Volume3
Numberl May, 2009
Hiroshi Katayama
Sue bs ak Nanthavanij, Prachya B oonpraswt, Wi krom Jarutphon gs a Ririn Diar Astanti, Huynh Tnmg Luong
Bttsaba Phruksaphanrat, P isal Yenradee, Ario Ohsato
Duangpun Kritchanchai, I(irachchaya Chanpuypetch
The Jin Ai, Voratas Kachitvichyanukul
Nobunori Aiura, Eiichi Taniguchi
Thananya Wasusri, C hariyaporn Rojntchiwit
Subhash Wadhv,a, Felix T.S. Chan, Madhawanand Mishra
Wij itra Naowap ad i'tv at, D ah- C hu an G ong, Vorat as Kac h inic hv anu ku I Hyunsoo Kim,Daehee Han, Yongjuttg Choi, Haejune Jeong
San Rathviboon, Mario T. Tabucanon, Mut ttrcu mant S iv a ku mur
Masatoshi Kitaoka, Hirokazu hva.se, Jtm Usuki. Rui l{zkamura
Capability Measures and Estimation Using Control Chart for Distribution Management Index
I nternational
Journal
of
Logrstics and
SCIW
Systems
The lnternational
Federation
of LOGISI/CS and SCM Sysfemr
The Asia Pacific Federation
of LOGISI/CS and SCM Sysfemr
Foreword
Vehicle Routing Problem with Manual Materials Handling: Fixed Delivery Crew - Vehicle Assignments
A Heuristic Method for SFI Policy with Increasing Power-Form Demand Pattern
Aggregate Production Planning with Labor Replacement in a Parallel Machine Environment: Possibilistic Linear Programming Approach
A Framework for Decision Support Systems in Logistics: A Case Study for Thailand Rubber Exports
A Particle Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem
Evaluation of a Reservation System for On-Street Loading-Unloading Spaces with an Emphasis on the Relationship Between Utilization Ratio and Benefits
The Effects of Rescheduling Periods and Dispatching Rules on Supply Chain Performance in an Apparel Supply Chain
Flexibility Construct Based Design of Agile Supply Chains Using a Network Approach
Recent Trends in Research on Collaborative, Planning, Forecasting, and Replenishment
Simulation Analysis of Recycling Process of End-of-Life Consumer Electronic Appliances Adopting RFID Technology in Korea
lnternational
Journal of Logisffcs and SCM Sysfems
CO EDITORS
GUEST
EDITOR
Dr. Katsuhisa
Ohno
Dr. Voratas
Kachitvichyanukul
Dept. ofApplied Information Science, Industrial Engineering & Management, Aichi Institute of Technology School ofAdvanced Technologies, Toyota, Aichi 470-0392, Japan Asian Institute of Technology, Thailand Dr. Shusaku Hiraki
Dept. of Economics & Information Science Hiroshima Shudo University, Japan
Hiroshima, Hiroshima 737 -2122, Japan
ADVISORY
BOARD
Dr. Hiroshi Katayama
Dr. Cheng-Min Feng
National Chiao Tung University, Taiwan
Waseda
University,
Japan
Dr. Takahiro FuJimoto
Dr. Young Hae Lee
The University of Tokyo, Japan
Hanyang
University,
Korea
Dr. Hark Hwang
Dr. Marlo Tabucanon
IfuraAdrurcedlnstofScience&Takrolqry,Korea
Asian Institute of Technology,
Thailand
Dr. Yutaka Karasawa
Dt. Christopher
O'Breien
Kanagawa
University, Japan
University of Nottingham,
Ningbo Campus,
China
REGIONAL
EDITORS
Dr. Bongiu Jeong
Dr. Voratas Kachitvichyanukul
Yonsei
University, Korea
Asian Institute of Technology,
Thailand
Dr. Zhihong Jln
Rajesh Poplani
Dalian Maritime University, China
Nanyang
Tech. University, Singapore
Dr. Lle€hien Lln
Dr. Shams Rahman
National Kaohsiung
University of Science
and
RMIT University,
Australia
Technology,
Taiwan
PARTICI
PATING
ORGAN
IZATIONS
The Japan Society of Logistics Systems
The Asia t*tcttic Federation of Logistics &
The Korean society of scM
sGM systems
The
Taiwan
soctety
of Logistics
systems
ll"riltf,jffii]nal
Federation
of Logistics
&
AIMS & SCOPE
Logistics and SCM Systems ins an international journal for reporting original quality works on Logistics and Supply Chain Management(SCM) systems. It is published by the Intemational Federations of Logistics and SCM Systems. The aims of the joumal are to
O publish original, high-quality research that will have a significant impact on Logistics and SCM systems. O develop, Promote and coordinate the theory and practice of Logistics and SCM systems;
O encourage the dissemination of new techniques and applications to Logistics and SCM systems;
O provide a forum for academics and professionals to share the advanced knowledge and experiences of Logistics and SCM systems.
Copyrlght @ The International Federation of Logistics and SCM Systems. All right reserved.
-I
I nternational
Editorial Board Members
of rhe lnternational Federation of Logisfics and s.c,n , s
Australia:
Dr. Erhan Kozan
School
of Management
Science,
Queensland
Univ. of Technology,
Australia
Dr. Shams Rahman
Logistics
and Supply Chain Discipline
School
of Management
RMIT University,
Australia
Ghina:
Dr. Masanobu Matsumaru
Dept. of Industial & Systems
Engineering
Tokai University, Japan
Dr. Keizou Wakabayashi
D9lt. Management
&Industrial Engineering
Nihon University, Japan
Korea:
Dr. Kap Hwan Kim
Dept. of Industial
Engineering
Pusan
National University, Korea
Dr. Suk-Chul Rim
Dept. of Industial
& Information
Systems
Engineering
Ajou University, Korea
Taiwan:
Dr. Yon-Chun Chou
Institute
of Industrial
Engineering
National Taiwan University, Taiwan
Dr. Yen-Chen Jim Wu
Dept. of Business
Management
National Sun Yat-Sen
University,
Taiwan
Thailand:
Dr. Voratas Kachitvichyanukul
Asian Institute of Technology,
Thailand
Dr. Paisal Yenradee
Sirithorn
Institute
of Technology,
Thailand
Dr. Jian Chen
Dept. of Management
Science
and Engineering
Tsinghua
University,
China
Dr. Peng Tian
Dept. of Management
Science
and Engineering
Shanghai
Jiaotong
University, China
Honq Kong:
Dr. Xiande Zhao
Dept. of Decision
Sci. & Managerial
Economics
The Chinese
University
of Hong Kong, H. K.
India:
Dr. Pramond K. Jain
Dept. of Mechanical
& Industrial
Engineering
Indian Institute
of Technology
Roorkee,
India
Japan:
Dr. Masatoshi Kitaoka
Organization
of The lnternationat Federation
of Logisfics and S,C.M. Sysfems
Ghairman
Karasawao
Yutaka
Chairman of The Japan Society
of Logistics
Systems
And Dr. & Emeritus
Professor
of
Kanagaw
a Un iv ers itY, JaP an
Vice Chairman
Feng, Cheng-Min
Chairman of The Taiwan Society of Logistics Systems
And Ph.D. & Professor of
National Chiao Tung University,
Taiwan
Fujimoto, Takahiro
Wce Chairman of The Japan Society
of Logistics Systems
And DBA & Professor
of The
UniversitY
of Tolqto,
JaPan
Katayama,
Hiroshi
Wce Chairman of The Japan Society of Logistics Systems
And Dn & Professor of
Waseda
UniversitY,
JaPan
Lee, Young Hae
Chairman of The Korea Society of SCM And Dr & Professor
of Hanyang University,
Korea
Pongchai Athikomrattanakul
ph.D. & Professor of King Mongkut's (Iniversity of Technologt Thonburi, Thoiland
lnternational
Journal
of Logisfics and scM sysfems
Volume3
Numberl MaY,
2009
CONTENTS
l 6
32
I HircshiKataYaru Foreword
2 Stebsak Notthavwti, Prachya Boonprasart' Ililoom Jaruphongsa
vehicle Routing'prourem witrr rr,ranr"t tvtaterial, itanJting: Fixed Delivery crew - vehicle Assignments
8 Ririn Diar Astefi, futynh Tnmg Luong
AHeuristic rur"tfoJ ro, sft rotty with Increasing Power-Form Demand Pattem
Busaba Phrulcsaphanrat, Pisal Yenrqdee' Ario Ohsato
Aggregate Productio-n Prunning with Labor Replacement in a Parallel Machine Environment: pJiitititti" Linear Programming Approach
Duangpun Kritchanchai, Wrachchaya Chanpuypetch
A Framework for Decision Support Systems"in Logistics: A Case Study for Thailand Rubber Exports
The Jin Ai, Voratas Kachitvichyanukul
A Particle Swarm Opti*iruiion for the Heterogeneous Fleet Vehicle Routing Problem
Nobunori Aiura, Eiichi Taniguchi
Evaluation of a Reservation System for on-Street Loading-Unloading Spaces with an Emphasis on itt" Relationship Between Utilization Ratio and Benefits
48 ThananyaWasusri, Chariyaporn Roiruchiwit
The Effects of Rescheduling Periods unJ birp"r"fring Rules on Supply Chain Perfiormance in an Apparel Supply Chain
Subhash Wadhwa, Felix TS' Chan, Madhawanand Mishra
Flexibility Con.t-"i-gur"J O".ign of Agile Supply Chains Using a Network Approach
Wij itra Naow'apadiwat, Dah-Chuan Gong' Voratas Kachiwichyanukul
Recent Trends in Research on collaborative, Planning, Forecasting, and Replenishment
Hyunsoo Kim,Daehee Han, Yongiung Choi' Haejune Jeong -simulation Analysis of Recycling process of
"End-of-Liie
consumer Electronic Appliances Adopting RFID TechnologY in Korea
San Rathviboon, Mario T. Tabucanon, Muttucumaru Sivakumar
vendor Evaluation System for a sustainable Supply chain Management
Masatoshi Kitaoka, Hiroknzu lwase, Jun Usuki' Rui Nakamura
Capability Measures anA nstimation Using Control Chart for Distribution Management Index
64
72
A Particle Swarm Optimization for the Heterogeneous
Fleet Vehicle Routing Problem
The Jin Ai-A and Voratas Kachitvichyanukul*B *^
Universitas Atma Jaya Yogyakarta, Indonesia, e-mail:iinai@mail.uaiv.ac.id*u Asia n I n stitute of Technolo gy, Thailand, e-mait t oo."tas@ait-:ac.th
Abstract
This paper presents an application of particle swarrn optimization (PSO) for solving the heterogeneous fleet vehicle routing problem (HVRP). HVRP is a vehicle routing problem (VRP) variant that takes different types ofvehicle into consideration. Based on the number of vehicles in each type, there are two types of HVRP in the literature: the vehicle fleet mix problem (VFM) that deals with unlimited number of vehicles and the fixed fleet version of HVRP that deals with fixed number of vehicles. This paper focus only on the latter since normally the number available vehicle is known in advance in the actual operations. A PSO algorithm, solution representations and decoding methods that have been successfully applied to the basic variant of VRP are re-utilized as the basic solution technique. In order to acquire the nature of heterogeneous type of vehicles into the technique, a special preprocessing method is incorporated to the vehicle list, so that a vehicle with lower relative routing cost is given higher priority over the bigger one. The proposed algorithm is tested using benchmark data set and the computational result shows that the proposed method is competitive with other published results for solving HVRP.
Keywords'. Vehicle Routing Problem,
Heterogeneous Fleet, Particle Swarm Optimization, Meta-heuristics
1. Introduction
The Heterogeneous Fleet Vehicle Routing Problem (HVRP) extends the Capacitated Vehicle Routing Problem (CVRP) by relaxing condition on vehicle characteristics. While in CVRP all vehicles are identical, in HVRP the vehicles may differ from one another as they may have different capacity, cost, and other characteristics. In the literature, the HVRP is defined as follows []. Let G : 0t A) be a graph where V: {v6,v1,...,v,} is the vertex set and I :
{(vi,v.)lvi,viev, i{l is the arc set. Vertex v0 represents a depot with a fleet of vehicles, while the remaining vertices correspond to customers. Each customer v; has a non-negative demand q1. There are several vehicle types, in which vehicle of type k is
Received Date: November 26, 2008 Accepted Date: February 25,2009
lnternationalJournal of Logistics and SCM Systems
characterized by its fixed cost 1[, variable cost per distance unit gp, capacity Qp. For each vehicle type k, m7, vehicles are available. With each arc (v;,vi), there is an associated distance d;i. The HVRP consists of designing a set of vehicle routes in such way that: (l) each route starts and ends at the depot, (2) each customer is visited exactly once, (3) the total demand ofa route does not exceed the capacity ofthe vehicle assigned to it, and (4) the total routing cost is minimized.
As defined above, the HVRP is dealing with many types of vehicles. With regard to the number of vehicle type k (mp), there are two types of problem in the literature. The first problem deals with unlimited number of mp, which is usually called vehicle fleet mix problem or the VFM, and the second problem deals with fixed and limited ze, which is called the fixed fleet version of HVRP [2]. This paper only focuses on the latter, since normally the number of available vehicles is known in advance in the actual operations.
Some research works that have dealt with the HVRP mainly proposed solution methodology for solving it. Taillard [2] proposed a method for solving the HVRP called heuristic column generation (HCG), which is a hybrid technique of tabu search with linear programming. Variants of simulated annealing algorithm which are called list-based threshold accepting (LBTA) algorithm [3] and backtracking adaptive threshold accepting (BATA) algorithm [1] have been proposed for solving the HVRP. Li et al. t4l also proposed another variant of simulated annealing which is called record-to-record travel (HRTR) algorithm for solving the HVRP. From the computational results of those methods over the benchmark data set of Taillard [2), it can be concluded that the HRTR method is able to provide better solution quality among others.
Recently, particle swartn optimization (PSO), which is an emerging evolutionary computing method, has been successfully applied for solving the CVRP [5, 6] and the vehicle routing problem with simultaneous pickup and delivery - VRPSPD [7]. It is noted that these VRP variants only cope with identical type of vehicles. Therefore, this paper attempts to extend these algorithms to take different type of vehicles into consideration, i.e., to solve HVRP. The same PSO framework and solution representation as previously published will be used; however, an additional procedure is developed in order to deal with heterogeneous fleet of vehicles.
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lnternational Journal of Logistics and SCM Systems
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[image:9.612.140.583.13.767.2]"TJi:*i" "Til:ji,1"
Figure 1: Solution Representation SR-1
r-t
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Vehicle I Vehicle I
Orientation Radius
Figure 2:
Two solution representations had 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 representation SR-2 is using 3m dimensions.
In brief, both representation SR-l and SR-2 are using real number in each dimension. In the representation SR-1, the first r dimensions represent priorities of customers and the other 2m dimensions represent the orientation point of vehicles (Figure l). While in the representation SR-2, 2nt dimensions represent the 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 representation SR-1, the decoding method starts with 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 based on 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 constructed based 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
Vehicle ni Orientation
Solution Representation SR-2
V e h i c l e n r R a d i u s
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 maintained. Finally, the local improvetlent procedures are re-applied to all ofthe routes.
It is noted that the differences among VRP variants are in the problem constraints. Therefore, both representations SR-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 Preprocessing Vehicle 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 * = { \ + c r
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For solution representation SR-1, overall results
International Journal of Logistics and SCM Systems
cornputational time for all problems is less than 74 seconds for 50 particles and less than 172 seconds for 100 particles. It is evident also that the solution quality with 100 particles is insignificantly better than from the solution with 50 particles.
Result for solution representation SR-2 is better than solution representation SR-l result, in which the results are very close to the best known solution. For all instances, the average percentage deviation is less
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3: Result ot PSO Alsonthm wrth Solutron ntation SR- br HVRP Instance
Obiective Function
Comp Time (s) Average Average
V"Dev
Standard
Deviation Minimum
Minimum V"Dev 50 narticles
1 3 t 7 4 3 . 1 6 14.84% 3 7 . 1 8 t 6 9 4 . 1 7 fi.62% 3 6
t 4 661.32 8 . 8 s % 17.25 640.90 5.49% z )
1 5 0 7 2 . 1 3 s.60% 1 5 . 1 6 1 0 5 4 . 1 3 3.83o/o 2 5
t 6 200.69 4.870/0 2 1 . 1 9 n70.82 2.26% 24
t 7 1 4 872 8 . l 1 Y o lt.29 1 1 2 7 . 6 6 6.19% 48
l 8 988.60 9.0s% 2 9 . 1 6 t937.73 6.26% 5 9
t 9 203.62 7 . 7 1 % 9 . 5 9 I 1 9 1 . 0 4 658% 74
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1 3 t744.84 l4.96Yo 4 4 . 3 1 t660.20 9.38Yo 9 1
t 4 6 6 1 . 5 3 8.89% 1 5 . 1 0 641.9r 5.66% 5 9
1 5 1067.03 5 . l 0 Y o 13.34 045.53 2.9804 63
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r9
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able 4: Result ot PSO Algonthm wrth Solutron Representatlon SR-z tor HVRf Instance
Obiective Function
Comp Time (s) Average Average
"hDev
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Minimum YoDev 50 particles
l 3 1 5 9 3 . 1 7 4.96% 16.22 1 5 7 8 . 9 1 4.02% 48
t 4 614.66 l . l 1 Y o 4 . 1 4 609.17 0.27% 2 8
1 5 0 3 1 . 0 6
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t 7 086.82 2.34% 12.60 1066.44 0.42% 70
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1 6 r152.84 0.69% 3.82 l 1 4 8 . 4 1 030% 66
t 7 1 0 7 8 . 1 8 1 5 3 % 7.83 1069.52 0.71% 143
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are as follow: the average percentage deviation is less than l5o/o, standard deviation is less than 45, and the
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lnternational Journal of Logistics and SCM Systems
