organiser - rp2u.unsyiah.ac.id

Proceedings of the 6th IMT-GT Conference onMathematics, Statistics and Its Applications

(ICMSA2010)

3 — 4 November 2010

Grand Seasons Hotel,Kuala Lumpur, Malaysia

Organiser

With support from:Universiti Tunku Abdul Rahman

With support from:

Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)

Progress in the mathematical sciences within the IMT-GT (Indonesia-Malaysia-Thailand Growth Triangle) region will benefit greatly from regular meetings and interactions amongst mathematicians, statisticians and scientists in the region. The main objective of this conference is to provide a forum for researchers, educators, students and industries to exchange ideas, to communicate and discuss research findings and new advances in mathematics. To explore possible avenues to foster academic and student exchange, as well as scientific activities within the region. ISBN 978-983-41743-3-0 [Proceedings of ICMSA2010 in one pdf file]

Content :

Message from UTAR President•Message from FES Dean•Message from the Chair•Biodata of Invited Speakers •Keynote and Invited Talks•Contributed Talks•

Pure Mathematics / Combinatorics

◦

Statistics / Miscellaneous◦Applied Mathematics◦

Poster Contributions•Organising Committee•Acknowledgement•

Organiser:

Sponsors:

i

Contents

Message from UTAR President . . . . . . . . . . . . . . . . . . . . . . . 1

Message from FES Dean . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Message from the Chair . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Keynote Lectures and Invited Talks . . . . . . . . . . . . . . . . . . . 4

Biodata of Invited Speakers . . . . . . . . . . . . . . . . . . . . . . . . . 4

Keynote Lecture : Wavelets, Multiwavelets and Wavelet Frames for PeriodicFunctionsSay Song Goh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Keynote Lecture : Data Depth for New Nonparametric Inference Schemesand Beyond (Abstract Only)Regina Y. Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Keynote Lecture : Stochastic Mixed Integer Nonlinear Programming (Ab-stract Only)Herman Mawengkang . . . . . . . . . . . . . . . . . . . . . . . . 23

Keynote Lecture: Contemporary Statistical Data VisualizationJunji Nakano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Keynote Lecture: Insurance Risk Models: With and Without Dividends(Abstract Only)Hailiang Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Invited Talk: Some One-sided Multivariate TestsSamruam Chongcharoen . . . . . . . . . . . . . . . . . . . . . . . 48

Invited Talk: On Dynamical Systems and Phase Transitions forQ+ 1-statep-adic Potts Model on the Cayley TreeFarrukh Mukhamedov . . . . . . . . . . . . . . . . . . . . . . . . . 68

Invited Talk: Quartic-Normal Distributions (Abstract Only)Ah Hin Pooi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Invited Talk: Research Collaboration Network Analysis of the Journal ofFinance (Abstract Only)Kurunathan Ratnavelu . . . . . . . . . . . . . . . . . . . . . . . . 83

CONTENTS ii

Invited Talk: The Ultimate Solution Approach to Intractable ProblemsAbdellah Salhi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Contributed Talks : Pure Mathematics / Combinatorics / Algebra /Analysis / Graph Theory . . . . . . . . . . . . . . . . . . . . . . 94

Minimal Realization of BL-General Fuzzy AutomataKhadijeh Abolpour and Mohammad Mehdi Zahedi . . . . . . . . . 94

Comparative Study of Geometric Product and Mixed ProductMd. Shah Alam and Sabar Bauk . . . . . . . . . . . . . . . . . . . 110

On Chromatic Uniqueness and Equivalence ofK4-Homeomorphic GraphsSabina Catada-Ghimire and Roslan Hasni . . . . . . . . . . . . . 115

Constructions of Non-commutative Generalized Latin Squares of Order 5H. V. Chen, A. Y. M. Chin, and Shereen Sharmini . . . . . . . . . . 120

Spectral Corrections for a Class of Eigenvalue ProblemsMohamed K. El Daou . . . . . . . . . . . . . . . . . . . . . . . . 131

On Special Solvents of Some Nonlinear Matrix EquationsYin-huan Han and Hyun-min Kim . . . . . . . . . . . . . . . . . . 144

n-fold Commutative Hyper K-idealsMona Pirasghari, Parvaneh Babari and Mohammad Mahdi Zahedi 150

On ξs-quadratic Stochastic Operators in 2-dimensional SimplexFarrukh Mukhamedov and Afifah Hanum Mohd Jamal . . . . . . . 159

Single Polygon Counting form Fixed Nodes over Cayley Tree of Order TwoChin Hee Pah and Mansoor Saburov . . . . . . . . . . . . . . . . 173

n-fold Positive Implicative Hyper K-idealsParvaneh Babari, Mona Pirasghari and Mohammad Mahdi Zahedi 186

On *µ-closed Fuzzy Sets, Fuzzy *µ-closed Maps, Fuzzy *µ-irresoluteMaps and *µ-homeomorphism Mappings in Fuzzy Topological SpacesSadanand N. Patil . . . . . . . . . . . . . . . . . . . . . . . . . . 201

On Fuzzy gµ-closed Maps, Fuzzy gµ-continuous Maps and Fuzzy gµ-irresolute Mappings in Fuzzy Topological SpacesSadanand N. Patil, A. S. Madabhavi, S. R. Sadugol and G. R. S. B.Madagi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

On Graph-(super)magic Labelings of a Path-amalgamation of IsomorphicGraphsA.N.M. Salman and T.K. Maryati . . . . . . . . . . . . . . . . . . 228

A Survey on Equations in Group RingTai Wei Hang and Denis Wong Chee Keong . . . . . . . . . . . . . 234

Groups with Small Conjugacy ClassesYean Nee Tan, Guan Aun How and Miin Huey Ang . . . . . . . . . 244

CONTENTS iii

An Explicit Basis on Riemann-Roch Space of Elliptic Function FieldsYean Nee Tan, Ti-Chung Lee and Miin Huey Ang . . . . . . . . . . 252

δθg-closed Fuzzy Sets and its ApplicationsA. H. Zakari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Contributed Talks : Statistics / Applied Statistics / Financial Mathe-matics / Operations Research . . . . . . . . . . . . . . . . . . . 280

Adaptive Blind Random SearchMaria Eda B. Arado, Emily Amor A. Balase and Roberto N. Padua 280

Configuration Change Test for Serial Contingency TablesEmily Amor A. Balase and Roberto N. Padua . . . . . . . . . . . . 295

Optimization of Dynamic Characteristics using Genetic AlgorithmsNicolo Belavendram . . . . . . . . . . . . . . . . . . . . . . . . . 306

Optimization of Dynamic Characteristics with Variable Objective FunctionsNicolo Belavendram . . . . . . . . . . . . . . . . . . . . . . . . . 317

Fuzzy Superfluous SubmoduleD. K. Basnet, N. K. Sarma and L. B. Singh . . . . . . . . . . . . . 330

Measuring Online Bank Profit Efficiency: A stochastic frontier analysisMd. Azizul Baten and Anton Abdulbasah Kamil . . . . . . . . . . . 336

SIR Epidemic Model with Varrying Total Population SizeDumrongpokaphan T., Kaewkheaw T., and Ouncharoen R. . . . . . 351

Comparing Models for Fitting Zero-inflated DataManad Khamkong . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Selecting among Families of Lifetime DistributionsPrasong Kitidamrongsuk and Pachitjanut Siripanich . . . . . . . . 367

Optimal Approach of Many Linear Objects to OneAtamurat Kuchkarov, Gafurjan Ibragimov and Marzieh Khakestari 377

A Simple Crank Nicolson Scheme for Asian OptionTse Yueng Lee and Seong Tah Chin . . . . . . . . . . . . . . . . . 381

Recent Advancements of Nurse Scheduling Models and a Potential PathHuai Tein Lim and Razamin Ramli . . . . . . . . . . . . . . . . . . 395

The Mean Difference between Two Populations for Bernoulli and NormalCovariate DistributionsMarzuki Abubakar . . . . . . . . . . . . . . . . . . . . . . . . . . 410

Maximum Likelihood Estimation of Parameters in Tobit-Piecewise RegressionModelTitirut Mekbunditkul and Pachitjanut Siripanich . . . . . . . . . . 418

Re-weighted Robust Control Charts for Individual ObservationsMandana Mohammadi, Habshah Midi and Jayanthi Arasan . . . . 426

CONTENTS iv

The Relationships of Real Estates and Stock Markets in AsiaAbdul Halim B Mohd Nawawi, Nurul Nisa’ Khairol Azmi and FuteriJazeilya Md Fadzil . . . . . . . . . . . . . . . . . . . . . . . . . . 436

Exchange Rates: A Comparison with Robust Regression ApproachL. Muhammad Safiih and D.A Anthea . . . . . . . . . . . . . . . . 449

Linear Programming for Parking Slot Optimization: A Case Study at Jl.T. Panglima Polem Banda AcehSaid Munzir, Mahyus Ikhsan and Zainal Amin . . . . . . . . . . . . 462

Estimation of Population Mean in Two Phase Sampling using AttributeAuxiliary InformationNadeem Shafique Butt and Muhammad Qaiser Shahbaz . . . . . . 473

A Comparative Study of Maximum Likelihood and Bayesian EstimationApproaches in Estimating Frailty Mixture Survival Model ParametersOh Yit Leng and Zarina Mohd Khalid . . . . . . . . . . . . . . . . 478

A Bound on the Thrifty Policy for Non-Preemptive Processing of Jobswith Increasing CostKatrina Gabrielle Padua and Marrick Neri . . . . . . . . . . . . . 493

Comparative Performance of Two Parametric Families of Universal PortfoliosSook Theng Pang and Choon Peng Tan . . . . . . . . . . . . . . . 503

Multiple Correspondence Analysis on Public Service in Sabang Tourism AreaEvi Ramadhani, Devi Susanti, Asep Rusyana and Nazaruddin . . . 515

A Proposed Model of a Microcredit Institution: Break-Even Analysis,Borrowing Group Creditworthiness and Risk AnalysisDebalina Roy and Koushik Ghosh . . . . . . . . . . . . . . . . . . 524

Linear Programming and Sensitivity Analysis for Optimizing NutrientSufficiencyAsep Rusyana, Dewi Susanti, Evi Ramadhani and Nazaruddin . . . 537

A Game Theory Framework for ClusteringAbdellah Salhi, Berthold Lausen, Fajriyah Rohmatul, Marwa Baeshen,and Ozgun Toreyen . . . . . . . . . . . . . . . . . . . . . . . . . . 552

Comparison Traditional and Model Assisted Estimators in Inverse Sam-pling with ReplacementSureeporn Sungsuwan and Prachoom Suwattee . . . . . . . . . . . 565

Performance of the Helmbold Universal Portfolio to the Initial StartingPortfolioChoon Peng Tan and Wei Xiang Lim . . . . . . . . . . . . . . . . . 577

Categorical Data Analysis on Labor Force Data in MalaysiaSin Yin Tan, Yue Fang Loh, Aminah Bte Ahmad and NithyaroobiniA/P Munian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

CONTENTS v

Can The Effects of Using All Suitable Lags of an Instrument Comparableto that of an Additional Basic Instrument In Instrumental VariableRegresssion Analysis of Heteroskedastic Linear Models?Chee Yin Yip, Hock Eam Lim, Pei Yee Hong and Seng Joe Yip . . . . 598

Revisit Problems Encountered in Linear Regression ModelsChee Yin Yip and Hock Eam Lim . . . . . . . . . . . . . . . . . . . 609

Survey of Notebook in Tertiary Education using Confounded FactorialCCE MethodChin Khian Yong and How Hui Liew . . . . . . . . . . . . . . . . . 620

Parameter Estimation of the SIR Model using the Multistage AdomianDecomposition Method (MADM)Nuraini Yusoff, Harun Budin and Salemah Ismail . . . . . . . . . . 635

A Stationarity Test on Markov Chain Models based on Marginal DistributionMahboobeh Zangeneh Sirdari, M. Ataharul Islam, and NorhashidahAwang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

Contributed Talks : Applied Mathematics / Image Processing / Com-puter Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

Embedding using Spread Spectrum Image Steganography with GF (2m)

Suhaila Abd Halim and Muhammad Faiz Abdullah Sani . . . . . . 659

A Novel Double Stage Dynamic Time Warping Algorithm for ImageTemplate MatchingSomya Adwan and Hamzah Arof . . . . . . . . . . . . . . . . . . . 667

Integer Programming Model for Operational Aircraft Maintenance Rout-ing Problem with Side ConstraintsSuaibatul Aslamiah, Siti R.Simamora, Tan Kim Hek, Novin M.Sarina,Edi L.Harahap, Malem Karina . . . . . . . . . . . . . . . . . . . . 677

Stochastic Programming Model for Production Planning of Fish Pro-cessed ProductsAna Uzla Batubara, Eri Saputra, Herman Mawengkang . . . . . . 690

The Shortest Path between Two Points on some Surfaces by using theApplication of Euler EquationNathaphon Boonnam and Pakkinee Chitsakul . . . . . . . . . . . . 704

Solving Nonlinear Algebraic Equation by Homotopy Analysis MethodChin Fung Yuen, Lem Kong Hoong and Chong Fook Seng . . . . . 712

An Alternative Homotopy Analysis Method in Solving Differential Equa-tion under Finite Order of DeformationChong Fook Seng, Lem Kong Hoong and Chin Fung Yuen . . . . . 721

A Modified Algorithm For The Homotopy Perturbation Method WithApplications To Lotka-Volterra SystemsM. S. H. Chowdhury, T. H. Hassan and A. F. Ismail . . . . . . . . . 731

CONTENTS vi

Numerical Solution of Nonlinear Fredholm-Volterra Integro-differentialEquations using Legendre WaveletsM. Dadkhah, M. Tavassoli Kajani and S. Mahdavi . . . . . . . . . 738

Development of Labor Force Condition in Solow Economic GrowthModelOpen Darnius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745

Generalized Space-Time Autoregressive ModelingDhoriva Urwatul Wutsqa, Suhartono and Brodjol Sutijo . . . . . . 752

Scenario-based Approach for Ranking DMUs in Stochastic DEA ModelSyahril Effendi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762

The Implementation of the Stochastic Progamming model for River Wa-ter Quality ManagementAdelina Harahap, Muda M.Ginting, Sopar Siregar, Muhammad NurEddy, Lesman Tarigan, Herman Mawengkang . . . . . . . . . . . . 772

An Optimization Model for Water Resources Management under Uncer-taintyIndriyani, Tohom P. Banjarnahor, Nelson Nababan,Yusleni, AturH.Samosir, Herman Mawengkang . . . . . . . . . . . . . . . . . . 786

Effective Neurospora Process Model on Light and FRQ ProteinKanchana Kumnungkit and Sarawut Suwannaut . . . . . . . . . . 796

Neurospora Biorhythm Mathematical Model with Light-Dark CycleKanchana Kumnungkit and Nipon Wongvisetsirikul . . . . . . . . 809

Variational Iteration Method for Euler Differential EquationWuryansari Muharini Kusumawinahyu . . . . . . . . . . . . . . . 822

An Optimization Model for Sustainable Forest Management to PreserveWater Allocation for Hydroelectric Power PlantErna Laily, Gevoner Harianjak, Nilawati, R.Harahap, Bistok Purba,Herman Mawengkang . . . . . . . . . . . . . . . . . . . . . . . . 834

A Numerical Study of Ships Rolling MotionHow Hui Liew and Yean Fong Pan . . . . . . . . . . . . . . . . . . 843

Exit Selection by Occupant During Building Evacuation using NeuralNetworkEng Aik Lim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852

Mathematical Model for Analyzing the Value of Cooperational Leader-ship Based on Multi Agent SystemAbil Mansyur, Elmanani Simamora . . . . . . . . . . . . . . . . . 865

Solving Systems of Nonlinear Equations Based on Constrained SearchApproachMardiningsih . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 886

CONTENTS vii

A Goal Programming Model for the Recycling Supply Chain ProblemPutri K.Nasution,Rima Aprilia,Amalia,Herman Mawengkang . . . 903

An Active Set Method with Central Measure on Removing Impulse NoiseMarrick Neri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917

Inner Solution for Oscillatory Free Convection about a Sphere Embeddedin a Porous MediumLai Zhe Phooi, Rozaini Roslan, Ishak Hashim, and Zainodin HajiJubok . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926

The use of Adomian Decomposition Method for Solving GeneralisedRiccati Differential EquationsT.R. Ramesh Rao . . . . . . . . . . . . . . . . . . . . . . . . . . . 935

Subclasses Discriminant Analysis by Fuzzy Cluster AlgorithmGhasem Rekabdar, Naser Haddadzadeh and Davood Seifipoor . . . 942

A Multi-stage Stochastic Optimization Model for Water Resources Man-agementElly Rosmaini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 951

Stochastic Programming Model for Land Management ProblemsSiti Rusdiana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 962

Predator-prey Model in a Bioreactor with Death CoefficientZubaidah Sadikin and Normah Salim . . . . . . . . . . . . . . . . 973

Recommending a Hybrid Method for Solving the Ordered CrossoverProblemBahador Saket and Farnaz Behrang . . . . . . . . . . . . . . . . . 984

Solving Integer Goal Programming Problems Based on a Reference Di-rection AlgorithmSawaluddin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000

Integer Programming Model for Supply Chain with Market SelectionSelamat Siregar, Agusman, Sindak Situmorang, Lisbet Marbun, Ab-dul Jalil, Herman Mawengkang . . . . . . . . . . . . . . . . . . . 1012

Automatic Gridding for DNA Microarray Image using Image ProjectionProfileJoko Siswantoro . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028

Efficient Reduction of Fuzzy Finite Tree AutomataSomaye Moghari, Mohammad Mehdi Zahedi and Reza Ameri . . . 1034

Minimization of Fuzzy Finite Tree AutomataSomaye Moghari, Mohammad Mehdi Zahedi and Reza Ameri . . . 1044

An Improved Strategy for Solving Quadratic Assignment ProblemsSusiana, Nunik Ardiana, Wahab Y.S.Hasibuan, Herman Mawengkang1053

CONTENTS viii

An Optimization Model for Multi-echelon Supply Chain Planning withReliability ConsiderationSuyanto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1061

An Algorithm Based on Direct Search Approach for Solving Mixed-Integer Nonlinear Programming ProblemsAstri Syafrianty, Nenna I.Syahputri, Meilinda Siahaan, Herman Mawengkang1082

Dynamic Properties of an Aggregate Econometric Model of IndonesiasEconomyIntan Syahrini . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1092

A Direct Search Algorithm for Solving the Multi-period Single-sourcingProblemMiduk Tampubolon, Vita Damayanti, Herman Mawengkang . . . . 1101

An Optimization Model for Cargo Container Loading Problems underUncertaintyDavidson Tarigan,Nurelista Dahyaruci,Rusli Tarigan, Herman Mawengkang1116

Comparisons of Effects for Reducing Geosmin Tainted Off-Flavor andPhysical Qualities in Frozen Thai Panga (Pangasius sp.) Fish FilletsPiyavit Thipbharos . . . . . . . . . . . . . . . . . . . . . . . . . . 1135

A Mixed Integer Nonlinear Stochastic Programming Model in Tacklinga Superstructure Synthesis Water Networks Optimization Problemwith Uncertainty ParameterEriek M.L.Tobing, Eva Y.Siregar, Mizan, Herman Mawengkang . . 1145

Optimal Control for SEIR Rabies Model between Dogs and Human withVaccination Effect in dogsEti Dwi Wiraningsih, Widodo, Lina Aryati, Syamsuddin Toaha andSuzanne Lenhart . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161

A Solitary-like Wave Generated by Flow Passing a BumpLeo Wiryanto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176

Titles of Poster Presentations . . . . . . . . . . . . . . . . . . . . . . . 1185

Organising Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186

Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187

Message from UTAR President

On behalf of Universiti Tunku Abdul Rahman (UTAR), I would like to extend my warmest

welcome to all participants to the International Conference on Mathematics, Statistics and Its

Applications (ICMSA 2010).

Aptly known as mother of all sciences, Mathematics has long been recognised as the prime

mover in the development of sciences and technologies. Statistics, a branch of Mathematics

which emerged at a later stage, has since been gaining attention from researchers in diverse

fields who seek its practicality. The advancement in computer technology has further

strengthened the functionality of Statistics, causing it to gain even wider acceptance across

multiple disciplines.

As the number of users of Mathematics and Statistics, especially those in the academic

community, grows, it is essential that a platform is available for these enthusiasts to congregate

to exchange ideas and explore together to extend the knowledge frontiers. I believe it was for

this purpose that ICMSA was started. And I am elated to say that UTAR, through its Centre for

Mathematical Sciences, has been given the opportunity and trust to host the Sixth ICMSA this

year.

The Centre for Mathematical Sciences is an interdisciplinary research centre where faculty

members and experts from different fields meet to pursue research in mathematical and

statistical sciences. It is indeed encouraging to note that this newly established research centre

has taken on the ambitious initiative of hosting such an international conference.

It is heartening to know that although originally started for the Indonesia-Malaysia-Thailand

Growth Triangle (IMT-GT), ICMSA has attracted participants beyond this region who include

those from Arab Saudi, India, Iran, Korea, Pakistan, the Philippines and the UK. The keynote

and invited speakers come from China, Indonesia, Japan, Malaysia, Singapore, Thailand, UK

and USA. It is also heartening to know that many papers received have skilfully integrated the

knowledge from different fields, while others have made intelligent use of computing

techniques in the particular disciplines. I am certain that this conference will achieve its goal

of serving as an effective platform for the participants and speakers to exchange ideas, network

and foster stronger ties among themselves.

Lastly, I would like to thank the Organising Committee for their hard work in making this

event successful. To all participants, I wish you to have fruitful interactions with your peers,

and to our foreign friends, an enjoyable stay in Malaysia too.

Thank you.

Sincerely yours,

_______________________

Ir. Professor Dato' Dr. Chuah Hean Teik

President, Universiti Tunku Abdul Rahman

Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010)Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia 1

Message from FES Dean

On behalf of the Faculty of Engineering and Science (FES), Universiti Tunku Abdul Rahman

(UTAR), I welcome all participants to the International Conference on Mathematics,

Statistics and Its Applications (ICMSA2010).

The faculty is honoured to host this distinguished and meaningful event. This conference

signifies yet another achievement by the Centre of Mathematical Sciences, UTAR in bringing

together scholars from all over the world to promote scholastic work. It is also in line with the

University’s commitment to the advancement of knowledge through pursuing scientific

discoveries and technological innovation.

Mathematics is a perfect integration of pragmatism and aesthetics. As a user of Mathematics,

I am grateful that mathematicians, including statisticians, have been producing countless

beautifully simple solutions to complex problems that play a vital role in Engineering and

Science. It is explicitly clear that Mathematics and Statistics have changed our world.

Advancement in Science and Technology can be mainly attributed to the collaborative

development and selfless sharing of knowledge and expertise among scholars. This is

particularly true in this rapid changing world. We hope that participants will exploit the great

opportunity provided by this conference to link with some of the world’s best brains and

establish collaborative ties. We also hope that it will spur inspirations for more innovative

ideas.

The response for the conference has been overwhelming. We are glad to receive submissions

from 19 countries all over the world. The response reflects that Mathematics and Statistics

continue to be the hot topics in research. Among the participants, there are not only

traditional mathematicians and statisticians but also researchers from emerging areas such as

Bioinformatics, Financial Mathematics, Data-mining and others. I am excited to witness such

development in the research scene.

Finally, I would like to thank the ICMSA2010 Organising Committee members for their

passion and dedication in ensuring this international conference a success. I am certain the

outcomes of the conference will be promising and pleasing.

Yours sincerely,

________________________

Associate Professor Dr. Ng Teong Kuen @ Wang Chan Chin

Dean, Faculty of Engineering and Science, UTAR


Message from the ICMSA2010 Chair

A very warm welcome to all the participants of the Sixth Indonesia-Malaysia-Thailand

Growth Triangle (IMT-GT) International Conference on Mathematics, Statistics and Its

Applications ICMSA2010.

The Centre of Mathematical Sciences, Universiti Tunku Abdul Rahman is honoured to

organise this meaningful annual event. One of the main aims of the ICMSA2010 is to bring

closer together mathematicians and statisticians around the world to share knowledge and

exchange new ideas in Mathematics. With this in mind, I wish all participants to have fruitful

and enjoyable discussions during the two-day conference.

The use of computer has fundamentally changed the landscape of research in Mathematics

and Statistics. Mathematical modelling, computational simulations, numerical algorithms,

computer algebra systems and easily accessible mathematical software and visualisation

software have made impacts on the ways that researchers analyse and solve complex

problems in Science and Engineering. Internet, emails and electronic journals have enabled

researchers to communicate faster and work closer together than ever before.

With the aid of modern computers, researchers’ expectations on the quality of research

questions and outcomes are getting more demanding. Gone are the days when a

mathematician could work solo in a closed office using pencil and paper to solve relatively

simple problems. A recognised effort in mathematical research today is expected to be

ambitious in pushing the knowledge frontier or solving real-world problems. Modelling real-

world problems now requires truly interdisciplinary collaborations among mathematicians,

computer scientists, and researchers in different scientific and engineering fields. Thus, it is

importance to provide more platforms for mathematicians, scientists and engineers to

interact. We hope that ICMSA2010 would continue to be an active forum for academia and

industry to discuss and exchange their ideas.

I would also like to thank the ICMSA2010 International Scientific Committee for their

guidance, and keynote and invited speakers for spending time and sharing with us the future

trends of interdisciplinary research in Mathematics. Last but not least, we would like to

express our appreciation to the reviewers for their supportive response and diligence that

have made the publication of the conference proceedings possible.

Yours sincerely,

_____________________

Assistant Professor Dr. Goh Yong Kheng

Chair, Organising Committee of ICMSA2010, UTAR


KEYNOTE / INVITED SPEAKERS

Prof. Junji NakanoChairperson-elect, International Association for Statistical Computing (Asian Regional Section)Professor, Department of Data ScienceDirector, Center for Engineering and Technical Supportlnstitute of Statistical Mathematics, JAPANhttp://jasp.ism.ac.jp/~nakanoj/Research interest: Computational Statistics, Time Series Analysis

Prof. Regina Y. LiuProfessor and Chair, Department of Statistics and BiostatisticsRutgers University, New Jersey, USFellow of ASA, IMSEditor: J. of Multivariate AnalysisAssociate Editor: Annals of Statistics, JASA, TEST - J. of Spanish Soc. of Statistics and O.R.http://www.stat.rutgers.edu/people/faculty/liu.htmlResearch interest: Data Quality, Text Mining, Nonparametric Inferences, Resampling, Applications of Data Depth, Aviation Safety Analysis

Prof. Herman MawengkangProfessor, Departemen MatematikaUniversitas Sumatera Utara, INDONESIAResearch interest: Optimisation, Financial Mathematics

Prof. Hailiang YangProfessor, Department of Statistics and Actuarial ScienceThe University of Hong Kong, Hong Kong SAR, CHINAAssociate of the Society of Actuarieshttp://www3.hku.hk/statistics/staff/hlyang/Research interest: Actuarial Science, Mathematical Finance

Dr. Say Song GohAssociate Professor, Department of MathematicsNational University of Singapore, SINGAPOREhttp://www.math.nus.edu.sg/~matgohss/Research interest: Wavelets, Approximation Theory, Complex Analysis and Harmonic Analysis


Dr. Farrukh MukhamedovAssociate Profrosser, Department of Computational and Theoretical SciencesInternational Islamic University Malaysia, MALAYSIAResearch interest: Pure Mathematics, Operator Theory

Dr. Samruam ChongcharoenAssociate Profrosser, Department of StatisticsNational Institute of Development Administration (NIDA), THAILANDResearch interest: Order Restricted Statistical Inference, Statistical Modeling

Dr. Abdel SalhiSenior Lecturer, Department of Mathematical ScienceUniversity of Essex, United KingdomResearch interest: Optimisation; Mathematical Programming and Heuristics; Numerical Analysis; Evolutionary Computing; Scheduling; MCDM; Parallel Processing; OR techniques applied to databases; Data Mining; Bioinformatics.

Prof. Kurunathan RatnaveluProfessor, Institute of Mathematical SciencesDeputy Vice-Chancellor (Development)University of Malaya, 50603 Kuala Lumpur, MALAYSIAResearch interest: positron-hydrogen atom scattering, hydrogenic-type atoms.

Prof. Ah Hin PooiSenior Research Fellow, Institute of Mathematical SciencesUniversity of Malaya, 50603 Kuala Lumpur, MALAYSIAResearch interest: statistics


Linear Programming for Parking Slot

Optimization: A Case Study at Jl. T. Panglima

Polem Banda Aceh

Said Munzir1 , Mahyus Ikhsan

1 and Zainal Amin

1

1 Mathematics Department, Faculty of Sciences, Syiah Kuala University, Banda Aceh,

Indonesia [email protected]

home page: http://www.math-usk.org/smunzir/

Abstract. This research investigate the optimization of the available parking

area, based on parking requirement analysis and the identification of existing

parking problem. The study is expected to provide information to reduce traffic

delay due to on-street parking. It is related to the need of parking area while off-

street parking area is not available. For a case study, the street of Panglima

Polem in Banda Aceh is chosen as it is located in the city central of Banda Aceh.

The model use linear programming supported by observation and survey data to

formulate optimization problem. The study has formulated a well-posed problem

for parking slot optimization based on the user needs, interpreted as parking slot

proportional to parking accumulation and duration.

Keywords: parking slot optimization, linear programming

1. Introduction Transportation plays an important and strategic role in the development of a

nation, particularly in distributing the product of the development for all

citizens. General problems that occur in urban transportation is the traffic jam.

One of the sources of the traffic jam is the decreases of road diameter due to

the use of the part of the road for on-street parking. This traffic jam has a

massive effect if it is considered comprehensively. One of this effects is, for

instance, the excessive use of fuels which cause a large amount of economic

losses. Hence, the effort to reduce the traffic jam is necessary, one of which is

the management of on-street parking problem.

The traffic flow problem due to on-street parking is an extremely serious

problem. Several researches has been conducted in relation to this particular

problem, such as works of Sinaga [10] and Setiawan [8]. The analysis of

parking demand based on characteristic of parking sites has been conducted by

Yosritzal [11] and Widanengsih [12]. In addition, they also suggested that

regression method can also be used to determine the standard of parking slot

demand around a hospital.


The parking management problems were also studied using transportation

management science as performed by Rapp [6]. Cannon [2] develop a

simulation program to handle the parking problem. On the other hand, model

using research operation employing linear programming is also utilized by

researchers such as Bruglieri [1], Cordone [3] dan Silva [9]. For long term

desain Djakfar [4] suggested a method using criteria analysis.

From a series of previous researches related to the parking problem

management, we cannot find a research related to parking slot allocation using

linear programming. The demand of parking slot is impossible to be fullfiled

entirely especially if the strategy is to use the on-street parking, as the space is

usually allocated for traffic flow.

In reality, the problem that usually emerge in relation to on-street parking is to

determine the best parking slot allocation to distribute among different types of

vehicle on limited parking space. In this study, we focus on building a

mathematical model describing the problem and try to allocate optimal parking

slot proportional to each type of vehicle using linear programming.

Peunayong area located in Banda Aceh is a center for bussiness activity in the

city. The problem occurred in the road around the area is a heavily massive

traffic activity, such as in the road segment of Jalan T. Panglima Polem. From

simple observation, obvious sources of low road performance in this area is the

on-street parking along the road and intersections. This on-street parking

decreases road capacity and increase road side obstacle. This problem is the

result of insufficient parking space available in the area.

2. Literature Review

Parking is defined as terminating a vehicle at a certain location and is a part of

traffic circulation. Based on its location, the parking is classified into two

categories, i.e.: on street parking and off street parking (Widanengsih dan

Elkhasnet [12]).

Parking Control Unit (PCU) is the parking space used for a vehicle, which

depend on vehicle dimension plus additional space needed for a vehicle to

maneuvre whose value depending on the parking angle. PCU of each vehicle

can be obtained in the Table 2.1.


Table 2.1 PCU of each type of vehicle

No Jenis Kendaraan Width

(meter)

Parking

Width

(meter)

Length

(meter)

Parking Length

(meter)

1 Becak 1 1,5 2,2 2,7

2 Motorcycle 0,8 1,3 1,9 2,4

3 Passenger Car 1,5 2,5 4,1 5,1

4 Medium Bus 2,1 3,1 6,0 7,0

5 Big Bus 3,5 4,5 9,3 10,3

6 Truck 2,4 3,4 7,2 8,2

7 Small Bus 1,6 2,6 4,1 5,1

Parking characteristics are parameters related to the amount of parking demand

that have to be provided. According to Hobbs [5], parking characteristics

includes:

a. Parking volume, i.e. number of vehicle entering a parking site.

b. Parking accumulation, number of vehicle parked at a parking site at a

certain time.

c. Parking index, i.e. percentage of the vehicle occupied the parking area.

d. Parking duration, i.e. time interval (in minute or hour) for a certain vehicle

parked at a parking site. Percentage amount of parking duration is

formulated as ratio between the amount of vehicle parked during certain

time interval and total number of vehicle observed.

e. Average parking duration, i.e. total number of vehicle parked during certain

time interval compared to vehicle enter parking site.

f. Parking exchanges, i.e. measurement of parking occupation calculated as

ratio between the number of vehicle parked compared to parking capacity

available.

g. Parking utilization level, computed from the ratio between average parking

and parking space capacity. Meanwhile, average parking is obtained from

the ratio between sum of parking accumulation for all observation time and

number of observation.

3. Research Method

Location of this survey is at Jln. T. Panglima Polem Peunayong Banda Aceh

and was conducted whole day beginning from 07.00 a.m. to 18.00 p.m..

Secondary supporting data and information for this research is obtained from

Dinas Perhubungan Provinsi Aceh. The method used to obtained parking space

geometric data and existing parking space capacity is through measuring the

parking space area and parking space allocation for each vehicle. Data

sampling for vehicle entering or leaving the parking site along with its parking


duration is obtained through a field survey walking along the parking site and

counting the number of vehicle and its parking duration. Data processing is

conducted using Microsoft Excel 2003 and QM for Windows 2.0.

In relation to data obtained from the field survey, model analysis to be

developed is conducted by including the user parking space demand

proporsional to average parking accumulation and average parking duration.

Proportionality of average parking accumulation is computed every 15 minutes

for each type of vehicle. This proportion for motor cycle, car and becak are

calculated using the following formulation:

( ),321

321

1xxx

ppp

p++

++

( ),2321

321

xxxppp

p++

++

( )321

321

3xxx

ppp

p++

++

where

1p : Average parking accumulation of motor cycle (number of vehicle/15

minutes)

2p : Average parking accumulation of car (number of vehicle/15 minutes)

3p : Average parking accumulation of motor becak (number of vehicle/15

minutes)

and

321 xxx ++ : Parking space capacity

Mean while, proportionality to average parking duration every 15 minutes for

motor cycle, car and becak are respectively formulated as:

( )321

321

1 xxxttt

t++

++,

( )321

321

2 xxxttt

t++

++,

( )321

321

3 xxxttt

t++

++

where

1t : Average parking duration for motor cycle (minute)

2t : Average parking duration for car (minute)

3t : Average parking duration for becak (minute)


The problem to solve is how to maximize parking space capacity at Jalan T.

Panglima Polem subject to available parking land, and the same time meet the

the demand of parking for each type of vehicle. The parking demand is based

on proportionality of average parking accumulation and average parking

duration.

The focus here is to allocate parking space for all three types of vehicle. Based

on parking space standard allocated for each type of vehicles by Dinas

Perhubungan Aceh, parking space for each vehicle in this study is sebagai

berikut:

a. Parking space for motor cycle is 3,12 m2.

b. Parking space for car is 12,75 m2.

c. Parking space for becak is 4,05 m2.

The structure of decision making for maximization of parking capacity can be

arranged as:

Tabel 3.1 The structure of decision making for maximization of parking capacity

No Coefficient of objective functions

activity Limitation

factor 321 xxx

321 ccc

1

2

3

4

5

6

7

Parking space area

Motor cycle parking accumulation

proporsional to all

Car parking accumulation proporsional to

all

Becak parking accumulation proporsional

to all

Proporsional waktu parkir rata-rata mobil

Proporsional waktu parkir rata-rata becak

motor 737271

636261

535251

434241

333231

232221

131211

aaa

aaa

aaa

aaa

aaa

aaa

aaa

7

6

5

4

3

2

1

b

b

b

b

b

b

b

≥

≥

≥

≥

≥

≥

≤

Proportion of vehicle average parking accumulation every 15 minutes for each

type of a vehicle is computed from the vehicle average parking accumulation

divided by total average parking accumulation for all vehicles and then

multiplied by parking space capacity. In mathematical model, it can be written

as:

1. Proportion of average parking accumulation for motor cycle is

( )321

321

1 xxxppp

p++

++


2. Proportion of average parking accumulation for car is

( )321

321

2 xxxppp

p++

++

3. Proportion of average parking accumulation for becak is

( )321

321

3 xxxppp

p++

++

Where 1p is motor cycle average parking accumulation (number of vehicles in

15 minutes), 2p is car average parking accumulation (number of vehicles in 15

minutes), 3p is becak average parking accumulation (number of vehicles in 15

minutes), while ( )321 xxx ++ is parking slot capacity to be allocated.

Proportion of vehicle average parking duration every 15 minutes for each type

of a vehicle is computed from the vehicle average parking duration divided by

total average parking duration for all vehicles and then multiplied by parking

space capacity. In mathematical model, it can be written as:

1. Proportion of average parking duration for motor cycle is

( )321

321

1 xxxttt

t++

++

2. Proportion of average parking duration for car is ( )321

321

2 xxxttt

t++

++

3. Proportion of average parking duration for becak is ( )321

321

3 xxxttt

t++

++

Where 1t is average parking duration for motor cycle (minutes), 2t is average

parking duration for car (minutes), and 3t is average parking duration for

becak (minutes).

3.1. Processing Model in Linear Programming

The problem of parking slot allocation at Jln T. Panglima Polem uses three

parts of linear programming model, i.e.:

Objective function:

321 xxxZ ++=

Subject to constraints:

areaspaceParkingxxx 05,475,1212,3 321 ≤++


1x ( ) α×++++

≥ 321

321

1 xxxppp

p

2x ( ) α×++++

≥ 321

321

2 xxxppp

p

3x ( ) α×++++

≥ 321

321

3 xxxppp

p

1x ( ) α×++++

≥ 321

321

1 xxxttt

t

2x ( ) α×++++

≥ 321

321

2 xxxttt

t

3x ( ) α×++++

≥ 321

321

3 xxxttt

t

And non-negativity constraints:

0,,,,,,, 32132,1321 ≥tttpppxxx

and 10 ≤≤ α

Table 4.1 Parking characteristics of Motorcycle, Car and Becak

Parking Characteristics Motor cycle Car Becak

Parking volume 1211 421 100

Parking capacity 147 16 9

Peak of parking accumulation:

- Time

- Jumlah Kendaraan (kendaraan)

14.30 – 14.45

p.m

135

11.30 – 11.45

a.m.

26

08.45 – 09.00

and

09.00–09.15

a.m

10

Parking index (%) 91.84 162,5 111.11

Parking duration:

- Parking duration of largest number of

vehicles (minutes)

- Percentage of the number of vehicle park

(%)

15

68.09

15

68.60

15

79.80

Average parking duration (minutes) 46,72 25,69 24,24

Parking exchanges 8.24 26.3 1.23

Parking utilization (occupation) (%) 67.18 106.875 51.67

After substitution of the values of 1p , 2p , 3p , 1t , 2t and 3t from field

survey into the model, the optimization problem can be written as:


Maximize

321 xxxZ ++=

Subject to constraints:

321 05,475,1212,3 xxx ++ ≤ 588

1x ≥ α×++ )(82,0 321 xxx

2x ≥ α×++ )(14,0 321 xxx

3x ≥ α×++ )(04,0 321 xxx

x ≥ α×++ )(48,0 321 xxx

2x ≥ α×++ )(27,0 321 xxx

3x ≥ α×++ )(25,0 321 xxx

Where 0,,, 321 ≥xxx

and 10 ≤≤ α .

4. Results and Discussions

The model was initially tested for values of α between 0.75 to 1 using QM

for Windows 2.0 to find optimal solution. However, no feasible solution was

found. This means that in trying to satisfy the average parking accumulation

and parking duration simultaneously for each vehicle at more than 75%

satisfaction, constraints cannot provide any feasible point in its interior.

Following up these results, more realistic scenarios for the optimization were

made, i.e.:

1. Optimization considering constraints only of average parking accumulation

with values of α from 0.75 up to 1.

2. Optimization considering constraints only of average parking duration with

values of α from 0.75 up to 1.

3. Optimization considering both constraints of average parking duration and

average parking accumulation with values of α from 0.5 up to 0.7.

4.1. Formulation Considering Parking Accumulation Only

Optimization considering constraints only of average parking accumulation

with values of α from 0.75 up to 1 was run using QM for Windows 2.0 with

the solution is shown in the Table 4.2.


Table 4.2 Solution for Optimization considering average parking accumulation only

Variable =α 0,75 =α 0,80 =α 0,85 =α 0,90 =α 0,95 =α 1

1x 121,6684 119,0373 115,8873 112,8731 109,8823 107,0182

2x 14,769 15,575 16,2817 16,966 17,6289 18,2714

3x 4,2197 4,45 4,6519 4,8474 5,0368 5,2204

Z 140,6571 139,0623 136,8209 134,6505 132,548 130,5101

From the solution in the Table 4.2, it shows that the higher the value of α (level of satisfaction) the smaller the parking slot obtained especially the

vehicle (motor cycle) having the highest accumulation in comparison to the

others.

4.2. Formulation Considering Parking Duration Only

Optimization considering constraints only of average parking duration with

values of α from 0.75 up to 1 was run using QM for Windows 2.0 with the

solution is shown in the Table 4.3.

Table 4.3 Solution for Optimization considering average parking duration only

Variable =α 0,75 =α 0,80 =α 0,85 =α 0,90 =α 0,95 =α 1

1x 68,3923 63,7555 59,3562 55,1768 51,2011 47,4146

2x 22,704 23,5808 24,4126 25,2029 25,9547 26,6707

3x 21,0222 21,8341 22,6043 23,3361 24,0321 24,6951

Z 112,1185 109,1703 106,3732 103,7158 101,1879 98,7804


vehicle (motor cycle) having the highest average parking duration in

comparison to the others. As average parking duration for all vehicle more

balance (the differences were not very extreme), the resulting parking slot

allocation also more balance between all three types of vehicle.


4.3 Formulation Considering Both Parking Accumulation and Parking

Duration

Optimization considering constraints for both average parking duration and

parking accumulation with values of α from 0.5 up to 0.7 was run using QM

for Windows 2.0 with the solution is shown in the Table 4.4.

Variable =α 0,5 =α 0,55 =α 0,60 =α 0,65 =α 0,70

1x 95,91958 89,74738 83,93796 78,46021 73,28654

2x 17,49884 18,66595 19,76446 20,80025 21,77855

3x 16,20263 17,28329 18,30043 19,25949 20,16532

Z 129,621 125,6966 122,0028 118,52 115,2304


vehicle (motor cycle) having the highest average parking accumulation and

parking duration in comparison to the others. In contrast, parking slots for both

Car and Becak increased with the increase of α (level of satisfaction).

Comparison of all three formulations suggests that the formulation considering

parking accumulation only is the best option if the total number of optimal

parking slot is used as a performance measurement. The formulation

considering average parking duration only is clearly less preferable as it give

the result of less number of parking slot and, in practice, it also usually does

not relate significantly with the customer satisfaction.

5. Conclusions

The results of this study suggest that the formulation of optimization for

parking slot allocation give significantly different results when the formulation

consider various aspects of parking requirements and demands. Trying to fulfill

all parking demands and requirements may lead to the optimization problem

without any feasible region in the optimization. The most important aspects

should come into the formulation before considering other aspects to see the

realistic optimal result for the problem.


References 1. Bruglieri Maurizio, Colorni Alberto, Lu´e Alessandro, “The Parking Warden Tour Problem”

Proceeding of CTW’09, pp. 11-15, (2009)

2. Cannon Stephen, Rehman Shakeb, Mendez Alberto, Vo Vincent, Ordoñez Maria Ana, and Singh

Amit, “Optimization of Resource Distribution in The George Mason University Parking System”

George Mason University Study Report, (2003).

3. Cordone Roberto, Ficarelli Federico and Righini Giovanni : Bounds and Solutions for Strategic,

Tactical and Operational Ambulance Location, a Dipartimento di Tecnologie dell’Informazione

Universit`a degli Studi di Milano”, Proceeding of CTW’09, pp 180-185, (2009).

4. Djakfar Ludfi, Indriastuti K. Amelia dan Wicaksono Achmad: Relokasi Pelataran Parkir Mobil

Barang Kota Kediri, Simposium VII FSTPT, Universitas Katolik Parahyangan, (2004).

5. Hobbs, F. D.,: Perencanaan dan Teknik Lalu Lintas, Cetakan I, Gajah Mada University Press,

Yogyakarta, (1995).

6. Rapp Matthias and Albrecht Christian : Capacity and Slot Management for Heavy Goods Vehicle

Traffic Across the Swiss Alps, Paper presented at the 10th World Congress on ITS, Madrid, (2003). 7. Renta Iskandar, Jinca M. Yamin and Parung Herman : Standar Kebutuhan Ruang Parkir pada

Rumah Sakit di Makasar, Simposium VII FSTPT, Universitas Katolik Parahyangan, (2004)

8. Setiawan Rudi : Penerapan Manjemen Transportasi Kampus Sebagai Upaya Mengurangi

Penggunaan Mobil (Studi Kasus : Universitas Kristen Petra), Simposium VII FSTPT, Universitas

Katolik Parahyangan, (2004).

9. Silva de Amal, “ Bus Driver Duty Optimization by Combining Constraint Programming and Linear

Programming”, ILOG (S) Pte Ltd. Singapore, (2000).

10. Sinaga Roberth and Priyanto Sigit : Penanganan Parkir Kendaraan pada Terminal dan Pasar (Studi

Kasus : Kawasan Condong, Sleman dan DIY), Simposium VII FSTPT, Universitas Katolik

Parahyangan, (2004).

11. Yosritzal, Gunawan H. and Justiawan A.A. : Analisis Perparkiran di Pasar Padang Raya, Simposium

VII FSTPT, Universitas Katolik Parahyangan, (2004).

12. Widanengsih and Elkhasnet: Karakteristik Parkir di Lingkungan Universitas Bandung, Simposium

VII FSTPT, Universitas Katolik Parahyangan, (2004).


ICMSA2010 Organising Committee

Chair: Dr. Goh Yong KhengCo-Chairs: Dr. Lee Chee Leong, Dr. Tan Choon PengSecretary: Dr. Liew How Hui, Mr Liew Kian WahTreasurer: Mr. Chang Yun Fah

Editors:Ms. Ng Wei Shean,Mr. Goh Khang Wen,Mr. Koay Hang Leen, Mr. Ong Kiah Wah, Ms. Yap Lee Ken

Members:Dr. Chen Huey Voon, Dr. Chua Kuan Chin, Dr. Chin Seong Tah, Dr. Lem Kong Hoong, Dr. Leong Loong See @ Leong Yoon Kwai, Dr. Ong Poh Hwa, Dr. Tan Son Len @ Tan Sin Leng, Dr. Wong Wai Kuan, Dr. Wong Wing Yue, Dr. Yong Chin Khian,Dr. Yosza Drasril, Ms. Chang Xiang-Yi, Ms. Chin Fung Yuen, Mr. Chong Fook Seng, Ms. Hii Siew Chen, Ms. Kavitha a/p Subramaniam, Mr. Lee How Chinh, Mr. Lim Foo Weng, Ms. Pan Wei Yeing, Ms. Pang Sook Theng, Ms. Pek Law Heong, Mr. Sue Chye, Ms. Teoh Lay Eng, Mr. Denis Wong Chee Keong, Ms. Wu Ziou Hon @ Go Ziou Hon, Mr. Yeo Heng Giap Ivan, Ms. Yik Lai Kuan,UTAR Mathematics Society.


Acknowledgments

We would like to express our appreciation to the sponsors for their support to make this ICMSA2010 possible. They are:

• Ministry of Higher Education Malaysia, • Malaysian Mathematical Sciences Society (PERSAMA), • SAS Institute Inc., and • John Wiley and Sons, Inc.

It should be recognized that the success of the conference was through the cooperation and support of the international scientific committee, the keynote speakers, the invited speakers, the reviewers, and all presenters and participants. Thank you.


Sponsors:

organiser - rp2u.unsyiah.ac.id

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