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"Facility location merupakan salah satu strategi penting bagi perusahaan atau fasilitas. Facility location dapat membantu pengambilan keputusan dalam penetapan lokasi atau relokasi suatu fasilitas. Pengambilan keputusan dengan kondisi adanya kompetisi di antara dua pihak sering disebut competitive facility location problem (CFLP). Dua pihak yang saling bersaing disebut leader dan follower. Tujuan leader adalah menentukan sehimpunan lokasi untuk membuka fasilitas yang dapat memaksimalkan keuntungannya dengan kondisi bahwa follower juga akan membuka beberapa fasilitas dan dapat merebut sejumlah konsumen dengan tujuan memaksimalkan keuntungannya sendiri. Model matematis CFLP bisa dimodelkan dalam bilevel integer programming problem yang terdiri dari upper level problem dan lower level problem. Karena adanya kemungkinan tidak uniknya solusi optimal untuk lower level problem, maka konsep optimality harus diperhalus, sehingga solusi optimal untuk masalah CFLP merupakan solusi optimal nonkooperatif.

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Facility location is one of the most important strategic to many business or facilities. Facility location problem support decision makers in the planning process of establishing or relocating existing facilities. Decision making process in competition between two firms usually called competitive facility location problem (CFLP). Two competing side usually called leaders and followers. The leader?s problem consist in choosing a set of opening facilities which yields maximal profit in the conditions that the followers will open some facilities and can captures consumers aiming to maximize his own profit. Mathematical model of CFLP can be modelled as bilevel integer programming problem that consist of upper and lower level problem. Owing to the possible nonuniqueness of optimal solution in the lower level problem, the concept of optimality has to be refined, so we called the optimal solution of CFLP as noncooperative optimal solution."

"Permasalahan tata letak fasilitas, khususnya dengan luas departemen yang tidak sama UAFLP , merupakan salah satu masalah yang dipelajari dalam combinatorial optimization dan telah mendapat perhatian dari banyak peneliti dalam satu dekade terakhir. Penelitian menggukanan masalah-masalah yang telah diketahui secaraumum sebagai masalah standar dalam permasalahan tata letak fasilitas. Terdapat beberapa masalah yang belum menemukan solusi yang optimal dan juga membutuhkan waktu komputasi yang cukup lama. Penelitian ini akan mengembangkan suatu model matematika dengan menggunakan metode Mixed Integer Programming berdasarkan pada Flexible Bay Structure, salah satu model representasi yang umum digunakan dalam UAFLP. Metode ini akan memenuhi kendala yang muncul sepanjang proses pembentukan hasil akhir. Tujuannya untuk mengurangi solusi yang tidak feasible sehingga dapat mengurangi kompleksitas solusi yang mungkin. Beberapa fungsi kendala tambahan akan dicoba untuk ditambahkan ke dalam model. Pengujian dilakukan dengan membandingkan kepengaruhan setiap fungsi kendala tambahan yang memiliki pendekatan yang berbeda-beda dalam memotong kompleksitas solusi yang mungkin. Hasil perbandingan kombinasi fungsi kendala yang dipakai menunjukkan fungsi kendala mana yang memiliki pengaruh besar dalam mengurangi waktu komputasi model. Sebagian besar hasil dari penelitian ini mendekati hasil terbaik yang diketahui.

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Facility layout problem, especially with the unequal departmental area UAFLP , is one of the problems studied in combinatorial optimization and has received the attention of many researchers in the past decade. The research used commonly known problems as a standard problem in facility layout problems. There are some problems that have not found the optimal solution and also require a long computation time. This research will develop a mathematical model using Mixed Integer Programming method based on Flexible Bay Structure, one of the common representation models used in UAFLP. This method will meet the constraints that arise throughout the process of forming the final result. The goal is to reduce nonfeasible solutions so as to reduce the complexity of possible solutions. Some additional constraint functions will be attempted to be added to the model. Testing is done by comparing the effect of each additional constraint function that has different approaches in cutting the complexity of possible solutions. The comparison result of the combination of the constraint function used indicates which constraint function has a major influence in reducing the computation time of the model. Most of the results of this study approached the best known results."

"ABSTRACTIn this paper, we introduce a new variant of Location Routing Problem with the name of Location Routing Problem with Arc Time Windows (LRP ATW), which emerges from the need of safe transportation in terror zones. In this specific problem, there are arc time windows on the arcs (roads) for transferring the vehicles like trucks and articulated lorries which means that these roads can be used for a specific period of time during a day. Within the scope of this paper, the problem and assumptions are described, and a Mixed Integer Programming (MIP) formulation is developed to solve the problem. Bounds are also improved using valid inequalities. The quality of the formulation is measured using the test problems in the literature. Computational results show that the proposed MIP formulation gives good quality results in a short computation time."

"Salah satu dari masalah-masalah dominan pada komputasi biologi molekuler adalah penyejajaran barisan berganda (Multiple Sequence Alignment - MSA) dari DNA. Banyak metode yang telah diajukan untuk menyelesaikan masalah MSA seperti pemrograman dinamik dan heuristik. Satu metode telah diajukan oleh Althaus et al. untuk menyelesaikan masalah MSA yang didasarkan pada pemrograman linear bilangan bulat (Integer Linear Programming - ILP). Formulasi ILP umum dari masalah MSA diturunkan dari representasi graf dari masalah MSA. Walaupun formulasi ILP umum dari masalah MSA diketahui, membentuk model ILP dari suatu masalah MSA yang dapat diselesaikan langsung menggunakan suatu solver ILP tidaklah mudah. Sebuah program yang dapat membangun dan menyelesaikan model ILP dari sebuah masalah MSA menggunakan MATLAB telah dibuat. Metode yang digunakan untuk menyelesaikan model ILP tersebut adalah branch-and-bound. Program yang telah dibuat dapat menghasilkan model ILP dari sembarang masalah MSA yang diberikan tetapi hanya dapat menyelesaikan masalah MSA dari sejumlah kecil barisanbarisan DNA yang pendek. Hasil dari program tersebut adalah penejajaran barisan-barisan DNA dari masalah MSA yang diberikan.

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One of the dominant problems in computational molecular biology is multiple sequence alignment (MSA) of DNA. Many methods have been proposed to solve MSA problem such as dynamic programming and heuristic. A method has been proposed by Althaus et al. to solve MSA problem which is based on integer linear programming (ILP). The general ILP formulation of the MSA is derived from the graph representation of the MSA problem. Although we have the general ILP formulation of the MSA problem, constructing the ILP model of an MSA that can be solved directly using an ILP solver is not straightforward. We develop a MATLAB program that can generate and solve the ILP model of an MSA problem. The method that is used to solve the ILP model is branch-and-bound. The constructed program can generate the ILP model of any given MSA problem but can only solve an MSA problem of a small number of short DNA sequences. The result of the program is the aligned sequences of the MSA problem."

"One of the dominant problems in computational molecular biology ismultiple sequence alignment (MSA) of DNA. Many methods have beenproposed to solve MSA problem such as dynamic programming and heuristic.A method has been proposed by Althaus et al. to solve MSA problem which isbased on integer linear programming (ILP). The general ILP formulation ofthe MSA is derived from the graph representation of the MSA problem.Although we have the general ILP formulation of the MSA problem,constructing the ILP model of an MSA that can be solved directly using anILP solver is not straightforward. We develop a MATLAB program that cangenerate and solve the ILP model of an MSA problem. The method that isused to solve the ILP model is branch-and-bound. The constructed programcan generate the ILP model of any given MSA problem but can only solve anMSA problem of a small number of short DNA sequences. The result of theprogram is the aligned sequences of the MSA problem."

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Industri penerbangan Indonesia diprediksi menjadi negara ke-6 di dunia yang memiliki penumpang pasar terbanyak. Jumlah penumpang pasar pada 15 tahun terakhirpun memiliki pertumbuhan yang signifikan, yang berjumlah 30 juta pada tahun 2005 dan ±97 juta pada tahun 2017. Hal ini merupakan sebuah kesempatan bagi PT. X, salah satu maskapai penerbangan di Indonesia, untuk mempersiapkan strategi-strategi yang dapat dilakukan untuk memenangkan pangsa pasar. Untuk mengimplementasikan strategistrategi tersebut, tentunya perusahaan perlu untuk mempersiapkan sumber daya manusia, material, dsb. Namun, berdasarkan laba rugi komprehensif 5 tahun terakhir, perusahaan mengalami defisit yang menyebabkan perusahaan akan fokus terlebih dahulu terhadap permasalahan saat ini sebelum bergerak kepada potensi di masa depan. Pada penelitian ini, peneliti membuat model tentang tail assignment problem, yang merupakan permasalahan dalam membuat jadwal penerbangan terhadap pesawat yang tersedia dengan memerhatikan keterbatasan yang ada. Tujuan dari dibahasnya tail assignment problem agar perusahaan dapat mengurangi jumlah penggunaan pesawat dari penyusunan ulang tail assignment untuk menghilangkan idle dengan mengaggregatkan penerbangan yang satu dengan yang lainnya, dan atau mengurangi jumlah penerbangan agar jumlah pesawat berkurang. Dengan berkurangnya jumlah pesawat, berkurang biaya sewa pesawat, yang merupakan biaya terbesar kedua dari total biaya yang ada. Penelitian ini menggunakan metode optimasi branch & cut, dengan solver engine COIN–OR CBC (Linear Solver).

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The Indonesian aviation industry is predicted to be the 6th country in the world that has the most market passengers. The number of market passengers in the last 15 years also has a significant growth, which amounted to 30 million in 2005 and ± 97 million in 2017. This is an opportunity for PT. X, one of the airlines in Indonesia, to prepare strategies that can be done to win market share. To implement these strategies, of course, companies need to prepare human, material, etc. However, based on the comprehensive income of the last 5 years, the company experienced a deficit that caused the company to focus first on current problems before moving on to future potential. In this study, researchers made a model by using the tail assignment problem, which is a problem in making flight schedules to the available airplane by taking into account existing limitations. The purpose of discussing the tail assignment problem is that the company can reduce the number of airplane usage by rearranging the tail assignment to eliminate idle by aggregating flights with one another and or reducing the number of flights so that the number of airplanes decreases. With the reduced number of airplanes, reduced airplane rental costs, which is the second-largest cost of total costs. This research uses the branch & cut optimization method, with COIN-OR CBC (Linear Solver) engine solver. 

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"ABSTRACTThis paper addresses a new robust multi objective multi period model for supply chain planning under uncertainty considering quantity discounts. The proposed model maximizes the current proht of the distributor by making a balance between the total costs of the supply chain and the distributor company s revenues of selling products and also maximizes the company s expected profit by introducing brands and taking the risk of loss on it. Considering uncertainty in the purchasing cost, selling fees, and demand fluctuations, the new robust multi objective mixed integer programming model is solved as a single objective mixed integer programming model by utilizing the LP metrics method. By settling regulatory penalty parameters and considering different economic scenarios, the robustness and effectiveness of the developed model are verified with the data from BEH PAKHSH Company, a commodities distributor in Iran. The outcomes show that the proposed model is a promising approach to run an efficient supply chain."

"Pemrograman linier (PL) bilangan bulat merupakan bentuk khusus dari pemrograman linier dengan seluruh variabel keputusan berupa bilangan bulat. Salah satu metode yang digunakan dalam menyelesaikan masalah PL bilangan bulat adalah metode branch and bound (B&B). Tugas akhir ini membahas metode perbaikan B&B, yaitu melakukan beberapa tahapan sebelum mengimplementasikan metode B&B. Tahapan yang dilakukan dalam metode perbaikan B&B adalah memperkecil daerah layak dan menghilangkan kendala redundant. Metode ini bekerja secara efisien saat menyelesaikan masalah PL bilangan bulat dengan banyaknya kendala jauh lebih besar dibandingkan banyaknya variabel. Percobaan numerik yang dilakukan menunjukkan tingkat efisiensi dari metode perbaikan B&B sebesar 85% dalam menyelesaikan permasalahan PL bilangan bulat dengan banyaknya kendala 235 lebih besar dari banyaknya variabel.

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Integer linear programming problem is a special form of linear programming with all the decision variables are integers. Branch and bound is one of the methods for solving an integer linear programming problem. This skripsi discusses an improved branch and bound method, which adding several steps before implementing the branch and bound method. New steps in the improved branch and bound method are narrowing down the feasible solution range and removing the redundant constraints.

This method works efficiently in solving an integer linear programming problem with the number of constraints are much more than the number of variables. Numerical experiments show that the efficiency of improved B&B method is about 85% for solving an integer linear programming problem with the number of constraints 235 more than the variables."

"ABSTRAKSpare part merupakan komponen yang esensial yang menunjang perangkat utama, ketika perangkat utama mengalami kerusakan, maka ketersediaan spare part merupakan hal yang sangat krusial. Sebagai contoh spare part dalam bisnis telekomunikasi dimana perangkat telekomunikasi memiliki batasan down time yang di hitung dalam jam, sehingga kebutuhan spare part harus di supply dalam waktu jam. Untuk memenuhi kriteria ini dengan biaya yang optimal, optimasi dalam proses distribusinya sangat diperlukan. Telah banyak penelitian yang dilakukan dalam bidang optimasi jaringan distribusi, namun kecenderungan mengarah pada perpindahan materialnya tanpa mempertimbangkan lokasi-lokasi pendukung dari distribusi, atau lebih sering diteliti secara terpisah. Tujuan dari penelitian ini adalah untuk mendesain jaringan distribusi ang optimal dengan mengoptimalkan perpindahan material dan juga mempertimbankan lokasi-lokasi pendukungnya.

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ABSTRACTSpare part is an essential component that support the main equipment once it down and become an outage once the spare part is not available. With that case the spare part availability become an important point. In some cases of business, the down time of the main equipment is crucial. For example, in the Telecommunication business where the down time tolerance calculated in hours, which is impact in delivery time. To achieve the service level requirement at the appropriate cost, optimization is required. In other research, to achieve the required service level at appropriate cost, optimization mostly considering only material movement cost or transportation cost where building right facility in the location is also very important to ensure the spare parts are delivered on time to the demand location. But building the facility location in demand area will take a huge cost of logistics, without proper planning and understanding demand location. This study aims to design an optimal distribution network by considering not only the material movement cost but also the demand location, facility location, and facility cost"