BoA InteriOR 2019

BO OK O F ABSTRACT

5th International Conference on Operational Research (interiOR) 201 9

August 20 - 21, 2019 | Grand Mercure Medan Angkasa Hotel, Indonesia

Inspec INIS NASA Astrophysics Data System | Polymer Library Chemical Abstracts Service

The 5th International Conference on Operational Research (InteriOR) 2019 Department of Mathematics Faculty of Mathematics and Natural Sciences Universitas Sumatera Utara Medan, Indonesia

August 20 - 21, 2019

Welcome Speech Dear Friends and Colleagues, It is a great honour for us to welcome you at Medan. We are delighted that you from all over the world have accepted our invitation to take part at the International Conference on Operational Research (InteriOR ) 2019. The InteriOR 2019 is jointly organized by The Department of Mathematics Universitas Sumatera Utara, the Indonesian Mathematical Society (IndoMS) Sumatera Utara and Aceh Region and the Indonesian Operations Research Association (IORA). The InteriOR 2019 will presents recent advances on various areas of modern Operational Research. This year theme is Better Living with Operations Research. I would like to report that more than 140 abstracts are accepted for presentation at the InterioR 2019. I would like to present our million thanks to our keynote speakers and great friends: • Prof. Dr. Gerhard Wilhem Weber from Poznan University of Technology, Poland • Prof. Dr. Ulrike Leopold-Wildburger from Department of Statistics and Operations Research, University of Graz/Austria • Prof. Dr. Tutut Hermawan form University of Malaya ¨ udar University, Turkey • Burcu Grbz, Ph.D. from Usk¨ for their priceless contribution to the InteriOR 2019. Our special thanks go to: • The Governor of Propinsi Sumatera Utara Bapak Letnan Jenderal TNI (Purn.) H. Edy Rahmayadi • The Mayor of Medan Bapak Drs. H.Tengku Dzulmi Eldin S, MSi • The Rector of Universitas Sumatera Utara Prof. Dr. Runtung, SH, M.Hum for their valuable supports to the InteriOR 2019. Last but not least our thanks go to InteriOR Committee members and all participants. Without your supports the InteriOR 2019 will not be possible to happen. We hope that you will enjoy our conference and wish you a very pleasant stay at Medan. We look forward to exciting days of scientific exchange, for future collaboration and friendship. Finally, We welcome you again at Medan and Horas. Your Sincerely, Saib Suwilo Chair of the InteriOR 2019 i

Contents Welcome Speech

i

Venue Map

1

Keynote Abstracts

2

Abstracts of Parallel Sessions

5

Estimation Model of Claim Risk and Premium for Motor Vehicle Insurance by Using Bayesian Method (Relita Buaton, Muhammad Zarlis, Herman Mawengkang ,Syahril Effendi ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Hamming index generated by vertex-edge incidence matrix of some composite graphs (Safri Ali, Saib Suwilo, Mardiningsih) . . . . . . . . . . . . . . . . . . . . .

5

Hamming index generated by vertex-edge incidence matrix of some composite graphs (Anna Angela Sitinjak, Herman Mawengkang, Marwan Ramli, Ferdinan Rinaldo Tampubolon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

A Decision Model of Hospital Capacity Management Problem using MINLP Approach (Suryati Sitepu, Herman Mawengkang) . . . . . . . . . . . . . . . .

6

A Discrete Optimization model for Sustainable Seafood Production Planning Problem (Tutiarny Naibaho, Herman Mawengkang) . . . . . . . . . . . . . . . .

7

Optimization of Knowledge Management Process Under Uncertainty Disruption for Small Medium Business Organization (Sajadin Sembiring, Herman Mawengkang, Tulus, M. Zarlis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

Solution of Non Linier Diferensial Equation to Lotka - Volterra Equation and Pendulum Equation Using Runge - Kutta Method (Fernandus Bobby Chandra Simalango, Sutarman, Open Darnius) . . . . . . . . . . . . . . . . . . . . .

7

Mathematical Model to predict the epidemic dynamic of infectious disease within network (Ismail Husein, Herman Mawengkang, Saib Suwilo, Mardingingsih)

8

A New Framework of Feature Selection Approach for Sentiment Analysis (Mochamad Wahyudi, Muhammad Zarlis, Herman Mawengkang, Syahril Effendi ) . . . .

8

A New Approach For Non Parametric Methods With C-MARS To Be Used In The Data Mining Process (Dadang Priyanto, Muhammad Zarlis, Herman Mawengkang, Syahril Effendi )

. . . . . . . . . . . . . . . . . . . . . . . . .

9

Optimization of determining School Promotion Locations by applying the Topsis Method (Case Study: Muhammadiyah Lubuk Pakam Private Elementary School) (Hengki Tamando Sihotang, Syahril Effendi, Elviawaty Muisa Zamzami, Herman Mawengkang) . . . . . . . . . . . . . . . . . . . . . . . . .

ii

9

Causal Loop Diagram (CLD) Model in Planning A Sustainable Smart Sharia Tourism (Husain, Muhammad Zarlis, Herman Mawengkang, Syahril Effendi ) . . . .

10

A Class of Primitive Two-Colored Digraph with Large Competition Index (Ema Sri Rezeki, Saib Suwilo, Mardiningsih) . . . . . . . . . . . . . . . . . . . . . . .

10

A Model for Optimizing the Facility Location-AllocationRouting Based on Periodic Deliveries (Dedy Juliandri Panjaitan, Saib Suwilo, Opim S Sitompul Sawaluddin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

A Model for Planning Sustainably of Forest Considering the Optimization of Water Allocation for Power Plant (Juli Antasari Sinaga, Herman Mawengkang, Tulus Muhammad Zarlis) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

Computational Analysis of Flow in Dam Using COMSOL Multiphysics (Masna Nasution, Tulus, Sawaluddin) . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

On Hamming index of (0,1)-matrices of graphs (Irma Wardani, Saib Suwilo, Mardiningsih) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

An Improved Active Constraint Approach for Tackling The Portfolio Optimization Problem (Riri Syafitri Lubis, Herman Mawengkang, Open Darius Mardiningsih) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

An Optimization Model For Solving Heterogeneous Vehicle Routing Problem With Big Data considering Level of Service (Enny Susilawati, Herman Mawengkang, Opim S Sitompul Sutarman) . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Implementation of The Problem with Perishable Inventory (PRPPI) Model with Optimize Delivery-Optimized Selling Policyon Tempe Production and Distribution (Aidil Fajar Akbar, Sawaluddin) . . . . . . . . . . . . . . . . . . .

13

A Model to Determine Optimally Hub Location for a Communication Network (Fibri Rakhmawati, Saib Suwilo, Sutarman Muhammad Zarlis) . . . . . . . . . . .

13

An Improved Search Direction Method Nonlinear Programming (Siswadi, Saib Suwilo, Tulus Sawaluddin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

A Model to Determine Optimally Hub Location for a Communication Network (Zulfi Amri, Herman Mawengkang, Tulus Opim Salim Sitompul ) . . . . . . . . . .

14

A Model to Determine Optimally Hub Location for a Communication Network (Zulfi Amri, Herman Mawengkang, Tulus, Opim Salim Sitompul ) . . . . . . . . .

14

Neighborhood Based Search Approach for Solving A Large Scale of Non-Convex Mixed-Integer Non Linear Programming Problems (Joni Wilson Sitepu, Herman Mawengkang, M. Zarlis, Saib Suwilo ) . . . . . . . . . . . . . . . . . .

14

Estimating the Distributions of Bitcoin Exchange Rate (Sutarman, Arianto) . . .

15

An Optimization Model for Managing Industries Hazardous Waste Disposal (Avery Boy Detinty, Herman Mawengkang) . . . . . . . . . . . . . . . . . . . . . .

15

Analysis of an Optimal Cluster Approach: A Review Paper (Deny Jollyta, Syahril Effendi, Muhammad Zarlis, Herman Mawengkang) . . . . . . . . . . . . . .

16

An improved approach for solving two-stage stochastic integer programs (Fatmah Syarah, Herman Mawengkang, Anton Abdulbasah Kamil, Sutarman) . . . .

16

An improved approach for solving two-stage stochastic integer programs (MD Nasution, H Mawengkang, A A Kamil, Syahril Effendi ) . . . . . . . . . . . . .

16

On solving stochastic DEA model using stochastic programming approach (MD Nasution, H Mawengkang, A A Kamil, Syahril Effendi ) . . . . . . . . . . . iii

17

Determination the Priority of Tourism Development in Sumatera Utara Province by Using Fuzzy Analytical Hirearchi Process Method (Pasukat Sembiring, Ujian Sinulingga, Sajadin Sembiring) . . . . . . . . . . . . . . . . . . . . .

17

Multi-Objective Program Model for Vehicle Routing Problem (Ermita Kamsiah Siadari, Herman Mawengkang, Syahril Effendi ) . . . . . . . . . . . . . . . .

18

On Some Properties of New Modular Sequence Space Determined by Phy-Function (Elvina Herawati, Muhammad Ofie) . . . . . . . . . . . . . . . . . . . . . .

18

Neighbourhood Based Search Approach For Solving A Class Of Mixed-Integer Nonlinear Programming Problems (Hardi Tambunan, Herman Mawengkang) . .

18

Optimization of Determining Promotional Strategies with Analytical Hierarchy Process (Winda Ade Fitriya B, Sawaluddin Nasution) . . . . . . . . . . . . . .

19

A Model for Tackling Hazardous Industries Waste Disposal Management Problem (Ronal Gomar Purba, Tulus,Herman Mawengkang, Saib Suwilo) . . . . . .

19

Capacity Optimization Model for Hospital Management Problem Under Uncertainty (Ruth Mayasari Simanjuntak, Herman Mawengkang, Tulus, Sawaluddin)

.

20

A Model to Determine Optimally Hub Location for a Communication Network (Fibri Rakhmawati, Saib Suwilo, Sutarman, M. Zarlis) . . . . . . . . . . . . . . .

20

Modeling of Cost And Time Optimization of Network Analysis Using Fuzzy Multiobjective Liner Programming (FMOLP) (Fibri Rakhmawati, Saib Suwilo, Sutarman, M. Zarlis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

Generalized Lambda Distribution Modelling on Financial Performance Data of Indonesian Banking Companies (Prana Ugiana Gio, Herman Mawengkang, M. Zarlis, Saib Suwilo) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

SIR Model (Susceptible, Infected, Recovered) for Transmission of Corrupt Behavior (Sutarman, Fitri Ardianti ) . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

Integer Programming Model for Solving Delay Problem in Air Traffic management system (Ellis Mardiana Panggabean, Herman Mawengkang, M. Zarlis, Syahril Efendi ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

Graph Theory and Its Application in Engineering (Zahedi, Mahrizal Masri, Yenny Suzana) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

Proof of Mathematical Fallacy (Yasmine Maharani Putri ) . . . . . . . . . . . . . .

22

The Solving of Linear Programming Problems Using Decomposition Method (Hendra Cipta, Saib Suwilo, Sutarman, Herman Mawengkang) . . . . . . . . . .

22

A Comparison for The Two Computation Approaches of Weilbull Distribution (Sutik Lestari, Sutarman) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

Optimization Model of Profit of Processed Food Production Made From Cassava Using Simplex Method (Firmansyah, Dedy Juliandri Panjaitan, Madyunus Salayan, Alistraja Dison Silalahi ) . . . . . . . . . . . . . . . . . . . . . . . .

23

Stochastic Chance Constrained Programming Model For Multi Criteria Decision Making Problems (Dame Ifa, Opim Salim Sitompul, Sutarman, Esther Nababan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

The Rotundity of the space (lp )Λ (E. Herawati, D.A. Harahap) . . . . . . . . . . .

24

The model of CVRP Using Sweep Algorithm for Determining The Route of Trash Carrier : Case Study (Putri K Nasution, Aghni Syahmarani ) . . . . . . . .

iv

24

Implementation of Generative ConvNet Learning on Generating Modern Batik Pattern (Maulida Yanti, Putri K Nasution) . . . . . . . . . . . . . . . . . . . .

24

The m-Competition Index of Primitive Two-Colored Wielandt Digraphs (Hari Sumardi, Saib Suwilo, Mardiningsih) . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Optimization of Scheduling Tutors with Linear Goal Program (Herlin Nikmah, Sutarman, Open Darnius) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Numerical Solution of Linear Differential Equations with ordr-n using Finite Difference Methode (Aghni Syahmarani, Putri Khairiah Nasution) . . . . . . . .

26

Penjadwalan Perawat Rumah Sakit menggunakan Fuzzy Goal Programming (Kiki Fatmala, Sutarman) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Modeling capacitated vehicle routing problem (CVRP) on vehicle capacity (Desy Nata Fristati, Herman Mawengkang, Sawaluddin)

. . . . . . . . . . . . . .

26

Share-Of-Choice Problem Models with Heuristics (Rima Aprilia, Rina Widya Sari, Rina Filia Sari ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

A Stochastic Programming Approach for solving Feature Selection Technique in Sentiment Analysis (Mochamad Wahyudi, Muhammad Zarlis, Herman Mawengkang, Syahril Efendi ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

Clarke and Wright Savings Algorithm as Vehicle Routing Problem With Simultaneous Pickup And Delivery (VRPSPD) Solution (Case Study: PT.PINANG BARIS LANGIT BIRU) (Fadlah Tunnisak, Sutarman) . . . . . . . . . . . .

27

Optimization for Supply Chain Planning of Crude Palm Oil Industry (Lilis, Opim S. Sitompul, Saib Suwilo, Sutarman) . . . . . . . . . . . . . . . . . . . . . .

28

A Development of Extreme Studentized Deviation Method in Detecting Bivariate Data Outliers (Candra Ardodo Simbolon, Open Darnius) . . . . . . . . . . .

28

Study Vehicle ROuting Problem Using Nearest Neighbor Algorithm (Rio Ferdiani Harahap,Sawaluddin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

Integrated Production Planning Model With Grace Period Of Loading Process And Safety Stock (Lusiana Tarihoran, Sutarman) . . . . . . . . . . . . . . . . .

29

An Algoritma Based on Genetic Optimization for Minimum Connected Dominating Set Problem (Muhammad Ridwan Mukti, Mardiningsih) . . . . . . . . . . .

29

Optimization model of water distribution network problems using a linear programing (Jelita Permata Sari, Sawaluddin) . . . . . . . . . . . . . . . . . . . . .

29

Comparison of Completion of VAM, TOCM-SUM Transportation Problems with Stepping Stone to Determin Optimal Solutions (Loria Amisah Lubis, Mardiningsih) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

Smart Analysis and Planning’ Data: From Big Data to Value Propositions (Gayus Simarmata, Saib Suwilo, Opim Salim S, Sutarman) . . . . . . . . . . . . .

30

A constrained based approach for solving the multi-period singlesourcing problem (Adi Suarman Situmorang, Heman Mawengkang, Tulus, Opim S Sitompul )

30

An optimization Model for Supply Chain System with Several Echelon (Amin Harahap, Herman Mawengkang) . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

A constrained based approach for solving the multi-period single-sourcing problem (Adi Suarman Situmorang, Herman Mawengkang, Tulus ,Opim S Sitompul )

31

Generalized Reduced Gradient Approach for Solving Heterogeneous Vehicle Routing Problem with Side Constraints (Herman Mawengkang, Sutarman) . . . . . v

31

The Dynamic Selection of Coordination Mechanisms for Sustainable School Using Markov Process (Maxtulus Junedi Nababan, Opim S. Sitompul, Tulus, Sutarman) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

Optimization Method of Selecting Control Strategy In Life System Approach With Big Data (Gayus Simarmata, Saib Suwilo, Opim S. Sitompul, Sutarman) .

32

Spatial Regression Model of Poverty in The Province of North Sumatera on 2017 (Yohana Tambunan, Open Darnius) . . . . . . . . . . . . . . . . . . . . . .

33

Modelling of Risk Factors that Inluence Malaria Infection using Binary Logistic Regression (Dessy Siahaan, Open Darnius) . . . . . . . . . . . . . . . . . .

33

Multi-Criteria Model of Logistic System And Waste Management In Crude Palm Oil Industry (Meslin Silalahi, Herman Mawengkang) . . . . . . . . . . . . .

34

The Concept Model of The Development of An Academic Data Processing System for Students Integrated Through A Database Using The Hierarchy of Grid Partition (HGP) Method (Verdi Yasin, Muhammad Zarlis, Opim Salim Sitompul, Poltak Sihombing) . . . . . . . . . . . . . . . . . . . . . . . . . .

34

Social Impact for Negatif Hoax Character Recognition user Behavior Using Backpropagation Neural Network (BPNN) (R Syah, H Mawengkang, M Elveny)

35

Determination Robust Requirement of Consensus System (MR Syahputra, IH Rambe, H Mawengkang) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Application of Genetic Algorithm Method in Optimization of Irrigation Water Flowing Scheduling System: A Case Study of Keuliling Reservoir in Aceh Besar District, Indonesia (Siti Rusdiana, Zahnur ) . . . . . . . . . . . . . . . . . .

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Venue Map Grand Mercure Medan Angkasa Hotel Jalan Sutomo No. 1, Perintis, Kec. Medan Timur Medan, Sumatera Utara Indonesia Phone : +62-61-4555888

1

Keynote Abstracts Modern Water-Resource Management: Application of Novel OR-Analytics Snow Classification on Sentinel 2 Imagery by MARS,

Gerhard W. Weber Poznan University of Technology, Poland Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Etiam tempor orci eu lobortis elementum. Feugiat sed lectus vestibulum mattis ullamcorper velit. Metus aliquam eleifend mi in nulla posuere sollicitudin aliquam ultrices. Eget mi proin sed libero enim sed. Turpis egestas maecenas pharetra convallis posuere. Risus nec feugiat in fermentum posuere urna nec. Non blandit massa enim nec dui. Ut tellus elementum sagittis vitae et leo duis ut. Mauris vitae ultricies leo integer malesuada. Integer vitae justo eget magna fermentum iaculis eu non. Integer eget aliquet nibh praesent tristique magna sit amet. Aliquet sagittis id consectetur purus ut. Lectus sit amet est placerat in. Velit laoreet id donec ultrices tincidunt arcu non sodales neque. Nullam vehicula ipsum a arcu cursus. Nunc sed augue lacus viverra vitae congue eu consequat. Congue eu consequat ac felis donec et odio pellentesque. Ultricies lacus sed turpis tincidunt id aliquet risus feugiat. Eu ultrices vitae auctor eu augue. Enim eu turpis egestas pretium. Magnis dis parturient montes nascetur ridiculus. Etiam dignissim diam quis enim lobortis scelerisque fermentum. Faucibus purus in massa tempor nec feugiat. Augue eget arcu dictum varius duis at consectetur lorem. Urna molestie at elementum eu facilisis sed odio. Venenatis lectus magna fringilla urna porttitor rhoncus dolor. Tempus imperdiet nulla malesuada pellentesque elit eget. Scelerisque eu ultrices vitae auctor eu augue. In fermentum posuere urna nec tincidunt praesent semper feugiat. Turpis egestas maecenas pharetra convallis. Eu feugiat pretium nibh ipsum consequat.

2

Classification and Generation of Digital Marble Art (EBRU) by revisiting OR via Deep Learning

Gerhard W. Weber and M. Atay Poznan University of Technology, Poland

3

A numerical approach for a class of partial differential equations and their applications in biology

Burcu G¨ urb¨ uz ¨ udar University, Turkey Assistant Professor, Usk¨ Visiting Research Fellow, University of Nantes, Laboratoire Mathmatiques Jean Leray, France In this study, a numerical scheme for the approximate solutions of a class of nonlinear partial differential equations is presented. These type of equations play an important role in biological models which describe disease dynamics, multi-species competition, heat and mass transfer, stochastic model for the spatial spread of a favoured gene in a population and the natural extension of the logistic growth population model so on. In order to find the numerical solution of these type of equations with initial and boundary conditions Laguerre collocation method is introduced. This method, by means of collocation points, is based on the matrix operations of the truncated Laguerre series and its derivatives along with initial and boundary conditions. The suggested scheme reduces the solution of the given problem to the solution of a matrix equation corresponding to algebraic equations system with unknown Laguerre coefficients. By solving this equation system, Laguerre coefficients can be computed. The usability and efficiency of the method are investigated together with error analysis.

4

Abstracts of Parallel Sessions Estimation Model of Claim Risk and Premium for Motor Vehicle Insurance by Using Bayesian Method Relita Buaton1 , Muhammad Zarlis2 , Herman Mawengkang3 ,Syahril Effendi2 1 Graduate

School of Computer Science, Universitas Sumatera Utara

2 Department

of Computer Science, Universitas Sumatera Utara

3 Department

of Mathematics, Universitas Sumatera Utara

Data mining is an analytical process of knowledge discovery in large and complex data sets. Many studies wish to explore data, to find information so that knowledge can be obtained through the grouping process, classification, rules discovery, associations and data mining visualization which shows similarity. Periodic data often occurs in business applications and sciences that has big size, high dimension and continuously updated. The similarity in periodic data is based on several approaches. One of common approaches is to transform periodic series into other domains so that dimensions are reduced, followed by index mechanism. Many studies of time series do not give optimal result because limited to extracting data not able to represent time series and its pattern which is then change into rules. Rules can be found in time series data, but they are still constrained by over fitting and difficult to present. It causes time series data and non linier function of data mining decision cant be optimal. The basic idea in the method proposed is to do periodic discretization for sub- sequential formation. These sub-sequences are grouped through a measure of similarity. The simple rule-finding technique is applied to obtain hidden rules in the temporal pattern. The optimal time series data expected to generate the uncertainty trend, previously unknown and can be used to make decisions or forecasting in the future.

Hamming index generated by vertex-edge incidence matrix of some composite graphs Safri Ali1 , Saib Suwilo2 , Mardiningsih3 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department

of Mathematics, Universitas Sumatera Utara

Let A be a vertex-edge incidence matrix of a graph G . The Hamming distance between two rows A(i, :) and A(j, :) of A is the number of coloumn ‘ such that A (i, ‘) 6= A (j, ‘) . In this paper, we discuss the sum of Hamming distances betwen all pairs of rows of A . We present a formula for the sum in terms of the number of edges and the number of vertices of the graph G . We then use this formula to determine the sum of Hamming distance for some composite graphs such as union of graphs, joint of graphs, cartesian product of graphs and corona product of graphs.

5

Hamming index generated by vertex-edge incidence matrix of some composite graphs Anna Angela Sitinjak1 , Herman Mawengkang2 , Marwan Ramli3 , Ferdinan Rinaldo Tampubolon4 1 Politeknik 2 Department 3 Department

Teknologi Kimia Industri Medan

of Mathematics, Universitas Sumatera Utara

of Mathematics, Universitas Syiah Kuala Banda Aceh 4 Politeknik

Negeri Medan

The problems in daily life can be solved with mathematical models, such as the model of Lotka-Volterra to find out how growth of animals. This model can be modified into the Predator-Prey Model of Hutchinson with delay time and Response Function of Holling type II in which one as active predator and the other as prey, delay time is considered on prey population with assuming that supporting resources of prey are adequate and this type of response function is as interactions between populations of predator and prey. In this paper, linearization and eigenvalues are used to analyze the stability solution of the fixed point so that it can be known the effect of delay time and response function of this type. There are three fixed points are obtained without delay time with two fixed points are stable under certain conditions, but delay time can change the stability of the fixed point.

A Decision Model of Hospital Capacity Management Problem using MINLP Approach Suryati Sitepu1 , Herman Mawengkang2 1 Universitas 2 Department

HKBP Nommensen, Medan

of Mathematics, Universitas Sumatera Utara

Nowadays the needs to get health services is rapidly growing. This situation occur due to the increasing number of populations. For inpatient hospital care, capacity management systems requires information on beds and nursing staff capacity. This paper presents a capacity model under uncertainty that gives insight into required nursing staff capacity and opportunities to improve capacity utilization on a ward level. A capacity model is developed to calculate required nursing staff capacity. The uncertainty turns up on the availability schedule of staff and the number of patient. A mixed integer nonlinear optimization is formulated to describe the problem.

6

A Discrete Optimization model for Sustainable Seafood Production Planning Problem Tutiarny Naibaho1 , Herman Mawengkang2 1 Universitas 2 Department

HKBP Nommensen, Medan

of Mathematics, Universitas Sumatera Utara

A multi-product fish production planning produces simultaneously multi fish products from several classes of raw resources. The sustainable production planning problem aims to meet customer demand subject to environmental restrictions. This paper considers the management which performs processing fish into several seafood products.The uncertainty of data together with the sequential evolution of data over time leads the sustainable production planning problem to a nonlinear mixed-integer stochastic programming. Direct search is used for solving the deterministic equivalent model.

Optimization of Knowledge Management Process Under Uncertainty Disruption for Small Medium Business Organization Sajadin Sembiring1 , Herman Mawengkang2 , Tulus3 , M. Zarlis4 1,4 Department

of Computer Science, Universitas Sumatera Utara

2,3 Department

of Mathematics, Universitas Sumatera Utara

Recently, knowledge, as a strategic resource, has become an essential driving forces for business organization success, in particular in competitive situation. Accordingly, the existence of knowledge management (KM) is to support the business firm to locate, select, organize, distribute, and transfer vital information within the firm. One of the methods to increasing effectiveness of knowledge management is to optimize its processes. However, during the process in order to increase the firm performance some disruption may occur. This paper describes a stochastic programming model to optimize the knowledge management processes problem within a firm, considering uncertainty disruption. We adopt scenario generation approach for tackling the stochastic problem.

Solution of Non Linier Diferensial Equation to Lotka - Volterra Equation and Pendulum Equation Using Runge - Kutta Method Fernandus Bobby Chandra Simalango1 , Sutarman2 , Open Darnius3 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department

of Mathematics, Universitas Sumatera Utara

This paper discusses the solution of non - linier diferential equations in Lotka - Volterra Equation and Pendulum Equation. The Lotka - Volterra Equation reviewing population growth in an ecosystems between preys and predators, while pendulum equation deals with simple swing motion in the second Newton Law equation. The first step to find the solutions is to take the first derivative of the Lotka - Volterra and the Pendulum equations . Next step is to give initial value to the first derivative obtained. Futhermore, the Runge - Kutta Method is applied to get the exact value in the range of iteration.

7

Mathematical Model to predict the epidemic dynamic of infectious disease within network Ismail Husein1 , Herman Mawengkang2 , Saib Suwilo3 , Mardingingsih4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

The model created for epidemic transmission of infectious disease usually is relied on the assumption in which the population are mixed randomly.. However, this is not true in reality , as each individual could have made contacts within a finite set of population in such a way they could transmit infection Consequently, the ensemble of these finite set forms a complex network. Therefore the structure of the dynamic network can be used to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. This paper proposes a mathematical model to compute the epidemic pattern of transmission of infectious disease within a dynamic network.

A New Framework of Feature Selection Approach for Sentiment Analysis Mochamad Wahyudi1 , Muhammad Zarlis2 , Herman Mawengkang3 , Syahril Effendi4 1 Graduate 2,4 Faculty

School of Computer Science, Universitas Sumatera Utara

of Computer Science and Information Tehnology, Universitas Sumatera Utara 3 Department

of Mathematics, Universitas Sumatera Utara

Undoubtedly that the huge business data could make data analysis becomes more complicated such that the decision making process would be out of reach. This condition happens. In the fields of consumer buying behaviour, A well known method called sentiment analysis can help in extracting information about the up-to-date trends and is able to increase market value of product through improving its quality. One of the approach in solving the sentiment analysis is feature selection technique. However this technique contains a combinatorial behaviour and the analysis of the huge data can experience uncertainty parameter. This paper describes a frame work for solving the sentiment analysis based on feature selection approach using a stochastic combinatorial programming.

8

A New Approach For Non Parametric Methods With C-MARS To Be Used In The Data Mining Process Dadang Priyanto1 , Muhammad Zarlis2 , Herman Mawengkang3 , Syahril Effendi4 1 Graduate 2,4 Faculty

School of Computer Science, Universitas Sumatera Utara

of Computer Science and Information Tehnology, Universitas Sumatera Utara 3 Department

of Mathematics, Universitas Sumatera Utara

Data Mining is the process of finding a number of certain patterns and knowledge from big data. In general, the data mining process can be grouped into two categories, namely descriptive data mining and data mining prediction. There are several Mathematical functions that can be used in the process of data mining, one of which is the function of Classification and Regression. Regression Analysis is also called Prediction analysis, which is a statistical method that is widely used to investigate and model relationships between variables. Regression analysis to estimate the regression curve can be done by analyzing Nonparametric Regression. One well-known method in non-parametric regression is MARS (Multivariate Adaptive Regression Spline). MARS method is used to overcome the weaknesses of the Linear Regression method. The use of backward stepwise algorithms with the framework of conic quadratic programming (CQP) from MARS produces a new method called CMARS (Conic Multivariate Adaptive Regression Splines). The CMARS method is capable of modeling high dimensional data with nonlinear structures. The flexible nature of CMARS modeling can be utilized in the data mining process to solve human life problems.

Optimization of determining School Promotion Locations by applying the Topsis Method (Case Study: Muhammadiyah Lubuk Pakam Private Elementary School) Hengki Tamando Sihotang1 , Syahril Effendi2 , Elviawaty Muisa Zamzami3 , Herman Mawengkang4 1 Graduate 2,3 Faculty

School of Computer Science, Universitas Sumatera Utara

of Computer Science and Information Tehnology, Universitas Sumatera Utara 4 Department

of Mathematics, Universitas Sumatera Utara

This research to determine the location of optimal school promotions. This study will design and build a decision support system that can optimize the determination of the location of school promotions to be more efficient and optimal with case studies in elementary schools. The data analysis in this study is the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method will calculate the value of data originating from the criteria for alternative school promotion locations that will result in a promotion location rating from the best alternative to the school’s needs. This research produces a system that is able to display recommendations for the best promotion location according to the ranking with the results of predetermined criteria according to system requirements.

9

Causal Loop Diagram (CLD) Model in Planning A Sustainable Smart Sharia Tourism Husain1 , Muhammad Zarlis2 , Herman Mawengkang3 , Syahril Effendi4 1 Graduate 2,4 Faculty

School of Computer Science, Universitas Sumatera Utara

of Computer Science and Information Tehnology, Universitas Sumatera Utara 3 Department

of Mathematics, Universitas Sumatera Utara

The development of sustainable tourism such as dynamic and complex smart sharia tourism consists of many interrelated and diverse components of stakeholders, which each has different management objectives, which can trigger unexpected conflicts among stakeholders. Regarding the dynamic and complex challenges in the field of developing sustainable tourism, the ability of identidying is really needed. For this reason, it is necessary to see further what are the factors that influence the plan for implementing sharia tourism intelligently and the strategies needed and analyze the relationship of dynamic causes of these factors using approachment methods which use the Causal Loop Diagram system ( CLD)). The purpose of this research is to get a solution to overcome conflicts among stakeholders through approachment system with the Causal Loop Diagram (CLD) model

A Class of Primitive Two-Colored Digraph with Large Competition Index Ema Sri Rezeki, Saib Suwilo, Mardiningsih Department of Mathematics, Universitas Sumatera Utara

The competition index of a primitive two-colored digraph D(2) , denoted k(D(2) ), is the smallest positive integer h + l such that for each pair of vertices u and v there is a vertex w with the property that there is a (h, l)-walk from u to w and there is a (h, l)-walk from v to w. For two-colored digraph on n vertices it is known that k(D(2) ) ≤ (3n3 + 2n2 − 2n)/2. In this paper we discuss a class of primitive two-colored digraph consisting of two cycles whose scrambling index closes to (3n3 + 2n2 − 2n)/2.

A Model for Optimizing the Facility Location-AllocationRouting Based on Periodic Deliveries Dedy Juliandri Panjaitan1 , Saib Suwilo2 , Opim S Sitompul3 Sawaluddin4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,4 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The focus of this paper is to decide the facility locations and allocations of products that can give result not only the profitability of an indusry but the ability to serve customers in a very short time. Generally the problem of facility location planning is to minimize the overall operation cost by simultaneously to choose a subset of candidate facilities and creating a set of delivery routes in such a way to meet some feasible restrictions. In this paper we consider the periodic deliveries of vehicle to be used to allocate goods. Integer programming model is generated to solve the problem. An improved feasible neighbourhood search is developed to solve the model.

10

A Model for Planning Sustainably of Forest Considering the Optimization of Water Allocation for Power Plant Juli Antasari Sinaga1 , Herman Mawengkang2 , Tulus3 Muhammad Zarlis4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Obtaining a sustainable forest management is unavoidable to integrate ecological, economic, and social concerns. One of the main function of forests is to protect watersheds in such a way to preserve water for rivers to be used as a resource of a power plant. Other objectives of economic and silvicultural nature of forestry should be taken into account in developing the sustainable forest management planning. This paper addresses a goal programming approach to model the forest management planning in which several objectives and constraints should be satisfied. The model is applied to the management of forest in North Sumatera province of Indonesia.

Computational Analysis of Flow in Dam Using COMSOL Multiphysics Masna Nasution, Tulus, Sawaluddin Department of Mathematics, Universitas Sumatera Utara

One way to utilize river flows in Indonesia is to make a dam to get benefits in various fields. The river flow that enters the dam and which will flow again makes flow in the dam which causes a fluid dynamic. The fluid dynamics that occur in dams produce several events such as precipitation, flow turbulence, and so on. To see how the flow is, in this study a simulation was carried out by making a dam model followed by fluid dynamics analysis of the dam model. Then it will be solved by the finite element method. In its completion, a Multiphysics COMSOL program is used that applies the finite element method to get results and simulations. The results to be obtained using the mesh transfer method. Where mesh displacement applies the speed of surface displacement as the velocity of fluid flow when entering, the solution to the equation in mesh displacement uses displacement on the node, and the Navier-Stokes equation is solved by substituting the displacement equation on the mesh. The results obtained at an interval of approximately 3 seconds with a speed of 0.7 m/s will produce turbulence flow at the dam where the maximum speed on the surface is 0.4 m/s. As a result, if there are other elements in the flow other than water, it will cause mixing of substances in the middle of the dam in 3 seconds and then precipitation will occur. In the next study, different dam models will be carried out and have a faster flow rate.

11

On Hamming index of (0,1)-matrices of graphs Irma Wardani, Saib Suwilo, Mardiningsih Department of Mathematics, Universitas Sumatera Utara

Let A be a (0,1)-matrix of size m by n. The Hamming distance between two rows A(i, :) and A(j, :) of A is the number of columns k such that A(i, k) 6= A(j, k). The Hamming index of A is the sum of Hamming distances between all pairs of rows of A. In this paper we discuss a way of determining the Hamming index of A by considering the total contribution of each column of A to Hamming distance between two rows. Using this approach we present a new proof to the Hamming index of A when A is a (0,1)-matrix of a graph such as adjacency and incidence matrix.

An Improved Active Constraint Approach for Tackling The Portfolio Optimization Problem Riri Syafitri Lubis1 , Herman Mawengkang2 , Open Darius3 Mardiningsih4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

Most often the mathematical model of portfolio optimization problem has been expressed in terms of minimizing the risk, given the return.The difficulty in dealing with the quadratic programming model due to Markowitz has been overcome by the recent progress in algorithmic research, the introduction of linear risk function has given rise to the interest in solving portfolio selection problems with real constraints. This paper deals with the portfolio selection problem with minimum transaction lots. An improved search algorithm based on active constrained is addressed to solve the integer programming model. The algorithm starts from the solution of the relaxed problem to find a solution which is close to the continuous solution.

An Optimization Model For Solving Heterogeneous Vehicle Routing Problem With Big Data considering Level of Service Enny Susilawati1 , Herman Mawengkang2 , Opim S Sitompul3 Sutarman4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,4 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

In logistic system, a Vehicle Routing Problem with time windows (VRPTW) is defined as a logistic problem to determine the optimal routes used by a fleet of vehicles to deliver a given set of customers considering a limited service time; the objective of the problem is to minimize the total travel cost (in terms the travel times or distances) and operational cost (in terms of the number of vehicles used). This paper addresses a variant of the VRPTW in which the fleet of vehicle is heterogenic due to the different size of demand from customers. The problem, called Heterogeneous VRP (HVRP) also includes service levels. As the data involved is so huge (big data) we use a modified integer programming model to describe the problem. An improved feasible neighbourhood approach is proposed to solve the problem.

12

Implementation of The Problem with Perishable Inventory (PRPPI) Model with Optimize Delivery-Optimized Selling Policyon Tempe Production and Distribution Aidil Fajar Akbar, Sawaluddin Department of Mathematics, Universitas Sumatera Utara

UD.Ponimin industry is a homei ndustry in Medan city. The tempe produced by UD. Ponimin is packaged in three packages, namely leaf tempeh, plastic chip tempeh and plastic bar tempeh, in this journal PRPPI model applied for the type of leaf tempe packaging. Tempe is one product that is perishable. This study aim is to minimize Production Routing Problem Perishable Inventory (PRPPI) model with an inventory policy of Optimized Delivery-Optimized Selling (ODOS). The PRPPI linear model was completed using Lingo 17 software.

A Model to Determine Optimally Hub Location for a Communication Network Fibri Rakhmawati1 , Saib Suwilo2 , Sutarman3 Muhammad Zarlis4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The hub location happened in telecommunication can be regarded as a special variant of facility location problem. Therefore it can be defined as a selection of facility problem to locate hubs and choosing the terminal nodes to these hubs. The aim of the problem is to find minimum costs of hub installation and the cost of routing the traffic in the communication network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. This paper describes how to get a model of the polyhedral properties of the network. We develop a feasible search method to solve the model.

An Improved Search Direction Method Nonlinear Programming Siswadi1 , Saib Suwilo2 , Tulus3 Sawaluddin4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

This paper considers the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The FrankWolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved FrankWolfe type algorithms based on conjugate directions. In the conjugate direction FrankWolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one.

13

A Model to Determine Optimally Hub Location for a Communication Network Zulfi Amri1 , Herman Mawengkang2 , Tulus3 Opim Salim Sitompul4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The management of drinking water pipelines can exhibit challenges. Mostly these pipelines are located in underground, therefore they are vulnerable to deteriorate over time. This deterioration leads to failures such as leaks and breakage. This paper proposes an integer programming model to select optimally the appropriate pipe diameter during pipeline replacement planning for drinking water pipeline networks. Firstly ,the problem was formulated to minimize the cost of replacement while taking into account hydraulic constraints such as flow velocity for each pipe and water pressure at each node. In addition in terms of the economic perspective, stability of flow velocity in pipes were considered . We solve the model using an improved direct search approach

A Model to Determine Optimally Hub Location for a Communication Network Zulfi Amri1 , Herman Mawengkang2 , Tulus3 , Opim Salim Sitompul4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The hub location happened in telecommunication can be regarded as a special variant of facility location problem. Therefore it can be defined as a selection of facility problem to locate hubs and choosing the terminal nodes to these hubs. The aim of the problem is to find minimum costs of hub installation and the cost of routing the traffic in the communication network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. This paper describes how to get a model of the polyhedral properties of the network. We develop a feasible search method to solve the model.

Neighborhood Based Search Approach for Solving A Large Scale of Non-Convex Mixed-Integer Non Linear Programming Problems Joni Wilson Sitepu1 , Herman Mawengkang2 , M. Zarlis3 , Saib Suwilo4 1 Graduate

School of Mathematics, University of Sumatera Utara, Medan, Indonesia

2,4 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara, Medan, Indonesia

of Computer Science and Information Technology, Universitas Sumatera Utara

The negative side of the fast advancement of industries and technology is the creation of hazardous waste, particularly at the urban area. Normally, due to the regulation, these wastes have been treated systematically in order to reduce the amount of waste. However, there are still large amounts of hazardous waste need to be managed in the effort to develop a sustainable area. The management of hazardous waste consists of collection, transportation, treatment, and 14

disposal. This paper proposes an optimization model for managing the waste disposal based on location-routing approach. The result of this paper is total cost saving or income from the recycled waste is estimated in the cost function. The objective of the model is to minimize the operational cost and risk involved.

Estimating the Distributions of Bitcoin Exchange Rate Sutarman, Arianto Department of Mathematics, Universitas Sumatera Utara

This paper proposes to estimate the best fitted distributions of the bitcoin exchange rate. we present a comparison of four statistical distributions used to fit bitcoin exchange rate data. These four distributions are the Burr Type XII, Paralogistic, Generalized Pareto and mixture of two Gamma distributions. The data sets demonstrate strong positive skewness, heavy tails and sometimes bimodality. In addition, we download the full history of bitcoin exchange rate data from the first day of 2015 to the last day of 2018. We provide a statistical analysis of the exchange rate between BTC/IDR. Predictions are given for future value of the exchange rate.

An Optimization Model for Managing Industries Hazardous Waste Disposal Avery Boy Detinty1 , Herman Mawengkang2 1 Department

of Chemistry, University Sains Malaysia, Penang, Malaysia

2 Department

of Mathematics, Universitas Sumatera Utara

It is normal that the advancement of industries and technology could create negative impact, such as, hazardous waste, particularly at the urban area. It is well understood that such waste has been treated systematically in order to produce minimum waste. Nevertheless there are still large amounts of hazardous waste need to be managed in the effort to plan and to develop sustainable area. The management of hazardous waste consists of collection, transportation, treatment, and disposal. This paper proposes an integer programming model based on location-routing system. The objective of the model is to minimize cost and risk involved.

15

Analysis of an Optimal Cluster Approach: A Review Paper Deny Jollyta1 , Syahril Effendi2 , Muhammad Zarlis3 , Herman Mawengkang4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

4 Department 2,3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Determining the optimal clusters can be regarded as a grouping problem that has produced many cluster approach methods in various studies. Each method has provisions that can solve one or more grouping problems in generating information from data set with a number of k being tested. The advantages and disadvantages of each method actually complement to each other in solving the grouping problems. This paper aims to describe the performance of cluster approach methods in determining the optimal clusters through a review by paying attention to the criteria of the problem which is an obstacle to the grouping problem. The results of this review are expected to be a reference for developing the new optimal cluster approach method through possible combinatorial optimization.

An improved approach for solving two-stage stochastic integer programs Fatmah Syarah1 , Herman Mawengkang2 , Anton Abdulbasah Kamil3 , Sutarman4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,4 Department

of Mathematics, Universitas Sumatera Utara 3 Telkom

University, Bandung

Stochastic integer programming model usually arise in many real life problems, which have random parameter and variables to be restricted to integer value. Some real applications, such as production and manpower planning, portfolio selections. A deterministic equivalent problem can be generated as long as a distribution function of the random parameter is known..However, in general, the deterministic equivalences of these problems can be very large, and may not be solvable directly by general-purpose optimization approaches. After using scenario analysis technique, a direct search approach based on reduced gradient method is exploited for solving the deterministic model which would be a nonlinear integer program.

An improved approach for solving two-stage stochastic integer programs MD Nasution1 , H Mawengkang2 , A A Kamil3 , Syahril Effendi4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2 Department

of Mathematics, Universitas Sumatera Utara 3 Telkom

4 Faculty

University, Bandung

of Computer Science and Information Technology, Universitas Sumatera Utara

In Indonesia, the higher education can be regarded as a system that would be able to create better living conditions and also to develop knowledge. The population in Indonesia is huge therefore it is not surprising that the demand for enrollments in higher education is getting more and more every year However, this situation could create implication such as, the government needs to support a lot of funds. In the accountability terms, it is necessary to measure the efficiency the performance of this higher institution. Data envelopment analysis (DEA) is usually 16

can be used as a method to evaluate the technical efficiency. The higher institution considered in this paper is Universitas Muhammadiyah Sumatera Utara (UMSU) located in Medan, Indonesia. This paper addresses a method to evaluate efficiency for all departments in UMSU using DEA which has bounded constraints. Simultaneously, we present some important differences in efficiency of those departments.

On solving stochastic DEA model using stochastic programming approach MD Nasution1 , H Mawengkang2 , A A Kamil3 , Syahril Effendi4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2 Department

of Mathematics, Universitas Sumatera Utara 3 Telkom

4 Faculty

University, Bandung

of Computer Science and Information Technology, Universitas Sumatera Utara

Data envelopment analysis (DEA) is well-known technique to measure the efficiency the performance of an organization. In optimization terms it is a nonparametric mathematical programming technique to estimate returns to scale through the construction of a best practice frontier. In classical DEA it works with deterministic data. However, sometimes we involve a problem in which the data to work with is uncertain or unknown. Therefore it is necessary to have an appropriate technique to solve the model in such a way to obtain the estimate efficiency. This paper proposes a stochastic programming approach to rank the efficiency of Decision Making Units (DMU) in DEA model with uncrtain data.

Determination the Priority of Tourism Development in Sumatera Utara Province by Using Fuzzy Analytical Hirearchi Process Method Pasukat Sembiring1 , Ujian Sinulingga2 , Sajadin Sembiring3 1,2 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Fuzzy Analytical Hirearchi Process is a combination of Analytical Hirearchi Process method with fuzzy approach. Where the fuzzy Analytical Hirearchi Process method is used Triangular Fuzzy Number (TFN), to replace the Saaty scale table in the Analytical Hirearchi Process. This Triangular Fuzzy Number makes multi-criteria decision-making that is normally completed by Analytical Hirearchi Process to be completed by a fuzzy approach where the Triangular Fuzzy Number is used to describe linguistic variables and provide a definite value in pairwise ˜ (l, m, u), where l ≤ m ≤ u and comparison matrix. Triangular Fuzzy Number is symbolized by M l are the lowest values, m is the middle value, u is the top value. In its application, the Fuzzy AHP method is used in simulation data that has been arranged in a pairwise comparison matrix in determining the priority of tourism development in the province of North Sumatra. Some steps in determining the priority by using Fuzzy AHP that is defining fuzzy synthetic values extent for ˜1 and M ˜2 ), determining the i-objects, determining the confidence level of fuzzy numbers (M weight vector (W 0 ), then the last weight vector will be normalized back so it’s no longer a fuzzy number.

17

Multi-Objective Program Model for Vehicle Routing Problem Ermita Kamsiah Siadari1 , Herman Mawengkang2 , Syahril Effendi3 1,2 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Vehicle routing problem is a combinatorial optimization and integer programming problem that is often used in many planning and decision-making processes, for example to determine the optimal route in the process of distributing goods from the company to consumers. The problem of vehicle routing problems is often used with the sole purpose of minimizing internal costs. The authors propose a multi-objective model based on the Tchebycheff method for vehicle routing problems with heterogeneous fleets, where vehicles are characterized by different capacities, costs and emission factors. Three objective functions are used to minimize total internal costs, while minimizing CO2 emissions and emissions of air pollutants such as NOx .

On Some Properties of New Modular Sequence Space Determined by Phy-Function Elvina Herawati, Muhammad Ofie Department of Mathematics, Universitas Sumatera Utara

In the present paper, we define the modular sequence space by modular supn≥1

P∞

k=1

λnk φk (xk )

with x = (xk ), Λ = (λnk ) is a special infinite matrix and (φn ) is a sequence of phy-functions. We study the structure of some subset in this space.

Neighbourhood Based Search Approach For Solving A Class Of Mixed-Integer Nonlinear Programming Problems Hardi Tambunan1 , Herman Mawengkang2 1 Nommensen 2 Department

HKBP University, Medan

of Mathematics, University of Sumatera Utara

Integer programming is not new subject in optimization. However, given its practical applicability, we face computational difficulties in solving the large scale problems. In this paper we solve a class of mixed-integer nonlinear programming problem by adopting a strategy of releasing nonbasic variables from their bounds found in the optimal continuous solution in such a way to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Some computational experiences are presented.

18

Optimization of Determining Promotional Strategies with Analytical Hierarchy Process Winda Ade Fitriya B, Sawaluddin Nasution Department of Mathematics, Universitas Sumatera Utara

Analytical Hierarchy Process (AHP) method is one of the decision-making methods that uses logic, experience, knowledge, emotions and feelings to be optimized in a systematic process. The functional hierarchy and pairwise comparison matrix are the main components in the AHP structure. In the paired comparison matrix we will find the weight of each criterion by normalizing the geometric mean. The maximum eigenvalues and normalized eigenvectors will be obtained from this matrix. In the process of determining hierarchical weighting and evaluation factors, consistency tests must be carried out (CR ≤ 0.100). The AHP method in this study is used to determine the weight of each criterion and sub criteria and obtain a ranking from the promotion strategy determination. The results of using AHP indicate that competitor criteria from constraints, sub-criteria of human resources from company criteria on supporting factors, are a priority in the determination of promotion strategies and the highest alternative is Alternative 1.

A Model for Tackling Hazardous Industries Waste Disposal Management Problem Ronal Gomar Purba1 , Tulus2 ,Herman Mawengkang3 , Saib Suwilo4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

The negative side of the fast advancement of industries and technology is the creation of hazardous waste, particularly at the urban area. Normally, due to the regulation, these wastes have been treated systematically in order to reduce the amount of waste. However, there are still large amounts of hazardous waste need to be managed in the effort to develop a sustainable area. The management of hazardous waste consists of collection, transportation, treatment, and disposal. This paper proposes an optimization model for managing the waste disposal based on location-routing approach. The result of this paper is total cost saving or income from the recycled waste is estimated in the cost function. The objective of the model is to minimize the operational cost and risk involved.

19

Capacity Optimization Model for Hospital Management Problem Under Uncertainty Ruth Mayasari Simanjuntak1 , Herman Mawengkang2 , Tulus3 , Sawaluddin4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

Capacity management planning involves predicting the quantity and particular attributes of resources required to deliver health care service for hospitals at specified levels of cost and quality. For inpatient hospital care, capacity management requires information on beds and nursing staff capacity. This paper presents a capacity optimization model that gives insight into required nursing staff capacity and opportunities to improve capacity utilization on a ward level with some uncertainty parameters. A capacity model is developed to calculate required nursing staff capacity. The uncertainty turns up on the availability schedule of staff and the number of patient.

A Model to Determine Optimally Hub Location for a Communication Network Fibri Rakhmawati1 , Saib Suwilo2 , Sutarman3 , M. Zarlis4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The hub location happened in telecommunication can be regarded as a special variant of facility location problem. Therefore it can be defined as a selection of facility problem to locate hubs and choosing the terminal nodes to these hubs. The aim of the problem is to find minimum costs of hub installation and the cost of routing the traffic in the communication network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. This paper describes how to get a model of the polyhedral properties of the network. We develop a feasible search method to solve the model.

Modeling of Cost And Time Optimization of Network Analysis Using Fuzzy Multiobjective Liner Programming (FMOLP) Fibri Rakhmawati1 , Saib Suwilo2 , Sutarman3 , M. Zarlis4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

The purpose of this article is to model cost and time optimization on network analysis by using Fuzzy Multi-objective Linier Programming. FMOLP steps to optimize cost and time of network analysis are: modeling each goal as a linear program, determining the value for each objective function, determining the highest and lowest achievement levels for each objective function, forming a fuzzy model and resolving fuzzy problems. In this article also is given an example of problem that is solved using two objective function, minimizing time and cost each.

20

Generalized Lambda Distribution Modelling on Financial Performance Data of Indonesian Banking Companies Prana Ugiana Gio1 , Herman Mawengkang2 , M. Zarlis3 , Saib Suwilo4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,4 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Fitting of probability distribution to empirical data is a basic part of any data analysis system. One of the important problems in statistical data analysis is finding a statistical probability distribution which is appropriate with empirical data. Generalized lambda distribution (GLD) is a statistical distribution that can be used to fit data. GLD can make various distributions in a variety of different forms. In this paper, a GLD model is developed on company performance data for banking sector in Indonesia.

SIR Model (Susceptible, Infected, Recovered) for Transmission of Corrupt Behavior Sutarman1 , Fitri Ardianti2 1 Department 2 Dinas

of Mathematics, Universitas Sumatera Utara

Komunikasi dan Informatika Sumatera Utara, Indonesia

The purpose of this article is to describe the use of SIR (Susceptible, Infected and Recovered) model in modeling the spread of corrupt behavior. In modeling, corrupt behavior is analogous to a disease. In this case, corrupt behavior can spread from one individual to another individual. People who have corrupt behavior can transmit if they are in a group with other people who do not behave corruptly. Furthermore, the measurement of variables related to corruption behavior can be done using a specific questionnaire.

Integer Programming Model for Solving Delay Problem in Air Traffic management system Ellis Mardiana Panggabean1 , Herman Mawengkang2 , M. Zarlis3 , Syahril Efendi4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2 Department 3,4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

Nowadays, due to the rapid growth of air traffic and airspace congestion flight delays are becoming serious problems. This situation happens due to the demand capacity imbalances in air traffic management system. The deterioration of the expected service and operational costs would be the direct impact of this problem. Network-wide air traffic flow management can be regarded as an effective way to ease demand-capacity imbalances globally and would be able to reduce airspace congestion and flight delays. This paper proposes an integer programming model to solve the problem. The objective function consists of minimizing operational costs and risk costs.

21

Graph Theory and Its Application in Engineering Zahedi1 , Mahrizal Masri2 , Yenny Suzana3 1 Institut

Teknologi Medan

2 IAIN

Langsa

The study of graphs is covered in graph theory, which is a mathematical structure used to model pairwise relationship between objects. Graphs in this context consist of vertices (also called nodes) that are connected by edges (also called lines). This paper will discuss several examples of the use of graph theory in engineering such as electrical, mechanical and chemical engineering, and also introducing some basic notions of theoretical graphs as well as laws related to engineering beforehand.

Proof of Mathematical Fallacy Yasmine Maharani Putri1 1

SMA Sutomo I Medan

In mathematics, there are often fallacious evidences,which are then collected into concept illustration of mathematical fallacy. There is a difference between errors or mistakes and mathematical fallacy in a proof: errors in proof refer to invalid evidences, while in mathematical fallacy there is a concealment in presenting the evidence. Mathematical fallacies are presented by mixing invalid deduction steps with the valid ones. Fallacy occurs in many branches of mathematics, such as elementary algebra, geometry, sequence and trigonometry, and so on. And, the dedication of mathematicians in exploring and proving many things related to these mathematical fallacy that are often unthinkable is something that needs to be much appreciated.

The Solving of Linear Programming Problems Using Decomposition Method Hendra Cipta1 , Saib Suwilo2 , Sutarman3 , Herman Mawengkang4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3,4 Department

of Mathematics, Universitas Sumatera Utara

Some of linear programming problems encountered in practice may be very large in terms of the number or variables and constraints. If the problem has some special structure, it is possible to obtain the solution by applying the decomposition method. This method allows determining the optimal solution by decomposing the problem into several parts of the problem, then completing the parts of the problem freely. The purpose of this study is to provide a solution to the problem by providing problems in a linear program that will be solved by the decomposition method.

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A Comparison for The Two Computation Approaches of Weilbull Distribution Sutik Lestari1 , Sutarman2 1,2 Department

of Mathematics, University Sumatera Utara

The paper discusses the estimation of weilbull parameters by using the maximum likelihood method and bayes methods. In addition, a comparison between the two methods was carried out through the data simulation. The evaluation of both the methods was carried out by observasing the root mean square error value

Optimization Model of Profit of Processed Food Production Made From Cassava Using Simplex Method Firmansyah1 , Dedy Juliandri Panjaitan2 , Madyunus Salayan3 , Alistraja Dison Silalahi4 1,2,3 Program 4 Program

Studi Pendidikan Matematika, Universitas Muslim Nusantara Alwashliyah Studi Akuntansi, Universitas Muslim Nusantara Alwashliyah, Indonesia

Cassava as a food that contains carbohydrates, and can be processed into a variety of inexpensive foods that are healthy and nutritious. Utilization of cassava as the main ingredient in the business of making opaque and animal feed can be an easily available resource in the community. Although cassava is an easily available resource, its supply is limited. The simplex method is offered to solve linear program problems, where the problems of the production and sale of opaque and animal feed are modeled first in the form of a linear program. So the business produces maximum production and profit with limited resources.

Stochastic Chance Constrained Programming Model For Multi Criteria Decision Making Problems Dame Ifa1 , Opim Salim Sitompul2 , Sutarman3 , Esther Nababan4 1 Graduate 2 Department

School of Mathematics, University of Sumatera Utara of Information Technology, University of Sumatera Utara

3,4 Department

of Mathematics, University of Sumatera Utara

This paper introduces a new combination method of multicriteria decision making. The paper combines two of the most extended multicriteria decision making techniques : AHP & GP. The method is specifically design for situations in which hardly find any decision because of compensation simply do not exist or cannot be modeled by costs in any reasonable way. This loose term refers once more to the fact that constraint violation can almost never be avoided because of unexpected extreme events. For this reason one would rather insist on decisions guaranteeing feasibility as much as possible. Chance constrained programming belongs to that situations for dealing with random parameters. The AHP approach is used in evaluation all criteria such as qualitative and quantitative factors. Then the Goal Programming (GP) model incorporating the constraints to select the best set of all goals without exceeding the limited avalaible resources. Finally, the real example, i.e Design network logistic distribution is applied to this model. The result perform by two packages software : expert choice and Lindo.

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The Rotundity of the space (lp )Λ E. Herawati1 , D.A. Harahap2 1,2 Department

of Math, Universitas Sumatera Utara, Medan 20155, Indonesia

The real sequence space lp for 0 < p < ∞ was introduced by Maddox. Recently, the domain matrix of λ-matrix in the sequence space related to the space lp has been studied by Mursaleen and Noman. In the present paper, the rotundity of the sequence space (lp )Λ is studied.

The model of CVRP Using Sweep Algorithm for Determining The Route of Trash Carrier : Case Study Putri K Nasution1 , Aghni Syahmarani2 1,2 Department

of Mathematics, Universitas Sumatera Utara

Vehicle Routing Problem (VRP) is a model that represents transportation problems and has many classications, one of them is Capacity Vehicle Routing Problem (CVRP). CVRP is one of the transportation models that has limited carrying capacity of goods that must be delivered to somewhere. The aim of this research is to nd a CVRP model for routing of trash carrier problem in Medan with sweep algorithm. The sweep algorithm has an accuracy rate about 90consists of two stages, clustering the location of the trash source and making route for each location of the trash source by the Nearest Neighbor method.

Implementation of Generative ConvNet Learning on Generating Modern Batik Pattern Maulida Yanti, Putri K Nasution Universitas Sumatera Utara

This research aims to implement Generative ConvNet for generating modern batik patterns. Batik is one of traditional fabric from Indonesia. Automatic batik generating is useful to enrich batik motive. Generative ConvNet is a generative random field model that can learn the filters without relying on the pre-learned filters. This learning can be used to generate blend pattern based on training images. The experiment results show that Generative ConvNet is possible to produce attractive batik pattern.

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The m-Competition Index of Primitive Two-Colored Wielandt Digraphs Hari Sumardi1 , Saib Suwilo2 , Mardiningsih3 1 Graduate

School of Mathematics Education, Bengkulu University

2,3 Department

of Mathematics, Universitas Sumatera Utara

A two-colored digraph D(2) is a digraph each of whose arcs is colored by red or blue. An (h, l)-walk in a two-colored digraph D(2) is a walk consisting of exactly h red arcs and l blue arcs. A strongly connected two-colored digraph is primitive provided there exist nonnegative integers h and l such that for each ordered pair of vertices vx and vy there is a (h, l)-walk for vx to vy . The competition index of a primitive two-colored digraph is the smallest positive integer h + l such that for each pair of vertices vx and vy there is a vertex vp such that there are (h, l)-walks from vx to vp and from vy to vp . For some positive integer m ≥ 1, we generalize the notion of competition index of primitive two-colored digraph to that of m-competition index of primitive two-colored digraphs. For a primitive two-colored digraph D(2) on n vertices {v1 , v2 , . . . , vn } and a positive integer m with 1 ≤ m ≤ n, the m-competition index of D(2) is the smallest positive integer h + l over all nonnegative integers h and l such that for every pair of vertices vx and vy in 0 D(2) , there exist m distinct vertices v10 , v20 , . . . , vm with the property that there are directed

(h, l)-walks in D(2) from vx to vt0 and from vy to vt0 for each 1 ≤ t ≤ m. We study the m-competition index of primitive two-colored Wielandt digraphs.

Optimization of Scheduling Tutors with Linear Goal Program Herlin Nikmah1 , Sutarman2 , Open Darnius3 1,2,3 Department

of Mathematics, Universitas Sumatera Utara

This article presents a linear goal program model for the problem of scheduling tutors in private junior high school whose mission is to provide qualied educational services by paying attention to the potential and individual needs. In term of scheduling concept that includes about producing individual schedule arrangement which teaching day pattern is adjusted to tutors time, in the planning cycle which is provided, it must produce good scheduling in order to make better credibilty of tutors . The useful objective function minimizes undesirable deviation variables or the number of irregularities weighted by paying attention to the constraints which is associated with the regulations of private junior high school (hard constrains) and considering the needs of each tutor (soft constraints). This model is solved by Linear Goal Program. The results of scheduling tutors by using the linear goal program model is better than creating the schedules manually.

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Numerical Solution of Linear Differential Equations with ordr-n using Finite Difference Methode Aghni Syahmarani1 , Putri Khairiah Nasution2 1,2 Department

of Mathematics, Universitas Sumatera Utara

Difference finite methode is one of the numerical approximations to solve differential equations. A finite difference method proceeds by replacing the derivatives in the differential equations with finite difference approximations. This gives a large but finite algebraic system of equations to be solved in place of the differential equation, something that can be done on a computer. The aim of this research is to find the general solution of numerical solution to solve linear differential equations, both ordinary differential equation and partial differential equation with order-n. We will also make a matlab program to solve this problems.

Penjadwalan Perawat Rumah Sakit menggunakan Fuzzy Goal Programming Kiki Fatmala1 , Sutarman2 1,2 Department

of Mathematics, Universitas Sumatera Utara

Nurse scheduling is a problem in health institutions that is complicated to solve, especially nurses who work in the hospital Emergency Unit. The Emergency Department is a 24 hour busy room and nurses must always be ready for morning, evening and night shifts. Nurse scheduling which is usually made by the head nurse manually does not provide an optimal solution. The purpose of this study was to determine the scheduling of hospital nurses using fuzzy goal programming. The results of this study show that scheduling hospital nurses using fuzzy goal programming is better than scheduling hospital nurses that are made manually.

Modeling capacitated vehicle routing problem (CVRP) on vehicle capacity Desy Nata Fristati1 , Herman Mawengkang2 , Sawaluddin3 1,2,3 Department

of Mathematics, Universitas Sumatera Utara

VRP is generally dened as a matter of determining the route for a number of vehicles, that aim to minimize total transportation costs and meet a number of restrictions that reect the characteristics of the real situation. CVRP as one kind of VRP, CVRP discusses the optimization of the costs of a number of homogeneous capacity vehicles that serve customer demand from adepot. This paper discusses the minimization of costs on shipping goods with homogeneous vehicle capacity. CVRP aims to minimize the number of vehicles and the total cost.

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Share-Of-Choice Problem Models with Heuristics Rima Aprilia1 , Rina Widya Sari2 , Rina Filia Sari3 1,2,3 Majoring

in Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sumatera Utara

Products and services can be considered as a collection of attributes which consist of many levels. A consumer usually will consider to exchanges between various needs and levels before decide to buy a product. The popular way to measure the success of a new product is calculating the amount of market share. It is expected to be taken in a competitive market. In this case using a share-of-choice problem model that aims to maximize the number of respondents from conjoint research. Conjoint research prefer to a new product and give to the status quo of their products. The share-of-choice problem is NP-Hard, Heuristics are seen as being able to solve problems Share-of-choice.

A Stochastic Programming Approach for solving Feature Selection Technique in Sentiment Analysis Mochamad Wahyudi1 , Muhammad Zarlis2 , Herman Mawengkang3 , Syahril Efendi4 1 Graduate

School of Computer Science, Universitas Sumatera Utara

2,3,4 Department

of Mathematics,Universitas Sumatera Utara

The opinion from people can be adopted as important piece of information for most of the management during the decision making process. The Internet and social media provide a major source of information about peoples opinions. Due to the rapidly-growing number of online documents, it becomes both time-consuming and hard to obtain and analyze the desired opinionated information. The exploding growth in the Internet users is one of the main reasons that a method called sentiment analysis can help in extracting information about the opinion of people to classifies whether the opinion is positive or negative. One of the approach in solving the sentiment analysis is feature selection method. However this technique contains a combinatorial behaviour and the analysis of the huge data can experience uncertainty parameter. This paper proposes a stochastic programming approach for solving the feature selection technique in order to obtain a decision from sentiment analysis..

Clarke and Wright Savings Algorithm as Vehicle Routing Problem With Simultaneous Pickup And Delivery (VRPSPD) Solution (Case Study: PT.PINANG BARIS LANGIT BIRU) Fadlah Tunnisak1 , Sutarman2 1,2 Fakultas

Matematika dan Ilmu Pengetahuan Alam Universitas Sumatera Utara

Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) is one typr of Vehicle Routing Problem (VRP) which the solution ultimately aims to get the minimum travel route. VRPSPD is a problem where the vehicle does a single stop for pickup and delivery of goods. This study aims to form a VRPSPD mathematical for the problem of the 3 Kg LPG gas distribution route PT. Pinang Baris Langit Biru using the clarke and wright savings algorithm. This algorithm uses the concept of savings distance and time and starting the process from 27

customers who have the biggest saving value. Based on the calculations carried out in solving the VRPSPD problem with clarke and wright saving algorithm, the total distance traveled by the vehicle is 160,75 km while the total distance traveled by this company is 201 km. thus the clarke and wright savings algorithms are able to provide mileage savings by a percentage of 20,03

Optimization for Supply Chain Planning of Crude Palm Oil Industry Lilis1 , Opim S. Sitompul2 , Saib Suwilo3 , Sutarman4 1 Graduate 2 Faculty

School of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara 3,4 Department

of Mathematics, Universitas Sumatera Utara

Crude palm Oil (CPO) industry belongs to an important business which has a network system, due to the fact that this product is not an end-product. The network system performs procurement of materials, then processing these materials into intermediate and finished products, and distribute of these intermediate/ finished products to customers. These process is called supply chain system. In this paper, the CPO milling industries does not have their own oil palm plantation, the FFB are supplied by surrounded public oil palm plantations. The availability of FFB is limited, therefore the management needs to choose from which plantations would be met the demand. This paper addresses a mixed integer linear programming model for the supply chain integrated problem, combined with waste processing. The mathematical programming model is solved using direct search approach

A Development of Extreme Studentized Deviation Method in Detecting Bivariate Data Outliers Candra Ardodo Simbolon1 , Open Darnius2 1,2 Fakultas

Matematika dan Ilmu Pengetahuan Alam Universitas Sumatera Utara

Extreme Studentized Deviation (ESD) method is one of the outlier detection for both single and multiple outliers in the case of univariate data. In this paper a development method of ESD is proposet to detect outlier for the case of bivariate data.The development of method is considered through a distance function.Furthermore the eucledean distance function is used to detect outliers of a sample data set as an example.

Study Vehicle ROuting Problem Using Nearest Neighbor Algorithm Rio Ferdiani Harahap1 ,Sawaluddin2 1,2 Department

of Mathematics, Universitas Sumatera Utara

Vehicle routing problem (VRP) has a key role in logistics management. VRP plays a role in designing the optimal route used by a number of vehicles placed at the depot to serve a number of customers with known requests. To solve the VRP, the nearest neightbor algorithm used to get the most optimal results. The Nearest Neightbor algorithm is a heuristic method which is done by starting the starting point then looking for the nearest point.

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Integrated Production Planning Model With Grace Period Of Loading Process And Safety Stock Lusiana Tarihoran1 , Sutarman2 1,2 Faculty

of Mathematics and Natural Sciences Universitas Sumatera Utara

The purpose of this article is to discuss a production planning model using linear programming. Inventories that are always excessive cause an increase in inventory costs, to overcome the problem of availability of goods, it is necessary to have a production plan to balance production capacity with the available resources so as to achieve minimal costs. From the results of the study, it is expected that producers can carry out planning by considering the grace period of the loading process and with sufficient amount of safety stock in order to meet the demand well.

An Algoritma Based on Genetic Optimization for Minimum Connected Dominating Set Problem Muhammad Ridwan Mukti1 , Mardiningsih2 1,2 Department

of Mathematics Universitas Sumatera Utara

In this paper we propose for minimum connected dominating set problem wtih algoritma Genetic. A Genetic Algorithm (GA) is a stochastic search method which is inspired by natural biological evolution. In this paper we present an application of genetic optimization to the minimum connected dominating set problem, which is an NP-hard combinatorial optimization problem. Given an input graph, valid solutions are connected subgraphs of the given input graph. Given an undirected graph G = (V, E), a subset S ⊆ V of the vertices of G is called a dominating set of G, if each vertex v ∈ V is either a member of S, or connected to at least one vertex from S by means of an edge from E.

Optimization model of water distribution network problems using a linear programing Jelita Permata Sari1 , Sawaluddin2 1,2 Faculty

of Math and Science Universitas Sumatera Utara

The increasing number of population and the extent of residential areas will affect the need for clean water which is limited in number. Therefore an optimization of the water distribution network is needed so that water can always be available and can meet the needs of consumers. in this paper we will discuss about optimization model of water distribution network problems using a linear programing.

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Comparison of Completion of VAM, TOCM-SUM Transportation Problems with Stepping Stone to Determin Optimal Solutions Loria Amisah Lubis1 , Mardiningsih2 1,2 Department

of Mathematisc Universitas Sumatera Utara

This paper discusses to optimize the path and find out the distribution of minimum transportation costs using the VAM (Vogels Approximation Method) method, TOCM-SUM is then optimized through the stepping stone test. The VAM method is one of the methods of preparing a feasible initial solution table by determining the distribution allocation to the cell that has the least cost. TOCM-SUM method to find a suitable initial solution of the transportation problem. The optimal stepping stone test aims to test the initial solution table by calculating the cost of empty cells that are passed by the stepping stone path.

Smart Analysis and Planning’ Data: From Big Data to Value Propositions Gayus Simarmata1 , Saib Suwilo2 , Opim Salim S3 , Sutarman4 1,2,3,4 Universitas

Sumatera Utara

Big data has great potential to generate business value. Advances in tools and technology that have been ongoing over the last few years have created new ecosystems full of opportunities for data-based innovation. However, as the amount of available data rises to new heights as well as its complexity, analysis needs to be used. Smart analysis and planning as part of smart farming contains big data. This article will analyze smart analysis and planning data to a value proposition.

A constrained based approach for solving the multi-period singlesourcing problem Adi Suarman Situmorang1 , Heman Mawengkang2 , Tulus3 , Opim S Sitompul4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

In this paper we propose a direct search algorithm for solving multi-period singlesourcing problems. In partiular, we generalize the strategy of releasing nonbasic variables from their bounds, combined with the acrive constraint method that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem, as well as variants of the GAP.

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An optimization Model for Supply Chain System with Several Echelon Amin Harahap1 , Herman Mawengkang2 1 FMIPA 2 Department

FKIP Universitas Labuhan Batu

of Mathematics, University Sumatera Utara

In this paper we consider a supply chain problem that will give significant benefit to the industry,. By using the guaranteed service approach to model the multi-echelon stochastic inventory system, we develop an MINLP model to optimize the costs of transportation, inventory and network structure of a multi-echelon supply chain. For solving the model we improve a direct search approach using a strategy of releasing nonbasic variables from their bounds, combined with the active constraint method. This technique is used in order to force the appropriate non-integer basic variables to move to their surrounding integer points. Then we use a heuristic method to get a better integer feasible solution.

A constrained based approach for solving the multi-period single-sourcing problem Adi Suarman Situmorang1 , Herman Mawengkang2 , Tulus3 ,Opim S Sitompul4 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2,3 Department 4 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

In this paper we propose a direct search algorithm for solving multi-period single-sourcing problems. In partiular, we generalize the strategy of releasing nonbasic variables from their bounds, combined with the acrive constraint method that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem, as well as variants of the GAP.

Generalized Reduced Gradient Approach for Solving Heterogeneous Vehicle Routing Problem with Side Constraints Herman Mawengkang1 , Sutarman2 1,2 Department

of Mathematics, Universitas Sumatera Utara

In order to deliver customers demand economically, such as, goods, meals etc it is often the delivery company relies on a model which is called vehicle routing problem (VRP). This model consists of a customer population with deterministic demands, and a central station which acts as the base of a set of vehicles. The objective is to design the vehicle routes starting and terminating at the assigned central station, such that the customer demands is met, within a time windows This paper develops an optimization model for the management of periodic deliveries of a given commodity. Due to the geographic location of customers the company needs to have different type of vehicles with different capacity to serve the commodity for customers. This kind of problem is called Periodic Heterogeneous Vehicle Routing Problem (PHVRP). The goal is to schedule periodically the deliveries according to feasible combinations of delivery days and to determine the scheduling of fleet and driver and routing policies of the vehicles. The aim 31

is to minimize the overall costs of all routes over the planning horizon. We propose a combined approach of reduced gradient and heuristic algorithm to solve the problem

The Dynamic Selection of Coordination Mechanisms for Sustainable School Using Markov Process Maxtulus Junedi Nababan1 , Opim S. Sitompul2 , Tulus3 , Sutarman3 1 Graduate 2 Faculty

School of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara 3 Department

of Mathematics, Universitas Sumatera Utara

This paper presents and evaluates a decision making framework that enables autonomous agents to dynamically select the mechanism they employ in order to coordinate their interrelated activities for sustainable school. Adopting this framework of Markov Process means coordination mechanisms move from the realm of something that is imposed upon the system at design time, to something that the agents select at run-time in order to ?t their prevailing circumstances and their current coordination needs. Using this framework, agents make informed choices about when and how to coordinate and when to respond to requests for coordination. The framework is empirically evaluated, in a grid world scenario, and we highlight those types of environments in which it is effective .

Optimization Method of Selecting Control Strategy In Life System Approach With Big Data Gayus Simarmata1 , Saib Suwilo2 , Opim S. Sitompul3 , Sutarman2 1 Graduate

School of Mathematics, Universitas Sumatera Utara

2 Department 3 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara

A life system concept can be regarded as a theoritical base for systems approach to population ecology. There are two different aspects of regulation in population should be considered, i.e., m− and v− stability. The quantitative characteristics of population dynamics pattern which depends on the structure of the life system is explored in this paper. Then we propose an optimization model for selecting the control strategy considering environmental uncertainty which involves big data.

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Spatial Regression Model of Poverty in The Province of North Sumatera on 2017 Yohana Tambunan1 , Open Darnius2 1 Undergraduate 2 Department

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

The research is done to determine the model of poverty in the Province of North Sumatera with spatial regression, to analyze the factors that affect it and to definite the effective spatial regression in analyzing it. Spatial regression used is Spatial Autoregressive Model (SAR). The data used is secondary data from Statistics Indonesia of Province of North Sumatra. The result shows that predictor variables which affect the response variable are The Index of Human Development (X3 ) and The Percentage of Population Density (X4 ) . The value of (R2 ) is 72:78%.

Modelling of Risk Factors that Inluence Malaria Infection using Binary Logistic Regression Dessy Siahaan1 , Open Darnius2 1 Undergraduate 2 Department

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

Malaria is a parasitic disease that is currently endemic in many countries, including in Indonesia. Batubara District in North Sumatera is one of the malaria-endemic areas. This study was conducted to make a mathematical model based on risk factors that influence malaria infection. The data used is secondary data from other researchers. The method used to model risk factors that influence malaria infection is the binary logistic regression with a categorical response variable, namely diagnosis by microscopic examination. There are 10 variable predictors; mosquito nets (X1 ), quality use of mosquito nets (X2 ), condition of the living environment (X3 ), knowledge (X4 ), attitudes (X5 ), actions (X6 ), quality of health workers (X7 ), use of mosquito coils (X8 ), use of topical insect repellent (X9 ), and access of health workers (X10 ). Maximum likelihood estimation method is used to findout the parameter estimates. From the 10 predictor variables studied, it was found that only 8 variables had a significant effect on the model. Based on the odds ratio, the most significant variable is the quality of health workers with 16,5. The magnitude of the influence of predictor variables on the response variable in the model formed is 87;8%. The classification function in this study is 96;3%.

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Multi-Criteria Model of Logistic System And Waste Management In Crude Palm Oil Industry Meslin Silalahi1 , Herman Mawengkang2 1 Tapanuli 2 Department

University, Siborong-borong, Indonesia

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

The crude palm oil (CPO) industry plays an important role for economic development However, it contributes to environmental degradation from both input and output sides at the milling process, such as high water consumption, the generation of a large amount of wastewater with a high organic content, and the generation of a large quantity of solid wastes and air pollution. From the environmental economics point of view, there would be three objectives which are necessarily to be satisfied. Therefore the formulation can be built in the form of a multi-criteria programming model. We develop an interactive approach for tackling logistics and environmental risk production planning problem for the crude palm oil industry.

The Concept Model of The Development of An Academic Data Processing System for Students Integrated Through A Database Using The Hierarchy of Grid Partition (HGP) Method Verdi Yasin1 , Muhammad Zarlis2 , Opim Salim Sitompul3 , Poltak Sihombing4 1 Graduate

Program in Computer Science, Universitas Sumatera Utara

2,4 Department 3 Department

of Computer Science, Universitas Sumatera Utara

of Information Technology, Universitas Sumatera Utara

Current developments in academic data are increasing and increasing, making researchers interested in conducting research in order to ensure student entities, especially validation of student data certainty, including ways to facilitate the process of finding student data, when verifying data certainty such as related attributes in a student, including: Student Number. Student Name, Place of Birth, Date of Birth, Gender, Study Program, College Name, Diploma Number, and other supporting data. Some of the attributes mentioned above are object attributes that need to be integrated into the data processing concept model in order to facilitate verification and validation through smart phone numbers or through the internet, using the hierarchical method of grid partitioning. As a solution to the above problems, the researchers formulated an integrated data processing system model between the academic attributes of the student data, so that it was easy to get information related to the student academic record entities. In describing the concept of this integrated data processing model, researchers also use object-oriented analysis with unified modeling language (UML) design tools, while also using structured entity relationship diagram (ERD) modeling relationships. From the above explanation it can be concluded that the processing of student academic data, in view of the need to create an appropriate model to overcome the difficulties in ensuring the academic data of students at a college.

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Social Impact for Negatif Hoax Character Recognition user Behavior Using Backpropagation Neural Network (BPNN) R Syah1 , H Mawengkang2 , M Elveny3 1 1Informatics

Engineering, Universitas Medan Area, Medan, Indonesia

2,4 Department 2 Faculty

of Mathematics, Universitas Sumatera Utara

of Computer Science and Information Technology, Universitas Sumatera Utara, Medan, Indonesia

Social Impact is currently often misused, including the distribution of news readings in the media interaction of character users usually do it repeatedly. so it is necessary to approach the BackPropagation Neural Network method in it. This approach can accomplish many criteria in reading the pattern of character image detection, with the aim that the introduction goes with maximum filtering and approach. Extraction feature in this case is one way to recognize objects by looking at certain characteristics that are mapped patterns based on the characteristics possessed by the character image. Research on the filtering image amount of 150 photo by using BPN to do the learning process over and over again. Targeted news that have been shared into 15 blocks then converted to target distribution users. The training process is only done once for the type and the same font size that starts with the font type arial, size 6, size 10. character photo Results Introduction of user behavior ranges from 75-95.75%. While the negative Hoax ranges from 80-90%.

Determination Robust Requirement of Consensus System MR Syahputra1 , IH Rambe2 , H Mawengkang3 1,3 Department

of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sumatera Utara

2 1Mathematics

Education, Faculty of Teacher Training and Education, Universitas Islam Sumatera Utara, Indonesia

Multi agent system problems are usually represented by communication graphs. Each agent has an uncertainty condition that is modeled as norm bounded uncertainty. This paper will discuss the requirements for achieving robust consensus conditions. The conditions achieved are characterized by the eigenvalue of the Laplace matrix of a communication graph.

Application of Genetic Algorithm Method in Optimization of Irrigation Water Flowing Scheduling System: A Case Study of Keuliling Reservoir in Aceh Besar District, Indonesia Siti Rusdiana1 , Zahnur2 1 Department

of Mathematics, Syiah Kuala University

2 Department

of Informatics, Syiah Kuala University

Keuliling Reservoir which is located in Kuta Cot Glie, Aceh Besar is one of the reservoirs that has a function as a provider of water for irrigation needs, supports food selfsufficiency programs and others. The reservoir area has limited volume of water so, the most important water-saving irrigation water should be done to determine the scheduling of the distribution of irrigation water to the area of rice fields. The purpose of this research is to develop a method that can be used to the calculation of scheduling and can be applied to the irrigation of the Keuliling Reservoir 35

watershed in Aceh Besar. In this study, the Genetic Algorithm method was used to determine the optimization of the Keuliling Reservoir in Aceh Besar District. From the analysis that has been done, the scheduling process carried out so far is 72 hours where the amount of water entering the rice fields is 1,038,211,600 liters and is wasted into the river by 257,788,400 liters. The best irrigation time obtained is based on the results of calculations using the 48 Genetic Algorithm method in which the amount of water entering the rice field area is 794,149,300 liters and is wasted into the river by 69,850,700 liters.

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