A New Algorithm for Privacy-Preserving Horizontally Partitioned Linear Programs

In a linear programming for horizontally partitioned data, the equality constraint matrix is divided into groups of rows. Each group of the matrix rows and the corresponding right-hand side vector are owned by different entities, and these entities are reluctant to disclose their own groups of rows or right-hand side vectors. To calculate the optimal solution for the linear programming in this case, Mangasarian used a random matrix of full rank with probability 1, but an event with probability 1 is not a certain event, so a random matrix of full rank with probability 1 does not certainly happen. In this way, the solution of the original linear programming is not equal to the solution of the secure linear programming. We used an invertible random matrix for this shortcoming. The invertible random matrix converted the original linear programming problem to a secure linear program problem. This secure linear programming will not reveal any of the privately held data.

Equilibrium Pricing with Duality-Based Method: Approach for Market-Oriented Capacity Remuneration Mechanism

The crucial design elements of a good capacity remuneration mechanism are market orientation, insurance of long-term power system adequacy, and optimal cross-border generation capacity utilization. Having in mind these design elements, this research aims to propose a financially fair pricing mechanism that will guarantee enough new capacity and will not present state aid. The proposed capacity remuneration mechanism is an easy-to-implement linear program problem presented in its primal and dual form. The shadow prices in the primal problem and dual variables in the dual problem are used to calculate the prices of firm capacity which is capacity needed for long-term power system adequacy under capacity remuneration mechanism. In order to test if the mechanism ensures sufficient new capacity under fair prices, the mechanism is tested on the European Network of Transmission System Operators for Electricity (ENTSO-E) regional block consisting of Austria, Slovenia, Hungary, and Croatia with simulation conducted for a period of one year with a one-hour resolution and for different scenarios of the credible critical events from a standpoint of security of supply; different amounts of newly installed firm capacity; different short-run marginal costs of newly installed firm capacity; and different capacity factors of newly installed firm capacity. Test data such as electricity prices and electricity load are referred to the year 2018. The results show that the worst-case scenario for Croatia is an isolated system scenario with dry hydrology that results with high values of indicators expected energy not served (EENS), loss of load expectation (LOLE), and loss of load probability (LOLP) for Croatia. Therefore, new capacity of several hundred MW is needed to stabilize these indicators at lower values. Price for that capacity depends on the range of installed firm capacity and should be in range of 1000–7000 €/MW/year for value of lost load (VoLL) in Croatia of 1000 €/MWh and 3000–22,000 €/MW/year for VoLL of 3100 €/MWh that correlates with prices from already established capacity markets. The presented methodology can assist policymakers, regulators, and market operators when determining capacity remuneration mechanism rules and both capacity and price caps. On the other hand, it can help capacity market participants to prepare the most suitable and near-optimal bids on capacity markets.

MEMAKSIMALKAN KEUNTUNGAN HARIAN PADA INDUSTRI RUMAHAN “NANDA JAYA” DENGAN PENERAPAN METODE SIMPLEKS

The home industry "Nanda Jaya" produces banana chips, cassava chips and tempe chips daily. From preliminary observations, information is obtained that in determining the composition of the number of units for each type of chips produced, and determining the selling price of the product per unit, is carried out on the basis of experience while running the business, so there is no optimal way to determine it. With this condition, the company's profit needs to be reviewed whether it is optimal or not. The purpose of this research is to determine the number of production units of each type of chips, in order to obtain maximum profit and also determine the efficiency that occurs in the utilization of cost and time resources. Data collection was carried out by observation and interviews. The mathematical model of the research problem is a linear program problem with three variables that can be solved by the simplex method. From the results of data analysis, it was concluded that in order to obtain maximum profit, the company had to produce 74 units of Banana Chips, 161 units of Cassava Chips and Tempe Chips not to be produced. Maximum profit is Rp. 285,387, - (previously Rp. 247,000, -), Production Capital was reduced to Rp. 889,613, - (previously Rp. 928,000, -), while the total available time was used up.

Finding orthologous gene blocks in bacteria: the computational hardness of the problem and novel methods to address it

Motivation The evolution of complexity is one of the most fascinating and challenging problems in modern biology, and tracing the evolution of complex traits is an open problem. In bacteria, operons and gene blocks provide a model of tractable evolutionary complexity at the genomic level. Gene blocks are structures of co-located genes with related functions, and operons are gene blocks whose genes are co-transcribed on a single mRNA molecule. The genes in operons and gene blocks typically work together in the same system or molecular complex. Previously, we proposed a method that explains the evolution of orthologous gene blocks (orthoblocks) as a combination of a small set of events that take place in vertical evolution from common ancestors. A heuristic method was proposed to solve this problem. However, no study was done to identify the complexity of the problem. Results Here, we establish that finding the homologous gene block problem is NP-hard and APX-hard. We have developed a greedy algorithm that runs in polynomial time and guarantees an O(ln⁡n) approximation. In addition, we formalize our problem as an integer linear program problem and solve it using the PuLP package and the standard CPLEX algorithm. Our exploration of several candidate operons reveals that our new method provides more optimal results than the results from the heuristic approach, and is significantly faster. Availability and implementation The software and data accompanying this paper are available under the GPLv3 and CC0 license respectively on: https://github.com/nguyenngochuy91/Relevant-Operon.

Exploring Students Computational Thinking based on Self-Regulated Learning in the Solution of Linear Program Problem

This study aims to analyze the students computational thinking in the solution of the linear program problem based on self-regulated learning. The data were collected by self-regulated learning questionnaire, computational thinking test, and depth interviews. This study was conducted in SMAN 10 Tangerang. Computational thinking in students with high and medium levels of self-regulated learning has no difference. Students still make a solution that is fixated with linear program problem-solving procedures in general, that is using examples, substitution, and elimination. In solving problems, students can reach the stages of decomposition and pattern recognition only. Students still do not evaluate the results of their work. Algorithmic performed is less coherent because the abstraction has not been done. The recommendation for further research is the need for research that can develop student abstraction in solving problems. Besides, there is also a need for research that analyzes the reflective of students in computational thinking when solving problems.

Program Linier Parametrik

This study aims to discuss a linear program problem where its constants can change, If a constant for a linear program problem is changed, then we don't need to count from the beginning again. Next, we will examine the properties of the objective function as a result of changes in these constants. In this discussion determine the non-negative "critical value" which provides the optimal solution to the problem of parametric linear programs. Searching for critical values in parametric linear programs is done by the matrix version method.

Profil Kemampuan Mahasiswa Tadris Matematika dalam Memecahkan Masalah Program Linear Ditinjau dari Perbedaan Tingkat Kemampuan Prasyarat dan Gaya Kognitif Fiel Dependent

This research has been carried out on Semester II students of Mathematics education Department, Faculty of Tarbiyah and Teacher Training at IAIN Palopo in 2017. The type of this research is qualitative descriptive. This research aims to describe the ability of students in solving Linear Program problems in terms of differences in the level of prerequisite ability and cognitive style. The instruments were (1) GEFT test, (2) Linear Algebra prerequisite ability tests, (3) Linear Program problem solving tests, (4) and unstructured task-based interviews. The results of this study are (1) research subjects with high prerequisite ability dependent field cognitive style, showing good ability in understanding problems correctly, planning solutions, solving problems in accordance with the plan and re-examining the results obtained. Subjects can solve Linear Program problems with graph and simplex methods (2) research subjects with prerequisite abilities while field dependent cognitive style, able to understand problems correctly, still unsure when carrying out solutions, but according to plan. Subjects can solve Linear Program problems with graphical methods and simplex methods, (3) research subjects with low prerequisite ability in field dependent cognitive style, lack of ability to understand problems, unable to carry out problem solving correctly, and unsure in explaining the completion steps taken.Abstrak: Penelitian ini dilaksanakan di IAIN Palopo Fakultas Tarbiyah dan Ilmu Pendidikan Tadris Matematika Semester III Tahun 2017. Jenis penelitian ini adalah deskriptif kualitatif. Yang bertujuan mendeskripsikan kemampuan mahasiswa dalam memecahkan masalah Program Linier ditinjau dari perbedaan tingkat kemampuan prasyarat dan gaya kognitif. Instrumen yang digunakan adalah (1) tes GEFT, (2) tes kemampuan prasyarat Aljabar Linier, (3) tes pemecahan masalah Program Linier, (4) dan wawancara berbasis tugas tidak terstruktur. Hasil penelitian ini adalah (1) subjek penelitian dengan kemampuan prasyarat tinggi gaya kognitif field dependen, menunjukkan kemampuan yang baik dalam memahami masalah dengan tepat, merencanakan pemecahan, menyelesaikan masalah sesuai dengan rencana dan memeriksa kembali hasil yang diperoleh. Subjek dapat menyelesaikan masalah Program Linier dengan metode grafik dan simpleks (2) subjek penelitian dengan kemampuan prasyarat sedang gaya kognitif field dependent, dapat memahami masalah dengan tepat, masih kurang yakin saat melaksanakan pemecahan, namun sesuai dengan rencana. Subjek dapat menyelesaikan masalah Program Linier dengan metode grafik dan metode simpleks, (3) subjek penelitian dengan kemampuan prasyarat rendah gaya kognitif field dependent, kurang mampu memahami permasalahan, tidak mampu melaksanakan pemecahan masalah dengan benar, dan tidak yakin dalam menjelaskan langkah-langkah penyelesaian yang ditempuh.