Judul: Application of Hungarian Algorithm Based on König and Egerváry Theorem in Assignment Problem
Abstrak: Masalah penugasan dapat dimodelkan dalam suatu bentuk integer programming. Masalah penugasan timbul akibat masing-masing sumber daya memiliki tingkatan efisiensi yang berbeda dalam menjalankan tugas yang berbeda. Karena itu pengalokasian sumber daya untuk mengerjakan tugas secara efisien merupakan keputusan yang penting. Secara umum, masalah penugasan dapat dituliskan sebagai pengalokasian sejumlah sumber daya ke sejumlah tugas agar mengoptimumkan suatu fungsi objektif tertentu. Salah satu metode yang dapat digunakan dalam masalah penugasan adalah metode Hungaria. Metode Hungaria merupakan algoritme yang diperkenalkan oleh Harold W. Kuhn, algoritme ini dikembangkan berdasarkan hasil kerja Denes König dan Jeno Egerváry. Tujuan dari penulisan karya ilmiah ini adalah mengkaji secara teoretis Teorema König dan Egerváry dan menerapkan algoritme Hungaria pada suatu kasus masalah penugasan. Teorema akan dikaji dengan pembuktian beberapa teorema teori graf terkait dan dengan teorema dualitas. Dalam karya ilmiah ini diterapkan algoritme Hungaria dengan kompleksitas O(n^4)., The assignment problem can be modeled as an integer programming. Assignment problems arise because each resource has different level of efficiency to perform different tasks. Therefore, allocating resources to perform tasks efficiently is an important decision. In general, assignment problem can be described as allocating a number of resources to a number of tasks in order to optimize a certain objective function. One method that can be used to solve assignment problems is the Hungarian method. Hungarian method is an algorithm introduced by Harold W. Kuhn, this algorithm was developed based on the work of Denes König and Jeno Egerváry. The purpose of writing this paper is to theoretically examine the König and Egerváry Theorem and apply the Hungarian algorithm to one case of the assignment problems. The theorem will be examined by proving several related graph theory theorems and the duality theorems. In this paper, the Hungarian algorithm with O(n^4) complexity is applied.
Keyword: assignment problem, Hungarian algorithm, König and Egerváry theorem

Judul: Penjadwalan Kegiatan Mengajar Bimbingan Belajar Menggunakan Integer Linear Programming: Studi Kasus Bintang Pelajar Cikarang
Abstrak: Penjadwalan menjadi salah satu permasalahan yang sering dihadapi dalam penugasan suatu organisasi termasuk lembaga pendidikan, salah satunya yaitu bimbingan belajar. Penjadwalan ini melibatkan kombinasi antara banyaknya tenaga pengajar, mata pelajaran, kelompok belajar, sesi belajar, dan ketersediaan ruangan. Tujuan dari penelitian ini adalah memodelkan masalah penjadwalan dengan meminimumkan bobot sesi belajar setiap kelompok lalu mengimplementasikan model tersebut pada masalah penjadwalan kegiatan mengajar di Lembaga Bimbingan Belajar Bintang Pelajar Cikarang. Masalah tersebut diselesaikan menggunakan integer linear programming. Dengan bantuan software Lingo 19.0 diperoleh solusi optimal berupa jadwal kegiatan mengajar untuk periode waktu satu bulan yang memenuhi seluruh kendala., Scheduling is one of the problems faced in the assignment of an organization including educational institutions, one of which is tutoring. This scheduling involves the number of teaching staff, subjects, study groups, study sessions, and room availability. The purpose of this study is to model the scheduling problem by minimizing the weight of each group's study sessions and then implement the model on the scheduling teaching activities at Tutoring Institutions Bintang Pelajar Cikarang. That problem was solved using the integer linear programming method. With the help of Lingo 19.0 software, an optimal solution is obtained in the form of a teaching activity schedule for one month that satisfies all constraints.
Keyword: Bintang Pelajar Cikarang, integer linear programming, learning session weight, scheduling, tutoring institutioins

Judul: Thermal Characteristics and Dynamics of Tropical Cyclone over Western North Pacific Ocean: A Case Study of Typhoon Songda (Chedeng) 2011
Abstrak: The frequent occasion of Tropical Cyclone (TC) over Western North Pacific (WNP) Ocean lies from 10˚N to 26˚N and 121˚E to 170˚E. Sources of TC development come from warm ocean temperature where latent heat is released during condensation processes and subsequently concentrated in the boundary layer. Relative humidity at 850-700 hPa is responsible to produce the most intense storm. Meanwhile, weak vertical wind shear between 850-200 hPa is one of the dynamical factors that lead to the development of TC. Pressure level of 850-200 hPa is chosen to minimize the thermodynamic effect in the lower troposphere. Typhoon Songda (Chedeng in the Philippines) or TSC lasted from May 18th to 30th, 2011 and strengthened into powerful Super Typhoon stage between May 24th and 27th. Long curving track and the exhibition of all sequences of TC life cycle, TSC is then considered as an ideal case of TC. The objective of the study with case of TSC is to investigate the role of thermal characteristics and dynamics on TC intensity. The research is carried out by using Advanced Research of Weather Research and Forecasting model (WRF ARW model) version 3.3. Two domains are employed in the model. The first domain situate from 02˚N to 40˚N and 118˚E to 149˚E and cover spatial resolution () of 33.1 km. The second domain situate from 09˚N to 27˚N and 119˚E to 132˚E with of 11 km. Timestep of the model () is 120 seconds. The model is supported by the following physical parameterization, i.e., Yonsei University Scheme (YSU) in the boundary layer, Kain-Fritsch scheme (KF) in the cumulus, and WRF Single-Moment 3-class scheme in the microphysics. Initial meteorological condition prior to the formation of the cyclone is generated using WRF ARW standard-release model. Sensitivity of the model output is obtained from a selected single-parameter change scenarios, namely, 10 % to 20 % decrease and increase of wind shear initial data at 850-200 hPa, and by 10 % to 20 % decrease of relative humidity initial data at 850-700 hPa. The result showed that the negative correlations between wind shear and intensity are found in wind shear scenarios. Wind shears of 10 ms-1 which lead to strengthening of the wind intensity in the early period of Typhoon development are found in wind shear scenarios. The effect of wind shear changes on wind intensity is statistically significant in the 20 % wind shear scenarios. During mature stage, weak wind intensity occurred when wind shear increase as given in the WRF standard-release and the 20 % decreasing scenario. Different situation is found in the 20 % increasing scenario where wind shear tend to weak and lead to strong wind intensity at this stage. Meanwhile, the reduction of moisture supply at 850-700 hPa resulting from 20 % decreasing relative humidity play a major role in the weakening of wind intensity and reduces mechanical energy of the cycle process as much as 300 J kg-1.
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