PENETAPAN DURASI CRASH DENGAN METODE LINEAR PROGRAM UNTUK PROYEK PEMBANGUNAN BOX CULVERT NO 409 PADA JALUR KA DI DAOP 3 CIREBON

Tujuan utama dari suatu proyek ialah menyelesaikan proyek tersebut sesuai dengan durasi dan biayanya. Durasi penyelesaian proyek tersebut disebut sebagai jalur kritis yang dipengaruhi oleh volume pekerjaan dan produktivitasnya. Durasi normal proyek merupakan waktu yang diperlukan untuk menyelesaikan kegiatan dengan sumber daya yang ada (tanpa input tambahan), sedangkan normal cost merupakan biaya yang diperlukan untuk durasi normal. Data durasi normal dan normal cost umumnya diperoleh dari statistik terhadap proyek-proyek serupa yang pernah dilaksanakan. Karena adanya tujuan tertentu, durasi tersebut memungkinkan untuk dipercepat dengan input tambahan, ini disebut sebagai crash program. Pada Proyek KA terdapat aturan bahwa pelaksanaan konstruksi tidak boleh mengganggu operasional KA apalagi sampai memberhentikan atau menutup jalur KA, sehingga Pembangunan Box Culvert No 409 harus dilaksanakan secepat mungkin. Berdasarkan statistik proyek sebelumnya, maka proyek ini direncanakan selesai dalam 92 hari kalender, namun dapat dipercepat menjadi 92 hari kalender

Matroids, Cyclic Flats, and Polyhedra

<p>Matroids have a wide variety of distinct, cryptomorphic axiom systems that are capable of defining them. A common feature of these is that they are able to be efficiently tested, certifying whether a given input complies with such an axiom system in polynomial time. Joseph Bonin and Anna de Mier, rediscovering a theorem first proved by Julie Sims, developed an axiom system for matroids in terms of their cyclic flats and the ranks of those cyclic flats. As with other matroid axiom systems, this is able to be tested in polynomial time. Distinct, non-isomorphic matroids may each have the same lattice of cyclic flats, and so matroids cannot be defined solely in terms of their cyclic flats. We do not have a clean characterisation of families of sets that are cyclic flats of matroids. However, it may be possible to tell in polynomial time whether there is any matroid that has a given lattice of subsets as its cyclic flats. We use Bonin and de Mier’s cyclic flat axioms to reduce the problem to a linear program, and show that determining whether a given lattice is the lattice of cyclic flats of any matroid corresponds to finding integral points in the solution space of this program, these points representing the possible ranks that may be assigned to the cyclic flats. We distinguish several classes of lattice for which solutions may be efficiently found, based upon the nature of the matrix of coefficients of the linear program, and of the polyhedron it defines, and then identify families of lattice that belong to those classes. We define operations and transformations on lattices of sets by examining matroid operations, and examine how these operations affect membership in the aforementioned classes. We conjecture that it is always possible to determine, in polynomial time, whether a given collection of subsets makes up the lattice of cyclic flats of any matroid.</p>

Matroids, Cyclic Flats, and Polyhedra

<p>Matroids have a wide variety of distinct, cryptomorphic axiom systems that are capable of defining them. A common feature of these is that they are able to be efficiently tested, certifying whether a given input complies with such an axiom system in polynomial time. Joseph Bonin and Anna de Mier, rediscovering a theorem first proved by Julie Sims, developed an axiom system for matroids in terms of their cyclic flats and the ranks of those cyclic flats. As with other matroid axiom systems, this is able to be tested in polynomial time. Distinct, non-isomorphic matroids may each have the same lattice of cyclic flats, and so matroids cannot be defined solely in terms of their cyclic flats. We do not have a clean characterisation of families of sets that are cyclic flats of matroids. However, it may be possible to tell in polynomial time whether there is any matroid that has a given lattice of subsets as its cyclic flats. We use Bonin and de Mier’s cyclic flat axioms to reduce the problem to a linear program, and show that determining whether a given lattice is the lattice of cyclic flats of any matroid corresponds to finding integral points in the solution space of this program, these points representing the possible ranks that may be assigned to the cyclic flats. We distinguish several classes of lattice for which solutions may be efficiently found, based upon the nature of the matrix of coefficients of the linear program, and of the polyhedron it defines, and then identify families of lattice that belong to those classes. We define operations and transformations on lattices of sets by examining matroid operations, and examine how these operations affect membership in the aforementioned classes. We conjecture that it is always possible to determine, in polynomial time, whether a given collection of subsets makes up the lattice of cyclic flats of any matroid.</p>

High School Students' Algebraic Thinking Ability in Solving Linear Program ProblemsHigh School Students' Algebraic Thinking Ability in Solving Linear Program Problems

Aljabar merupakan bagian matematika yang berperan penting dalam proses penyelesaian masalah pada bidang matematika maupun bidang ilmu lainnya. Mulai dari konsep-konsep hingga cara berpikir aljabar. Sehingga penting bagi siswa untuk menguasai kemampuan berpikir aljabar. Oleh karena itu penelitian ini akan memberikan gambaran terkait kemampuan berpikir aljabar dalam menyelesaikan masalah matematika. Model penelitian yang digunakan adalah kualitatif analisis deskriptif. Penelitian dilaksanakan pada salah satu SMA di kabupaten Karawang.

Analisis pemahaman siswa SMA kelas XI materi program linear berdasarkan teori apos ditinjau dari gaya belajar

The purpose of this study is to describe the understanding of high school students in class XI linear program material based on APOS theory in terms of learning styles. The researcher chose six subjects consisting of two subjects for each learning style. The results of this study indicate the visual group reaches the highest percentage in the stages of action and objects. At the process stage the auditory group is able to reach the highest percentage. As for the stages of the scheme, almost all subjects of the three learning styles are unable to surpass it well. Tujuan penelitian ini adalah untuk mendeskripsikan pemahaman siswa SMA kelas XI materi program linear berdasarkan teori APOS ditinjau dari gaya belajar. Peneliti memilih enam subjek yang terdiri dari dua subjek untuk masing-masing gaya belajar. Hasil penelitian ini menunjukkan kelompok visual mencapai presentase tertinggi pada tahapan aksi dan objek. Pada tahapan proses kelompok auditori mampu mencapai presentase tertinggi. Sedangkan untuk tahapan skema, hampir semua subjek dari ketiga gaya belajar tidak mampu melampauinya dengan baik.

NEEDS ANALYSIS OF THE DEVELOPMENT STUDENT WORKSHEET BASED BLENDED LEARNING TO ENCOURAGE MATHEMATICAL LITERACY

Mathematical literacy is the ability of students to carry out activities formulate, apply, and interpret & evaluate mathematics in various contexts. This study aims to analyze the needs of student worksheet development which can stimulate students' mathematical literacy. This type of research is a qualitative descriptive study involving 15 students of class XI MIPA and 2 mathematics teachers of SMA Negeri 1 Gresik. This needs analysis includes material analysis, curriculum analysis, and student analysis. The results showed that one of the difficult mathematics materials for class XI MIPA was linear program, mathematics learning was carried out according to the 2013 Curriculum with the application of Blended Learning in the new normal era, and students still had difficulty solving problems on indicators of interpreting & evaluating mathematical process abilities. Therefore, Student Worksheet based Blended Learning will be developed which is more focused on activities that prioritize the interpretation and analysis of problem solving results according to the limitations and context of the problem in the Linear Program material.

Penerapan discovery learning untuk meningkatkan keaktifan dan hasil belajar materi program linear

This study aims to determine the increase in student activity and learning outcomes in Linear Program material through the application of discovery learning learning models. This research was conducted at SMA Negeri 1 Karangrayung, Grobogan Regency, Central Java Province. This research method uses classroom action research with two cycles. Each cycle consists of four stages which include action planning, action implementation, observation of action results, and reflection of action results. The results showed that the average score of student learning activity in the initial conditions was 27.67 (=55.33%) then in the first cycle was 29.83 (=59.67%) and in the second cycle was 38.33 (= 76.67%. While the average value of student learning outcomes in the initial conditions was 65.87 then in the first cycle was 68.77 and in the second cycle was 75.50. The percentage of students' learning completeness in the initial condition is 10.00%, then in the first cycle it is 46.67% and in the second cycle it is 96.67%. Based on the results of the study, it can be concluded that the discovery learning model can increase the activeness and learning outcomes of students in the Linear Program material.

Pengungkapan Aspek Matematis pada Aktivitas Etnomatematika Produksi Ecoprint di Butik El Hijaaz

AbstrakButik El Hijaaz merupakan pengrajin kain ecoprint di Tulungagung yang mengembangkan teknik ecoprint menggunakan bahan alam sebagai pewarna kain dan pencetak motif yang ramah lingkungan. Penelitian dilakukan untuk mengungkap aspek matematika yang terkandung dari proses pembuatan kain ecoprint, seperti membilang, mengukur, mendesain. Tujuan dari penelitian ini adalah mengungkap aspek-aspek matematis dan aktivitas-aktivitas fundamental matematis yang terdapat dalam aktivitas ecoprint di butik El Hijaaz Tulungagung. Penelitian ini menggunakan pendekatan kualitatif dengan metode etnografi yakni observasi, wawancara, dokumentasi. Subjek penelitian yaitu karyawan butik dan pemilik Butik El Hijaaz. Lokasi penelitian yaitu di butik El Hijaaz Kabupaten Tulungagung. Hasil penelitian menunjukan bahwa: 1) aktivitas fundamental yang ditemukan pada proses pembuatan kerajinan kain ecoprint di Galery El Hijaaz antara lain counting, measuring, design, locating, playing dan explaining. 2) Konsep matematis yang dapat diungkap adalah perbandingan, konversi waktu, konversi suhu, konsep membilang, himpunan, konsep pecahan, konsep pengukuran, refleksi, kesebangunan, kongruensi, program linier, aritmatika sosial. Disclosure of Mathematics Aspects on Ethnomathematics Activities of Ecoprint Production in El Hijaaz BoutiqueAbstractButik El Hijaaz is an ecoprint fabric craftsman in Tulungagung who develops ecoprint techniques using natural materials as fabric dyes and prints environmentally friendly motifs. The research was conducted to reveal the mathematical aspects contained in the process of making ecoprint fabrics, such as counting, measuring, designing. The purpose of this research is to reveal the mathematical aspects and mathematical fundamental activities contained in the ecoprint activity at El Hijaaz boutique Tulungagung. This study uses a qualitative approach with ethnographic methods namely observation, interviews, documentation. The research subjects are boutique employees and El Hijaaz Boutique owners. The research location is the El Hijaaz boutique, Tulungagung Regency. The results of the study show that: 1) the fundamental activities found in the process of making ecoprint fabrics at the El Hijaaz Gallery include counting, measuring, design, locating, playing and explaining. 2) Mathematical concepts that can be revealed are comparison, time conversion, temperature conversion, counting concept, set, fraction concept, measurement concept, reflection, similarity, congruence, linear program, social arithmetic.