
'able
ntationSR- br HVRP
ObiectiveFunction
Comp
Instance
Average Standard
Minimum
Time (s)
Average
Minimum
Deviation
V"Dev
V"Dev
50 narticles
13
t 7 4 3 . 1 6 14.84%
37.1
8
t694.17
fi.62%
36
17.25
z)
t4
661.32 8 . 8 s %
640.90
5.49%
15
1 5 . 1 6 10 5 4 . 3
1
3.83o/o
25
0 7 2 . 1 3 s.60%
200.69
4.870/0
21.19
24
t6
n70.82
2.26%
t7
1 4 872
8.l1Yo
lt.29
1127.66
6.19%
48
l8
988.60 9.0s%
29.16
t937.73
6.26%
59
t9
203.62 7 . 7 1 %
9.59
I191.04
658%
74
20
2r.94 t672.87
7 1 2 . 0 0 1r.59%
9.04%
69
100 narticles
13
t744.84 l4.96Yo
44.31
t660.20
9.38Yo
91
t4
6 6 1 . 5 3 8.89%
15.10
641.9r
5.66%
59
15
1067.03 5 . l 0 Y o
13.34
2.9804
045.53
63
t204.62 5 . 2 r %
20.27
1 7 163
2.33%
16
63
t7
fis2.29 8 . 5 1 %
12.63
137.72
7.13%
t7
18
40
t 9 7 3 . 9 8 8.250h
22.05
944.36
6.62yo
r9
1r94.69 6 . 9 r %
10.92
r68.62
4.s7%
72
20
1 6 8 3 . 8 0 9.7s%
25.34
640.24
6.9r%
67
3: Resultot PSO Alsonthm wrth Solutron
able 4: Result ot PSO Algonthm wrth Solutron RepresentatlonSR-z tor HVRf
Instance
Average
ObiectiveFunction
Average Standard
Minimum
Deviation
"hDev
Minimum
YoDev
Comp
Time (s)
50 particles
l3
t4
15
16
t7
18
19
20
16.22
4.14
7.50
4.36
1578.91
609.17
l0l9.ll
1r48.62
4.02%
0.27%
0.38%
0.32%
2.34%
12.60
24.46
9.46
1066.44
1840.82
0.9s%
85
r50.39
3.44o/o
2.940h
r135.97
r.65%
r04
589.25
359%
17.03
t561.29
1.77%
ll5
14.80
4.10
156t.21
609.17
2.860io
t07
4.s6
3.82
t019.27
0.27%
039%
030%
58
66
66
143
t75
15 9 3 . 7
1
614.66
4.96%
l.l1Yo
031.06
r.55%
t52.84
086.82
886.38
0.69%
0.42%
48
28
32
3l
70
100 particles
13
l4
l5
16
t7
18
t9
20
t586.ll
613.29
1025.19
r152.84
10 7 8 . 8
1
1869.81
r148.24
1578.09
4s0%
0.9s%
0.98%
0.69%
153%
2.s4%
2.75%
2.86%
areas follow: the averagepercentage
deviationis less
than l5o/o,standarddeviationis lessthan 45, and the
7.83
13.l8
l148.41
1069.52
1852.36
0.71%
t.58%
t0.25
fi3r.32
r.24%
9.58
t561.80
t.80%
206
233
than 4o/o,standarddeviation is less than 25, and the
computationaltime for all problemsis lessthan 115
- /,(, 'sI'uelqord
Surlno; elJrr{ol uo uorl€zrulldo u:e,,rrs aycrgud go
uorlucryddeeql uo 8ur1;om sr eq ',{11ue:rn3'sruelsfs
uoqecrldde
Ieulsnpur uo
pue
sll
uorlelndruoc
fueuorlnlona
opnlsul
slseJolurr{JJsaseJsrH '8002
ur pu8lrer{J ',{3o1ouqcel go
.
aln1rlsuluursv lB ,{8olouqcal
pue Suueeur8ug ;o looqcs
eqt tuo{ '8uA'C € polracaraH
'Brseuopul'ege>1e,{3oa
e,\e1
erulv selrsJenrun'fSolouqcol
,(l1nceg
leulsnpul
Jo
'Surreaur8uE
lurJlsnpulur JoJruco'Je sl !V ulf aqJ
selqdurSolgrorllnv
'v861
'99-6V'
I l'qzrDasay suot1otadgpuo stalndwoS
'..ura1qord
''g
Surlnorelorqel xnu puu azrs1aa1g,,
'suas,(eqgpu€ 'T 'frta'I ''V 'pussy ''g 'uaplog
tztl
'
t1OZ'lzl-0 11' acuatatuo3 uo1p 1ndwo3
[touo4n1o,tg puo olpuaD lo sButpaaco.t4
'..uoI1JeJe1uIroqq8teu Jeeu qllrtA srr rel\s
elcrged Eursn uorlezrurrldg,,''V "I ',rrcp€so
''1 'ruere4'';1 'rueueqceur€Jea1
pue 'J 'ueqo141
l rr l
'9002'20-EVnde4'8ut1aporypuD uoqzlnutlS
uo acuatatuoJ lDuorlDutaluJto s8utpaacot4
'..seJn1cru1s
lercos egdrllnr.uqlrA\ uorlezrulldo
uuel{s
olcrgud
snouaSouroq-uou V,,
''n'1n4nuu,{qcrllrqoe)
pue'd's4rerruqc8uo4t o r l
'9002'uopuo-I
'9791 'uot1oztutttdowtolts apluDd '';41'cre13
tol
'[002'ocslcu?rJ
ueg'sreqsrlqnduuutuJn€;tr
uuSroq'acua3111a1u1
wrDAS ''J 'U 'geqraqg puu 'f ',{peuuay tsl
' 6 0 0 2_' z 0 L t - t 6 9 t ' 9 t
' t1c,to
asay suotTotadgpuo sta1ndwo3',,fsa n11ep
pus dnlcrd snoeuellnurs qlr^\ ualqo:d
Suqnor elJrqe^ aql JoJ uorlezrurqdo urre^\s
alcrgedV,, ''A'lnlnuefqcy4rqoe) pup 'f 'I'lV Ltl
'6002'tg€-09€'9S'SuuaautBug
lDlustxpul
puD stalndutoS '..rua1qo.ld Eurlno.t alJrqel
pelelrcudec eql Surrrlos JoJ suorleluaserdar
uoqnlos ollu pu€ uorlezrunldo uu€,/r\s
pue 'f 'I 'lV tgl
elcrUed,,''6 '1n1nuu.(rlcrllrr.lce)
'
puo sct1
n3o7
74J39
L00Z'SS-OS'7'suta6,(g
',.rualqord 6urlno.l
to putnof lDuorlouJauJ
elcrqenpelelrcedeceql JoJ uorlezrurldo uuel,\,s
a1cryudV,, ''A'1n1nue,{qcrnl!{ce;pu€ 'f 'J'lV tsl
'1002-zvLz-ntLz
'Vt 'tlctoasay suolptadg puo sta\ndwoS
'..rua1qo:dEuqnor elcrqel
loag snoeueSoralaq
aql 8un1osro; urqlrroEl?IeA?JlpJocaJ-ol-pJoceJ
''A 'llsu11 pue 'g 'ueplog ''C 'l'I
V,,
Lvl
't002
'lL-99 'yg '{lalcog qznasay puogotad1 aqt
to putnoT'..rue1qordEurlno;alorr{alleeg poxg
snoauaSorelaqeql JoJ crlsuneqsleu Suqdaccu
ploqsaJql peseq lsll v,, ''s'A 'srpsrlrsss^
'srpnousJr) ''c'J
'srlrlueJ?I
pu€ 'J'J
tel
'666r
'VVI 'gg 'allauuoglotadg aq)raq)ay
OUIVA
'..dUA
taeg snoaueSorataq eql JoJ poqleu
uorlereue8 urunJoc crlsr:neH,, ''C 'A 'p:e11re1 [7]
't002 '891-8vl 'z9I 'qcntasaypuot1rc.tadg
'.,ruelqord Surlno-tolcrqei.
to 1ou"utoquoadotng
pexg
snoaueSoraleqeql JoJ orlsrJnoq€leu
leag
Surldaccu ploqseJql V,, ''S'n 'srperlrsse4
'srpnouelr;'1 ''C'J
'srp1uele1
pue 'J'J
[1]
saJueJeJ0u
'puEIIeqJ,{Solouqcel eln1qsul
Jo
uursv ur fpnls srqrog uoddnsIercu€uuaql Surpr.tord
JoJ ersauopuy'uge4efSoa e,{e1 etulv selrsJalrun
ol apnlllu:3 sesserdxe Jor{lne lsJg oql
'uoddns
Surlndruoc
lucruqoeleql pue,Q111ceg
3o
sse333eql roJ reluoS cruD IB[{J eql pu? (f,dHJIV)
,{3o1ouqce;Jo alnlrlsul u€rsv le dno:g 3ur1nduo3
eou€nrroJJed
q8rg eqt {ueql ol qsr.{\sJoqlneeqI
fueIuaSpal^aou{rv
'el'url
oql ecnpeJo1pazrruqdoJequrgeq osl€
leuorlelnduroc
uec sdalsleuoqelnduocaq1 'Surgessrelaurured
694
'poqleu Surpocap
Jo uoquzrturldoaql tuog osl€ pue
oloq,lr oql ur spopr Joglo ,{ue Eurlerofuocur ro
dals uorlcrulsuof,alnoJor{1ur eJnpe3o:dluaurenordrur
luaJafllp Jo uorluluaureldun eqt ruo.r; pacu€qua
eq ,{eu .fir1enb uorlnlos 'aurll leuorlelnduroc
Surcnper pu€ ,{rylenb uorlnlos Surno;drur
:suoqceJrpo^q ul reded srql ur peure8 Unsar ar{l
a.ro:dturo1 elqrssodIIIIs oJeseqcr€esalJequnC
'selcrueo
09 r{tl,r\ z-us oql sr stFser luuoqelndtuoc eq1
uro{ pepnlJuocaq uec leqt alcrgedJo lequnu puu
uoqeluasardal
uorlnlosJo uorleurquoJpepueuuoceJ
aql 'uorlrpp€uI 'l-US uorleluasordoJ
eql ueql uoge
perrnbar
eJor,u
leuorlelnduroc
Z-US uorleluasatder
aql
laneno11 'l-US
uorleluasa:der qllit\
{Jo/y\eLuuIJaql uPt{l Jeueq sI Z-US uoll8lueserda:
r{lr^{ IJo^\eurB{ OSd pesodord aill leql u^loqs sr
ll ,{fllunbuorlnlosJo uuel uJ 'arurlIeuorl€lnduocpuu
,t11enbuorlnlos qloq Jo uuel ur 4UAH aql 3ur,r1os
roJ elrlcega or€ Z-US pue I-US suorleluasardar
qloq qll,r\ osd
pasodord aql lsql ^loqs
sllnser luuoqelnduro) eql 'dgAJ rog uorlecrldde
OSd Surlsrxe ue pourpou ,{pq8rls ,{q (aUng)
uelqord Suqnog elclqa1 leelC snoauaSoralell
aql 3un1os roJ (OSa) uoqezrur4dg (ru€ly\S
elcrued3o uorlecrydde
aqt slueserdreded srql
uollupualllruoJall pus uolsnlJuoJ'v
'etuq
I€uorl€lnduroc
elqeuos€or ur uorlnlos ,lllenb qEH elqeuosear
epr,ro:d ol olqe sr ll ecurs 'se1cq:ed 0S qly(
Z-US eql sr alcrged Jo Jeqrrlnupue uoqeluesarda.l
uorlnlos Jo uoq€urq{uoctrseq aql leql papnlcuoc
eq uec 1r 'ero;areq1 'selcrged 0S qlp\ uorlnlos
ueql reueq ,(lluucgru8rslou sr salcrged 001 qtF\
fit1enbuollnloseql luril u/v\oqsoslusr t1 'salcrgedgg1
roJ spuocesggTuelqtsselpue selclgud0SJoJspuoces
lnternational Journal of Logistics and SCM Systems
Voratas
Kachitvichyanukul is an Associate
Professor in
Industrial
Engineering& Management,
School of Engineering and
Technology,Asian Institute
of Technology,Thailand.He
received a Ph.D. from the
School
of
Industrial
Engineering at
Purdue
University in 1982. He has
extensive experiences in
simulation rnodelins of
manufacturing systems. He had worked for
FORTUNE 500 Companies such as Compaq
Computer Corporation and Motorola Incorporated.
He had also worked for SEMATECH as technical
coordinator of the future factory program. His
teachingand researchinterestsinclude planning and
scheduling,high performancecomputingand applied
operations research with special emphasis on
industrialsvstems.
Volume3Numberl May,2009
International
Journalof
Logrsticsand
SCIWSystems
ThelnternationalFederationof LOGISI/CSand SCMSysfemr
The AsiaPacificFederationof LOGISI/CSand SCM Sysfemr
Hiroshi Katayama
Foreword
Suebsak Nanthavanij, Prachya
B oonpraswt, Wikrom Jarutphongs a
VehicleRoutingProblemwith ManualMaterialsHandling:FixedDelivery
Crew- VehicleAssignments
Ririn Diar Astanti, Huynh Tnmg Luong
A HeuristicMethodfor SFI Policy with IncreasingPower-FormDemand
Pattern
Bttsaba Phruksaphanrat, P isal
Yenradee,Ario Ohsato
in a Parallel
AggregateProductionPlanningwith LaborReplacement
MachineEnvironment:PossibilisticLinearProgrammingApproach
Duangpun Kritchanchai, I(irachchaya
Chanpuypetch
A Frameworkfor DecisionSupportSystemsin Logistics:A CaseStudyfor
ThailandRubberExports
The Jin Ai, Voratas Kachitvichyanukul
FleetVehicle
A ParticleSwarmOptimizationfor the Heterogeneous
RoutingProblem
Nobunori Aiura, Eiichi Taniguchi
Evaluationof a ReservationSystemfor On-StreetLoading-Unloading
Spaceswith an Emphasison the RelationshipBetweenUtilizationRatio
andBenefits
Thananya Wasusri, Chariyaporn
Rojntchiwit
The Effectsof Rescheduling
Periodsand DispatchingRuleson Supply
ChainPerformance
in an ApparelSupplyChain
Subhash Wadhv,a,Felix T.S. Chan,
Madhawanand Mishra
FlexibilityConstructBasedDesignof Agile SupplyChainsUsinga
NetworkApproach
Wijitra Naowap ad i'tvat, D ah- Chu an
Gong, Voratas Kac h inic hvanu ku I
and
on Collaborative,Planning,Forecasting,
RecentTrendsin Research
Replenishment
Hyunsoo Kim,Daehee Han, Yongjuttg
Choi, Haejune Jeong
of End-of-LifeConsumer
Analysisof RecyclingProcess
Simulation
in Korea
AdoptingRFID Technology
Electronic
Appliances
San Rathviboon, Mario T. Tabucanon,
Mut ttrcumant Sivakumur
SupplyChainManagement
VendorEvaluationSystemfor a Sustainable
Masatoshi Kitaoka, Hirokazu hva.se,Jtm
Usuki. Rui l{zkamura
Capability Measuresand EstimationUsing Control Chart for Distribution
Management Index
lnternationalJournalof Logisffcs and SCM Sysfems
GUESTEDITOR
Dr.VoratasKachitvichyanukul
COEDITORS
Dr.KatsuhisaOhno
IndustrialEngineering& Management,
SchoolofAdvanced Technologies,
Asian Institute of Technology,Thailand
Dept. ofApplied Information Science,
Aichi Instituteof Technology
Toyota,Aichi 470-0392,Japan
Dr. Shusaku Hiraki
Dept. of Economics& Information Science
HiroshimaShudoUniversity,Japan
Hiroshima,Hiroshima 737-2122,Japan
ADVISORY
BOARD
Dr.Cheng-MinFeng
NationalChiaoTungUniversity,Taiwan
Dr. HiroshiKatayama
WasedaUniversity,Japan
Dr.TakahiroFuJimoto
TheUniversityof Tokyo,Japan
Dr.YoungHae Lee
HanyangUniversity,Korea
Dr. Hark Hwang
IfuraAdrurcedlnstofScience&Takrolqry,Korea
Dr. Marlo Tabucanon
Asian Instituteof Technology,
Thailand
Dr.YutakaKarasawa
KanagawaUniversity,Japan
Dt. ChristopherO'Breien
Universityof Nottingham,
Ningbo Campus,China
REGIONAL
EDITORS
Dr. BongiuJeong
YonseiUniversity,Korea
Dr.VoratasKachitvichyanukul
AsianInstituteof Technology,
Thailand
Dr.ZhihongJln
DalianMaritimeUniversity,China
RajeshPoplani
NanyangTech.University,Singapore
Dr.Lle€hien Lln
NationalKaohsiungUniversityof Scienceand
Technology,Taiwan
Dr.ShamsRahman
RMIT University,Australia
PATING
IZATIONS
PARTICI
ORGAN
The Asia t*tcttic Federationof Logistics &
sGM systems
The JapanSociety of Logistics Systems
The Koreansociety of scM
TheTaiwansoctetyof Logisticssystems
ll"riltf,jffii]nal
Federation
of Logistics&
AIMS& SCOPE
Logisticsand SCM Systemsins an internationaljournal for reportingoriginal quality works on Logisticsand Supply
ChainManagement(SCM)systems.It is publishedby the IntemationalFederationsof Logisticsand SCM Systems.The
aims of the joumal are to
O publish original, high-quality researchthat will havea significantimpacton Logisticsand SCM systems.
O develop,Promoteand coordinatethe theory and practiceof Logisticsand SCM systems;
O encouragethe disseminationof new techniquesand applicationsto Logisticsand SCM systems;
O provide a forum for academicsand professionalsto sharethe advancedknowledgeand experiencesof Logisticsand
SCM systems.
Copyrlght @ The InternationalFederationof Logistics and SCM Systems.All right reserved.
andIndividualsubscription:
50US$/year
Subscllption: Institutionalsubscription:l00US$(12,000JP+)lyear
I
InternationalEditorialBoard Members
of rhe lnternational Federation of Logisfics and s.c,n , s
Australia:
Dr. Erhan Kozan
Schoolof Management
Science,
Univ. of Technology,
Queensland
Australia
Dr. ShamsRahman
LogisticsandSupplyChainDiscipline
Schoolof Management
RMIT University,Australia
Ghina:
Dr. Jian Chen
Dept.of Management
ScienceandEngineering
Tsinghua
University,China
Dr. PengTian
Dept.of Management
ScienceandEngineering
ShanghaiJiaotongUniversity,China
Honq Kong:
Dr. Xiande Zhao
Dept.of DecisionSci.& Managerial
Economics
TheChineseUniversityof HongKong,H. K.
India:
Dr. PramondK. Jain
Dept.of Mechanical& IndustrialEngineering
IndianInstituteof Technology
Roorkee,India
Dr. Masanobu Matsumaru
Dept.of Industial& SystemsEngineering
TokaiUniversity,Japan
Dr. Keizou Wakabayashi
D9lt. Management&IndustrialEngineering
Nihon University,Japan
Korea:
Dr. Kap Hwan Kim
Dept.of IndustialEngineering
PusanNationalUniversity,Korea
Dr. Suk-ChulRim
Dept.of Industial& InformationSystems
Engineering
Ajou University,Korea
Taiwan:
Dr. Yon-ChunChou
Instituteof IndustrialEngineering
NationalTaiwanUniversity,Taiwan
Dr. Yen-ChenJim Wu
Dept.of BusinessManagement
NationalSunYat-SenUniversity,Taiwan
Thailand:
Dr. VoratasKachitvichyanukul
Asian Institute of Technology,Thailand
Japan:
Dr. MasatoshiKitaoka
Dept.of InformationSystemCreation,
KanagawaUniversity,Japan
Dr. PaisalYenradee
SirithornInstituteof Technology,
Thailand
Organization
of The lnternationatFederationof Logisfics and S,C.M.Sysfems
Ghairman
KarasawaoYutaka
And Dr. & EmeritusProfessorof
Chairmanof TheJapanSocietyof LogisticsSystems
Kanagawa UniversitY,JaPan
Vice Chairman
Feng, Cheng-Min
Chairman of The TaiwanSociety of LogisticsSystemsAnd Ph.D. & Professorof
National Chiao TungUniversity,Taiwan
Fujimoto, Takahiro
And DBA & Professorof The
WceChairmanof TheJapanSocietyof LogisticsSystems
UniversitYof Tolqto,JaPan
Katayama,Hiroshi
Wce Chairmanof The Japan Societyof LogisticsSystemsAnd Dn & Professorof
JaPan
WasedaUniversitY,
Lee, Young Hae
Chairmanof TheKorea Societyof SCMAnd Dr & Professorof HanyangUniversity,
Korea
PongchaiAthikomrattanakul
ph.D. & Professorof King Mongkut's(Iniversityof TechnologtThonburi,Thoiland
.,:
Journalof Logisficsand scM sysfems
lnternational
NumberlMaY,2009
Volume3
CONTENTS
HircshiKataYaru
Foreword
I
2 StebsakNotthavwti, PrachyaBoonprasart'Ililoom Jaruphongsa
Fixed Delivery crew - vehicle Assignments
vehicle Routing'prouremwitrr rr,ranr"ttvtaterial,itanJting:
8 Ririn Diar Astefi, futynh TnmgLuong
DemandPattem
AHeuristic rur"tfoJ ro, sft rotty with IncreasingPower-Form
l6
BusabaPhrulcsaphanrat,Pisal Yenrqdee'Ario Ohsato
in a ParallelMachine Environment:
AggregateProductio-nPrunningwith Labor Replacement
pJiitititti" Linear ProgrammingApproach
DuangpunKritchanchai, WrachchayaChanpuypetch
A CaseStudy for ThailandRubberExports
A Frameworkfor DecisionSupportSystems"inLogistics:
32 TheJin Ai, VoratasKachitvichyanukul
Fleet VehicleRouting Problem
A ParticleSwarmOpti*iruiion for the Heterogeneous
Nobunori Aiura, Eiichi Taniguchi
Loading-UnloadingSpaceswith an Emphasis
Evaluationof a ReservationSystemfor on-Street
Benefits
on itt" RelationshipBetweenUtilization Ratio and
48
ThananyaWasusri,ChariyapornRoiruchiwit
in an Apparel Supply
Rules on Supply Chain Perfiormance
The Effectsof ReschedulingPeriodsunJ birp"r"fring
Chain
Mishra
SubhashWadhwa,Felix TS' Chan, Madhawanand
ChainsUsing a Network Approach
Supply
Agile
of
O".ign
Flexibility Con.t-"i-gur"J
Kachiwichyanukul
64 Wijitra Naow'apadiwat,Dah-Chuan Gong' Voratas
and Replenishment
in Researchon collaborative, Planning,Forecasting,
RecentTrends
Jeong
Choi' Haejune
"End-of-Liie72 Hyunsoo Kim,DaeheeHan, Yongiung
process
simulation Analysis of Recycling
TechnologYin Korea
of
consumerElectronicAppliancesAdopting RFID
Sivakumar
SanRathviboon,Mario T. Tabucanon,Muttucumaru
chain Management
Supply
sustainable
vendor Evaluation Systemfor a
Rui Nakamura
88 Masatoshi Kitaoka, Hiroknzu lwase, Jun Usuki'
Chart for Distribution ManagementIndex
Control
Using
CapabilityMeasuresanAnstimation
lnternationalJournal of Logistics and SCM Systems
A Particle Swarm Optimization for the Heterogeneous
Fleet Vehicle Routing Problem
*^
The Jin Ai-A and Voratas Kachitvichyanukul*B
UniversitasAtma Jaya Yogyakarta, Indonesia,e-mail:iinai@mail.uaiv.ac.id
*u
Asian I n stitute of Technology, Thailand, e-maittoo."tas@ait-:ac.th
Abstract
1ts fixed cost1[, variable cost per
characterizedby its
This paper presentsan applicationof particle
swarrn optimization (PSO) for solving the
heterogeneous
fleet vehicleroutingproblem(HVRP).
HVRP is a vehicle routing problem (VRP) variant
thattakesdifferenttypesofvehicle into consideration.
Basedon the numberof vehiclesin eachtype, there
are two types of HVRP in the literature:the vehicle
fleet mix problem (VFM) that deals with unlimited
numberof vehicles and the fixed fleet version of
HVRP that dealswith fixed numberof vehicles.This
paper focus only on the latter since normally the
numberavailablevehicle is known in advancein the
actual operations. A PSO algorithm, solution
representations
and decodingmethodsthat have been
successfullyappliedto the basicvariant of VRP are
re-utilizedas the basicsolutiontechnique.In orderto
acquirethe natureof heterogeneous
type of vehicles
into the technique,a specialpreprocessing
methodis
incorporated
to the vehiclelist, so that a vehiclewith
lower relative routing cost is given higher priority
over the biggerone.The proposedalgorithmis tested
using benchmark data set and the computational
resultshowsthat the proposedmethodis competitive
with otherpublishedresultsfor solvingHVRP.
distance unit gp, and capacity Qp. For each vehicle
type k, m7,vehiclesareavailable.With eacharc (v;,vi),
thereis an associateddistanced;i. The HVRP consists
of designinga set of vehicleroutesin suchway that:
(l) eachroute startsand endsat the depot,(2) each
customeris visitedexactlyonce,(3) the total demand
ofa routedoesnot exceedthe capacityofthe vehicle
assignedto it, and (4) the total routing cost is
minimized.
As defined above, the HVRP is dealing with
many typesof vehicles.With regardto the numberof
vehicle type k (mp),thereare two types of problem in
the literature.The first problemdealswith unlimited
number of mp,which is usually called vehicle fleet
mix problem or the VFM, and the secondproblem
dealswith fixed and limited ze, which is called the
fixed fleet version of HVRP [2]. This paper only
focuseson the latter, since normally the number of
availablevehiclesis known in advancein the actual
operations.
Some researchworks that have dealt with the
HVRP mainly proposed solution methodology for
solving it. Taillard [2] proposeda methodfor solving
the HVRP calledheuristiccolumngeneration(HCG),
which is a hybrid techniqueof tabu searchwith linear
programming. Variants of simulated annealing
Problem,
Routing
Keywords'. Vehicle
algorithm which are called list-based threshold
HeterogeneousFleet, Particle Swarm
accepting (LBTA) algorithm [3] and backtracking
Optimization,Meta-heuristics
adaptive threshold accepting (BATA) algorithm [1]
have been proposedfor solving the HVRP. Li et al.
t4l also proposed another variant of simulated
annealing which is called record-to-record travel
1. Introduction
(HRTR) algorithm for solving the HVRP. From the
FleetVehicleRoutingProblem
The Heterogeneous
(HVRP) extends the Capacitated Vehicle Routing
computational results of those methods over the
benchmark data set of Taillard [2), it can be
Problem (CVRP) by relaxing condition on vehicle
concludedthat the HRTR method is able to provide
characteristics.While in CVRP all vehicles are
bettersolution quality amongothers.
identical, in HVRP the vehicles may differ from one
Recently, particle swartn optimization (PSO),
anotheras they may have different capacity,cost, and
is
the
HVRP
which is an emergingevolutionarycomputingmethod,
other characteristics.In the literature,
:
graph
a
A)
be
has been successfullyapplied for solving the CVRP
defined as follows []. Let G
0t
:
and
I
set
where V: {v6,v1,...,v,}is the vertex
[5, 6] and the vehicle routing problem with
v0
represents
Vertex
simultaneouspickup and delivery - VRPSPD [7]. It
{(vi,v.)lvi,viev,i{l is the arc set.
the
remaining
while
is noted that these VRP variants only cope with
a depotwith a fleet of vehicles,
v;
customer
Each
identical type of vehicles. Therefore, this paper
vertices correspondto customers.
are
several
q1.
There
attemptsto extend thesealgorithms to take different
has a non-negative demand
is
k
type
type
of vehicles into consideration,i.e., to solve
vehicle
of
which
vehicle types, in
HVRP. The same PSO framework and solution
as previouslypublishedwill be used;
representation
however, an additional procedure is developed in
ReceivedDate: November 26, 2008
AcceptedDate: February25,2009
fleet of vehicles.
orderto dealwith heterogeneous
oc
uolluluasardouuopnlos z'z
Ir'o]
[eAJAlUrOq1Ur Joqunu ulopusJ rrrJoJrun
uorlrsodlseq .roqq8rau
JeeuJoJluslsuoc uorlEJelsccsaqJ
uorlrsod
lseq lusol JoJluelsuos uorleJalocreor{J
uollrsoo
lseq 1uqo13roJ tu€tsuoc uorleJelecJeeqJ
uorlrsodlseq
leuosradJoJ luelsuoJ uorleJeloooueqJ
uorsueulp ,t/.1atqtle alcrued ,,,7
eqtgo (lsequ) uotltsod lsag roqq8tau reeN
uorsusrurp u,L! egt 1eelcryed
aIilJo
(tseq1;uotltsod lseq Isco'I
{,/
uoISue|.uIp
(1seq8)
uotltsod
a1t
lseq
1e
lpqolD
u,tl
uorsue{urp o,4 e471eelctued
1,/ eW3o Qsaqd)uotltsod lseq leuosrad
uorleJoll ,,-t aq! ur lq8rervruruoul
uorl€Jelr ,t/ at41ur uorsuaurp
elql1e
elctgud ,1rl et{lJo uolllsod
q,Ll
uorlEJelr q/. etll ur uorsueurp
q,t! e1l1u alcqud ,r,/ erllJo ftrco;en
'J
,)
o)
Y!/h
'l/h
,tBh
'11
/h
(')^
\')"'e
(')'',
:eJaq/Y\
k)
(l)
+ (t) "'e= (l + t) "'e
(r * ,; atro
((')-e - ffrh)n"c+
q:/h)ntc+
ftt\''e q'/h)n'c+
((t)''a ((t).e - o'rh)no+ (t)'ttot(t),u = (t + z)'ttco
"
:u
eqt elepdno1pes
oprsodr{ceeJo uollrsodpue ,{1rco1err
n eJesuorlenbeEurnollog'ssecotduorleJalreql uI 'sal
crged11eJoJsJolJeAoJezsr Jolcel ,{1rco1ar
Ieqrureql
'enl€AI'untllrxBr.u
e puB [unrurultu€ uea/$eq peleJaue
3,{luropue;sr uorsueulpelcrpedqcueqcrq/( ur u'1 de
ls ut pozrlerlrureJesolcrgud7'ryorneurergsrr{lul
'Z dels
leodor
osr/$Jeqlo'letu
sr uorJelrj3SurddolseqtSrdolg
Surddo1g't dats
'senl€Apelepdnaql uo peseqalcrged
qc€eJo uorlrsodpue ,Qrco1e,r
eqt atepdn 'p
'senl€A
6aq roqqSreuJeaupu€
'c
lseqIecollseq 1eqo13'1seq
luuos:edalepdn
'elctgedSurpuodsa.uoc
eql Jo anle^ sseulg oql su enlP^
acueuuogredoql los pue salnoJ olcrqal
Jo les qcua Jo acueuuo;radeql et€nl€^g'q
'(7'3 uoqcegaes)salno:elorqe^
'u
Jo las e o1uorlrsoda1cryedqc€eepoceq
ssacolduouaratl '7 dets
'alcrged
q3peJo,frco1e,r
pueuorlrsodIerlru oql las 'q
'r.ruu,lns
eqlJoJeqr.uetu
seselJru€deleraueg'u
'1 dets
uottoztlDtttul
dUA roJ {roaauurd OSd :t ruql.tro8ly
'dU,\H 3ur,r,1os
JoJ{Jo,{rerlre{srr{}esno1alqrssodoslesr 1r'erogareql
'q'Z pue e'7 dalg ur pelscol are sdals cgrcads
rualqordoql l€ql polou sr t1 '1 ruqluoElv ur pa.rer^ar
,{UaFq sr lro,&\eru€{ OSd eql 'ror^eqaqSulureal
aq seprseq'[1 1]
sElseq 1eqo13
IurcosroJ slueuodruoc
'p p
luaueqcellleJaa^,(q pesodordldacuoc Jor^eqoq
SururealluroosE sl qJrq^\'1seqroqq8reuJBeueql pue
'selcrged
Euoureuorlrsod lseq eql
luacuhe l€Je./\es
sI qJlq.ry\'1seq
eqt selurofuocurosle uorsJa^OSd
1eco1
qlr,r
slql '[01] sarntcrulsSurureallurcos e1dr11nru
tuqruoSly OSd e 'OSdN'IC aql uo peseqpesodord
ueaq puq 4an SurnlosroJ lro^1our€gOSd e'[L-g]
lnlnuufqcr4lqce) pue rV Jo $lro.,YrJerlJBoul
'[6] crol3 osl€puu
[g] ueq:eqEpuu
Kpouue;1,{q papl,tordsr uoqecrlddepue 'anbruqcal
'tusrueqcatu
',!rco1a,r
OSd uo uorluuuoJur eJot{
alcrpedEurlepdnJoJpasno;e uorlrsodtsaq1uqo13
pue
'lseq
lseq leuos:adesaql
leuos:ed11uSuoue lsaq oql
sr qcrr.l^r'uorlrsodlsaq 1uqo1E
eql pue 'alcrgedaq ,{q
pollsrl uaoq eleq leql suorlrsodeqt Suoue uorlourg
e,il1cefqolseq eql se,ilEluql uorlrsodaql se paugap
sr qcrr.{^r'alctged qoee Jo uorlsod lseq yeuosrad
aql lnoqe uorleuuoJuraql surelureluosl? rusru€q3er,u
'uuei$s aql
OSd oql
Jo rol^Bqeg lslcos pue
elrlruEoc eql SurtrelnuruI 'urelqordeqt go uoqnlos
arrqcadsord
sr alcrpedu leqlou€
lualeJlrpEurlunlerra
ol uorlrsodauo uro{ Suvrolq ,firco1e,reql uo peseq
lxou eql ol uorltsod auo tuo{ ulre,r\s aql ur alcrped
,{ranago lueluenotu aql Jo slsrsuoJdals uorleralr
'alcrged aqt
OSd qcEA
Jo fitgqu Eurqcruasaql
Surluesarder
sr Jolcen,{1rcolen
€ pu€ uorlnlosuralqo:d
u EurluaserdeJ
sr uorlrsodelcrgud l€uorsuaurp-plnr.u
'luo8e Sutqcreose se
ItB leql seloru€dgo uuerrs
V
e fq :ege lqEnossr ruelqordcgrcedse Jo uorlnloslsaq
oql 'OSd oql uJ 'por{loruSurqcreasB sB rrr€/r\saql
ur sl€nprlrputaql Jo $lueuenou 1ecrs,(qd
eql seleutur
qorq^\poqlaruqcreespes€quorlelndode sl OSd
IuqtlroSlv osd I'z
f8o1opoqlatr^l
uognlos pesodordaql 'z
uo uorlcerrp
requryspuauruocar
or" ,".;I:t;'ll
'tas
polueserdIJo/$ eql sepnlcuoc? uorpes ',(11uurg
Bl€p{Jerrrqcueqeql uo poqleu pasodordeqlJo sllnsar
'paureldxesr
leuoqulnduoc eql sluesardg uorlcag
qly( leapo1a:npacord
solJrqelJolaeg snoaueSoJalog
'po,roner ,{UaFqeru uorluluesardar
Ieuorlrpp€aql pue
uorlnlos eql pus urqluoSlu OSd aql :,{Eolopoqleu
uonnlos pesodordaql saqucsapZ uoqcas :^\olloJ
se pazueS:o sr raded srgl Jo JapururuoJaql
lnternational Journal of Logistics and SCM Systems
-al,;;J;l;i;F,+--
List
Priority
tocustomer
convert
r-t
-t-
VehicleI
Orientation
j--.,-
I
i2,,,
-l
Vehicle ri
Orientation
"TJi:*i" "Til:ji,1"
SR-1
Figure 1: SolutionRepresentation
VehicleI
Radius
Figure2: Solution
Two solution representationshad been proposed
in previous works of Ai and Kachitvichyanukul [5-7],
which are called solution representation SR-l and
SR-2. For representing VRP with /4 customers and m
vehicles, the representation SR-l is using particle
with (n+2m) dimensions and the representationSR-2
is using3m dimensions.
In brief, both representationSR-l and SR-2 are
using real number in each dimension. In the
representationSR-1, the first r dimensions represent
priorities of customers and the other 2m dimensions
representthe orientation point of vehicles (Figure l).
While in the representation SR-2, 2nt dimensions
representthe orientation point ofvehicles and another
rrt dimensions represent the coverage radius of
vehicles(Figure 2).
In the PSO application for VRP, a specific
decoding method must be defined to transform a
particle with specific representation into vehicle
routes.For representationSR-1, the decoding method
startswith creating a priority list of customers based
on the first n dimensions of a particle. The priority
list is constructed by sorting in ascending order the
position values and taking the dimension index as the
list. The priority matrix of vehicle is then created
basedon the last 2lrl dimensions that are used as the
route orientation point of vehicles, in which a
customer is prioritized to be served by vehicle with
closer distance between customer location and the
vehicle route orientation. Finally, the vehicle routes
are constructedbased on the customer priority list and
vehicle priority matrix. One by one, each customer in
the customer priority list is assigned to a vehicle
based on its priority and such problem constraints as
vehicle capacity constraint and service duration
constraint. This newly assigned customer is inserted
to the best position in the existing vehicle route based
on the least additional cost. Another effort to improve
solution quality of the route is to re-optimize the
emerging route using local improvement procedure,
i.e. 2-opt.
The decoding method for solution representation
SR-2 is slightly different with SR-l. It starts by
transforming a particle into the vehicle orientation
points and the vehicle coverage radius. The vehicle
Vehicleni
Orientation
Vehicle nr
Radius
Representation SR-2
routes are then constructed based on these points and
radius. For each vehicle, starting from the first to the
last vehicle, a feasible route is constructed by
including customers that are located within the
coverage radius and are not yet assigned to other
vehicle. Afterward, local improvement procedures,
such as 2-opt, l-l exchange,and l-0 exchange,are
applied to the constructed routes. If there are
remaining customers that have not been assigned to
any vehicle, the customers are inserted one by one to
the existing routes as long as the route feasibility is
improvetlent
local
the
maintained. Finally,
routes.
ofthe
to
all
re-applied
proceduresare
It is noted that the differences among VRP
variants are in the problem constraints. Therefore,
both representationsSR-l and SR-2 can deal with
the HVRP. Slight modification is needed in the route
construction steps to form feasible routes that did not
violate the problem constraints. To be more specific,
the HVRP has the same problem constraints as the
CVRP, however, different vehicles may have different
capacity and duration limit for the HVRP.
2.3 PreprocessingVehicle List
In the HVRP, different vehicles may have differe
nt fixed and variable cost. This characteristic is not pr
esent in the CVRP case where all vehicles are identic
al. To deal with different cost scheme among vehicles
, an additional procedure is proposed here to preproce
ss the vehicle list based on a cost parameter e* that i
s calculated usine following formula:
6*={\+cr
An ideal formula is to use the expectedtravel
distanceof vehicleas the denominatorof fixed cost.
However,it is difficult to estimatethe expectedtravel
distanceso half of the time durationlimit is set as the
denominator.A vehicle with lower cost parameter
will be preferred over one with higher cost, so that
the routing cost will be reduced.In the solution
representationSR-l and SR-2, the result of this
procedureis implementedby settingthe lowest cost
-:4,-
IAI\.u ShtgSZ
zqcl uolqlv
LW
rr't[sI
v0,
,E'OZII
89'fZ8r
96'I90I
998
9tz
88r
I^IVU 8hI8ZI
zqntrO0tII unrlued
s t ' 9 9 Is
9SI
8Zb
IL6
t8'EZtl
9E'9t81
IO'I/OI
t9t
ZqN OE uorlecUtceds
'uollets{Jo1d
credg ung
relnduo3
I,^{VUSI^I8ZI
zqhtrOsgIII urllrlued
SL9
9E'8SS
60t
O I€
,9'9ZI
t I'298
tzz
L 9 ' IL O
zjtt
ttSs
LL'6SS
IS'TII
9L8Z
SVZZ
OEE
6 L ' IL O
6I
8
L
s0'tsI
o
s
OZ
9r ' 0 / 8
n6'?vtl
M
zs'svl
II
991
WI
89E
6t'8fl
6Z'SI0I
89t
L8t
6Z'SI0I
v6
6 € 'rr9
98'910
er8
n6'Lrj
t9'zr9
s€t
IE
SL9
anrlra[q6
96'6t9r
c/t
(s) atur1.
96'6rSr 0l
v9's19
s0'8tsr
(s)aura
an;1ra[q6
ts't09
t8'Lrgr
(s)aura
ltlu.r.us
a,rqca[q6
(s)aur.1. aa;1ra[q6
lelvrsr
II YIvs
oqlJo uos
dUAH uo lJnseupeqsrlqnd
'
v
0'z 00s
L
9
0
C
b
!
V
z
z
00s
6'Z
6
v
v
ut
'llnser
OOZ
I
008
00b
081
b'z
002
0rl
0 0 r 09
0 0 t z 00€
0
z't
h
z
00€
00r
9t
0l
002
00r
00t
092
0sl
00r
0s
0z
0 s€
J
B
V
J
s
V
J
E
C
J
0zt
002
0zl
3
0'l
08
SZ
0s
I
V
t
o
aqAI
.IJqA
Q
o
0sl
0z
C
00r
SL
Z
6I
8I
C
9L
LI
'lsnJ
'oN
'qoJJ
l'7
9'l
h
B
V
R
s
z'
001
0'l
z
€
0'z
v
9'l
0'l
I
b'l
I'I
z
n
0'l
z't
z
!c
+a
L'l
v
7
z'l
0'l
v
ut
JO'ON
ds uJcU irur,uqcueg duAH sqlJo
v
eJuBlsuI
[z]crH
Iuo J : Z e l q B l
00t
002
001
09v
0il
J
08
TI
V
oc
9I
J
g
V
J
I
09
SI
0s
vl
0s
EI
0v
091
0sz 0 0 r
0 0 r 0s
00s€ 00€
009I
091
000r
00v
0zl
0zI
OL
V
002
I
s7,z 0zr
0s
0v
OZ
0€
07.
T
o
st
a
o
gI
3
CI
J
I
V
aqAI
'Icrt
A
s : t alqEl
'lsnJ
JO'ON
'oN
.qOJJ
luauruedxe yeuorlelnduror aql sl\oqs
'selrriled
puu
g
elq€I
t
oql rog Xysnoauellnuls
pasnlou aru sanle^qloq
001 pue 0S qrrrnu.rq1r.ro81y IAtrCA
'1aselup >lJpr.ur.louaq
aql
uo
pelcnpuor
sr luauruadxa eql
OSd
srql ur paugopflreelc aJeslsoc
'Z
lu€lsuocuorleJelacJe
alqerrunpuu poxg q8noqlly .l alqeJ ur paluasardsr
uorlrsodlsaqroqq8reu
Jueupu?'1 luelsuocuorlsJaleoJe
uorlrsodlsaqIBJoI.0
les elep>lJur.ur{cuoq
srqtJo uorlucgrceds
eql .ocuelsrp
.1
luslsuo3uorlzJalacoe
uorlrsodlsaq 1uqo18
upepllcng
paugep
ss
aJe ueql Buouresecuelsrpaql
luelsuoc
uorl€Jalecce
uorlrsodlseq l€uosJad.y.g lq8rarneruaur
pue deuroleurpJooc
u?rsaueJur uelr8 aJ€sJeruolsnJ
lsul '6'0 lq8ra,r.erileur NJg .g roqq8reuJo Jeqr.unu pue lodep3o suorlrsodeqJ .9 ol tuo.r;sauu,rsad,e
E
'0001 uorlurelr
alJrqe^Jorequnu aql pu€ sjeruolsnc
qloq JoJ
Jo requnu :suorleluasarde:
001 ol 0g Luo{
pelerodrocureJ€ sJoleruzJsdOSd oruusaql .asod:nd
serJelslaruolsncJo Jaqunu oql qlr/\t ,sacuelsur
3;o
uosrruduoc rog 'W11U Jo BD I pue rosseco.rd slsrsuorlas el€p
.[ZI] .le uoploC
{rerrrqcueqslqJ
le
zHD V't td letul r{ll^AJd B uo uru puu
uo4 ,{lyeur8uosr qclq/rr ,(6661) p.ru111e1 les
I.l uolsre^
Jo
elBpegl sl duAHJo uorsra^laau pexu pus
{roaeuerC lEN.$osorclhtr uo a8un8uulg3 Bursn
qloq
rtrc^
.4UAH
pelueuraldurrsr uqtuo8lv OSd eqJ
JoJdunH eql JoJles el8p {rerrqJueq uolllurocv
eql roJ
alq?lre^ules el€p secu?lsurg eql JeAosuorluluesardar
.t
lJnseulsuorlBlnduoJ
uorlnlos qloq qlr^\ {ro^\orue{ OSd aql Eur,{1dde
fq palcnpuoJsr luarurJadxaluuoqelndurocaq1
'rusrueqcausrql
uro{ palcadxa
'lJnsaJ sr
aql Jo uorlcnpeg .elJrrla^ anrsuadxa1sua1
lsoJ
paqsrlqndlseq eql selecrpuracugedflploq (elqelstql
aql ol ^llJolJdreq8rqueurrS
sl qclr{/y\.1sr1
passecordard
ul 'Z alqeJ uo pelsrlsl dUAH eql uo rlnsarpeqsrlqnd aql ur alcrqen
eql
roJ
pelrrutsuoc
lsrg
,{11srgsr
eql Jo uosueduoc .uorluru;ogurslql ol uorlrppe
.lsrl alJrqe^eql uo peseq
olnoJ
eql'aJoJaJeqJ
Xlureu
uI 'lsll eql ur sanle^ eql ol sleJeJlsoc elqBrre^
sl z-us roJ poqleu uorl3rulsuocolnoJ oql asurs
'Z-US uon€luesarde:
eql puu selcrqa^ lle roJ (g__!) otaz sr lsor pexg
to; ,{lyercedsalueuodun .(re,r
'4UAH
.salcrqel
aql
Jo uorsJel leag paxg eql JoC
sr arnpacordSursseco:da-td
srqt teqt pe1o.l,, i1
'ut elJrr{s^er{lsBolcrqe^
IIBroJ (t:ta) auo ol slenbelsoc alqerr€Aeql puu lsrl
oqt se atuesaql sr lsoc paxg aql ler1lpeugep{11ensn
lsoc lseqSrqeq1f11eugpue,Z elcrqe^eql s? elcrqe^
sl ll 'ntrg^ eql uI auAH Jo uorsre^laau psxg puu
puooas eql ,l elcrqa^ aql sE olcrr{e^
lsoc lsa^4,o1
InternationalJournal of Logistics and SCM Systems
cornputationaltime for all problems is less than 74
secondsfor 50 particlesand lessthan 172secondsfor
100 particles. It is evident also that the solution
qualitywith 100particlesis insignificantlybetterthan
from the solutionwith 50 particles.
Resultfor solutionrepresentation
SR-2 is better
thansolutionrepresentation
SR-l result,in which the
resultsare very closeto the bestknown solution.For
all instances,
the averagepercentage
deviationis less
comprises of the average, standard deviation, and the
minimum objective function of each instance over 10
iterations, altogether with
its
corresponding
percentagedeviation and the average computational
time (in second) for solution representationSR-l and
SR-2, respectively. The percentage deviation is
calculatedas the ratio between the deviation of the
resultfrom the best published result.
For solution representationSR-1, overall results
'able
ntationSR- br HVRP
ObiectiveFunction
Comp
Instance
Average Standard
Minimum
Time (s)
Average
Minimum
Deviation
V"Dev
V"Dev
50 narticles
13
t 7 4 3 . 1 6 14.84%
37.1
8
t694.17
fi.62%
36
17.25
z)
t4
661.32 8 . 8 s %
640.90
5.49%
15
1 5 . 1 6 10 5 4 . 3
1
3.83o/o
25
0 7 2 . 1 3 s.60%
200.69
4.870/0
21.19
24
t6
n70.82
2.26%
t7
1 4 872
8.l1Yo
lt.29
1127.66
6.19%
48
l8
988.60 9.0s%
29.16
t937.73
6.26%
59
t9
203.62 7 . 7 1 %
9.59
I191.04
658%
74
20
2r.94 t672.87
7 1 2 . 0 0 1r.59%
9.04%
69
100 narticles
13
t744.84 l4.96Yo
44.31
t660.20
9.38Yo
91
t4
6 6 1 . 5 3 8.89%
15.10
641.9r
5.66%
59
15
1067.03 5 . l 0 Y o
13.34
2.9804
045.53
63
t204.62 5 . 2 r %
20.27
1 7 163
2.33%
16
63
t7
fis2.29 8 . 5 1 %
12.63
137.72
7.13%
t7
18
40
t 9 7 3 . 9 8 8.250h
22.05
944.36
6.62yo
r9
1r94.69 6 . 9 r %
10.92
r68.62
4.s7%
72
20
1 6 8 3 . 8 0 9.7s%
25.34
640.24
6.9r%
67
3: Resultot PSO Alsonthm wrth Solutron
able 4: Result ot PSO Algonthm wrth Solutron RepresentatlonSR-z tor HVRf
Instance
Average
ObiectiveFunction
Average Standard
Minimum
Deviation
"hDev
Minimum
YoDev
Comp
Time (s)
50 particles
l3
t4
15
16
t7
18
19
20
16.22
4.14
7.50
4.36
1578.91
609.17
l0l9.ll
1r48.62
4.02%
0.27%
0.38%
0.32%
2.34%
12.60
24.46
9.46
1066.44
1840.82
0.9s%
85
r50.39
3.44o/o
2.940h
r135.97
r.65%
r04
589.25
359%
17.03
t561.29
1.77%
ll5
14.80
4.10
156t.21
609.17
2.860io
t07
4.s6
3.82
t019.27
0.27%
039%
030%
58
66
66
143
t75
15 9 3 . 7
1
614.66
4.96%
l.l1Yo
031.06
r.55%
t52.84
086.82
886.38
0.69%
0.42%
48
28
32
3l
70
100 particles
13
l4
l5
16
t7
18
t9
20
t586.ll
613.29
1025.19
r152.84
10 7 8 . 8
1
1869.81
r148.24
1578.09
4s0%
0.9s%
0.98%
0.69%
153%
2.s4%
2.75%
2.86%
areas follow: the averagepercentage
deviationis less
than l5o/o,standarddeviationis lessthan 45, and the
7.83
13.l8
l148.41
1069.52
1852.36
0.71%
t.58%
t0.25
fi3r.32
r.24%
9.58
t561.80
t.80%
206
233
than 4o/o,standarddeviation is less than 25, and the
computationaltime for all problemsis lessthan 115
- /,(, 'sI'uelqord
Surlno; elJrr{ol uo uorl€zrulldo u:e,,rrs aycrgud go
uorlucryddeeql uo 8ur1;om sr eq ',{11ue:rn3'sruelsfs
uoqecrldde
Ieulsnpur uo
pue
sll
uorlelndruoc
fueuorlnlona
opnlsul
slseJolurr{JJsaseJsrH '8002
ur pu8lrer{J ',{3o1ouqcel go
.
aln1rlsuluursv lB ,{8olouqcal
pue Suueeur8ug ;o looqcs
eqt tuo{ '8uA'C € polracaraH
'Brseuopul'ege>1e,{3oa
e,\e1
erulv selrsJenrun'fSolouqcol
,(l1nceg
leulsnpul
Jo
'Surreaur8uE
lurJlsnpulur JoJruco'Je sl !V ulf aqJ
selqdurSolgrorllnv
'v861
'99-6V'
I l'qzrDasay suot1otadgpuo stalndwoS
'..ura1qord
''g
Surlnorelorqel xnu puu azrs1aa1g,,
'suas,(eqgpu€ 'T 'frta'I ''V 'pussy ''g 'uaplog
tztl
'
t1OZ'lzl-0 11' acuatatuo3 uo1p 1ndwo3
[touo4n1o,tg puo olpuaD lo sButpaaco.t4
'..uoI1JeJe1uIroqq8teu Jeeu qllrtA srr rel\s
elcrged Eursn uorlezrurrldg,,''V "I ',rrcp€so
''1 'ruere4'';1 'rueueqceur€Jea1
pue 'J 'ueqo141
l rr l
'9002'20-EVnde4'8ut1aporypuD uoqzlnutlS
uo acuatatuoJ lDuorlDutaluJto s8utpaacot4
'..seJn1cru1s
lercos egdrllnr.uqlrA\ uorlezrulldo
uuel{s
olcrgud
snouaSouroq-uou V,,
''n'1n4nuu,{qcrllrqoe)
pue'd's4rerruqc8uo4t o r l
'9002'uopuo-I
'9791 'uot1oztutttdowtolts apluDd '';41'cre13
tol
'[002'ocslcu?rJ
ueg'sreqsrlqnduuutuJn€;tr
uuSroq'acua3111a1u1
wrDAS ''J 'U 'geqraqg puu 'f ',{peuuay tsl
' 6 0 0 2_' z 0 L t - t 6 9 t ' 9 t
' t1c,to
asay suotTotadgpuo sta1ndwo3',,fsa n11ep
pus dnlcrd snoeuellnurs qlr^\ ualqo:d
Suqnor elJrqe^ aql JoJ uorlezrurqdo urre^\s
alcrgedV,, ''A'lnlnuefqcy4rqoe) pup 'f 'I'lV Ltl
'6002'tg€-09€'9S'SuuaautBug
lDlustxpul
puD stalndutoS '..rua1qo.ld Eurlno.t alJrqel
pelelrcudec eql Surrrlos JoJ suorleluaserdar
uoqnlos ollu pu€ uorlezrunldo uu€,/r\s
pue 'f 'I 'lV tgl
elcrUed,,''6 '1n1nuu.(rlcrllrr.lce)
'
puo sct1
n3o7
74J39
L00Z'SS-OS'7'suta6,(g
',.rualqord 6urlno.l
to putnof lDuorlouJauJ
elcrqenpelelrcedeceql JoJ uorlezrurldo uuel,\,s
a1cryudV,, ''A'1n1nue,{qcrnl!{ce;pu€ 'f 'J'lV tsl
'1002-zvLz-ntLz
'Vt 'tlctoasay suolptadg puo sta\ndwoS
'..rua1qo:dEuqnor elcrqel
loag snoeueSoralaq
aql 8un1osro; urqlrroEl?IeA?JlpJocaJ-ol-pJoceJ
''A 'llsu11 pue 'g 'ueplog ''C 'l'I
V,,
Lvl
't002
'lL-99 'yg '{lalcog qznasay puogotad1 aqt
to putnoT'..rue1qordEurlno;alorr{alleeg poxg
snoauaSorelaqeql JoJ crlsuneqsleu Suqdaccu
ploqsaJql peseq lsll v,, ''s'A 'srpsrlrsss^
'srpnousJr) ''c'J
'srlrlueJ?I
pu€ 'J'J
tel
'666r
'VVI 'gg 'allauuoglotadg aq)raq)ay
OUIVA
'..dUA
taeg snoaueSorataq eql JoJ poqleu
uorlereue8 urunJoc crlsr:neH,, ''C 'A 'p:e11re1 [7]
't002 '891-8vl 'z9I 'qcntasaypuot1rc.tadg
'.,ruelqord Surlno-tolcrqei.
to 1ou"utoquoadotng
pexg
snoaueSoraleqeql JoJ orlsrJnoq€leu
leag
Surldaccu ploqseJql V,, ''S'n 'srperlrsse4
'srpnouelr;'1 ''C'J
'srp1uele1
pue 'J'J
[1]
saJueJeJ0u
'puEIIeqJ,{Solouqcel eln1qsul
Jo
uursv ur fpnls srqrog uoddnsIercu€uuaql Surpr.tord
JoJ ersauopuy'uge4efSoa e,{e1 etulv selrsJalrun
ol apnlllu:3 sesserdxe Jor{lne lsJg oql
'uoddns
Surlndruoc
lucruqoeleql pue,Q111ceg
3o
sse333eql roJ reluoS cruD IB[{J eql pu? (f,dHJIV)
,{3o1ouqce;Jo alnlrlsul u€rsv le dno:g 3ur1nduo3
eou€nrroJJed
q8rg eqt {ueql ol qsr.{\sJoqlneeqI
fueIuaSpal^aou{rv
'el'url
oql ecnpeJo1pazrruqdoJequrgeq osl€
leuorlelnduroc
uec sdalsleuoqelnduocaq1 'Surgessrelaurured
694
'poqleu Surpocap
Jo uoquzrturldoaql tuog osl€ pue
oloq,lr oql ur spopr Joglo ,{ue Eurlerofuocur ro
dals uorlcrulsuof,alnoJor{1ur eJnpe3o:dluaurenordrur
luaJafllp Jo uorluluaureldun eqt ruo.r; pacu€qua
eq ,{eu .fir1enb uorlnlos 'aurll leuorlelnduroc
Surcnper pu€ ,{rylenb uorlnlos Surno;drur
:suoqceJrpo^q ul reded srql ur peure8 Unsar ar{l
a.ro:dturo1 elqrssodIIIIs oJeseqcr€esalJequnC
'selcrueo
09 r{tl,r\ z-us oql sr stFser luuoqelndtuoc eq1
uro{ pepnlJuocaq uec leqt alcrgedJo lequnu puu
uoqeluasardal
uorlnlosJo uorleurquoJpepueuuoceJ
aql 'uorlrpp€uI 'l-US uorleluasordoJ
eql ueql uoge
perrnbar
eJor,u
leuorlelnduroc
Z-US uorleluasatder
aql
laneno11 'l-US
uorleluasa:der qllit\
{Jo/y\eLuuIJaql uPt{l Jeueq sI Z-US uoll8lueserda:
r{lr^{ IJo^\eurB{ OSd pesodord aill leql u^loqs sr
ll ,{fllunbuorlnlosJo uuel uJ 'arurlIeuorl€lnduocpuu
,t11enbuorlnlos qloq Jo uuel ur 4UAH aql 3ur,r1os
roJ elrlcega or€ Z-US pue I-US suorleluasardar
qloq qll,r\ osd
pasodord aql lsql ^loqs
sllnser luuoqelnduro) eql 'dgAJ rog uorlecrldde
OSd Surlsrxe ue pourpou ,{pq8rls ,{q (aUng)
uelqord Suqnog elclqa1 leelC snoauaSoralell
aql 3un1os roJ (OSa) uoqezrur4dg (ru€ly\S
elcrued3o uorlecrydde
aqt slueserdreded srql
uollupualllruoJall pus uolsnlJuoJ'v
'etuq
I€uorl€lnduroc
elqeuos€or ur uorlnlos ,lllenb qEH elqeuosear
epr,ro:d ol olqe sr ll ecurs 'se1cq:ed 0S qly(
Z-US eql sr alcrged Jo Jeqrrlnupue uoqeluesarda.l
uorlnlos Jo uoq€urq{uoctrseq aql leql papnlcuoc
eq uec 1r 'ero;areq1 'selcrged 0S qlp\ uorlnlos
ueql reueq ,(lluucgru8rslou sr salcrged 001 qtF\
fit1enbuollnloseql luril u/v\oqsoslusr t1 'salcrgedgg1
roJ spuocesggTuelqtsselpue selclgud0SJoJspuoces
lnternational Journal of Logistics and SCM Systems
Voratas
Kachitvichyanukul is an Associate
Professor in
Industrial
Engineering& Management,
School of Engineering and
Technology,Asian Institute
of Technology,Thailand.He
received a Ph.D. from the
School
of
Industrial
Engineering at
Purdue
University in 1982. He has
extensive experiences in
simulation rnodelins of
manufacturing systems. He had worked for
FORTUNE 500 Companies such as Compaq
Computer Corporation and Motorola Incorporated.
He had also worked for SEMATECH as technical
coordinator of the future factory program. His
teachingand researchinterestsinclude planning and
scheduling,high performancecomputingand applied
operations research with special emphasis on
industrialsvstems.