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Focusing on the extreme points of the solution sets of matrix two-person games, we propose the notions of characteristic sets and characteristic numbers. The characteristic sets (resp., the characteristic numbers) are the sets (resp., the numbers) of the extreme points of the solution set of the game and the optimal solution sets of the players. These concepts allow us to measure the complexity of the game. The larger the characteristic numbers, the more complex the game is. Among other things, we obtain upper bounds for the characteristic numbers and give a novel geometric construction. By the construction, we get useful descriptions of the optimal strategy set of each player of a game given by any nonsingular square matrix. Namely, the investigation of the geometry the just-mentioned sets reduces to computing or studying certain simpler sets. We also formulate several open problems. [ABSTRACT FROM AUTHOR]

Linear programs are frequently employed to optimize national energy system models, which are used to find a minimum-cost energy system. For the operation, they assume perfect forecasting of the weather and demands over the whole optimization horizon and can therefore perfectly fit the energy systems’ design and operation. Therefore, they will yield lower costs than any real energy system that only has partial forecasting available. We compare linear programming with a priority list, a heuristic operation strategy which uses no forecasting at all, in a model of a climate-neutral German energy system. We find a 28% more expensive energy system under the priority list. Optimizing the same energy system model with both strategies envelopes the cost and design of any energy system that has partial forecasting. We demonstrate this by incorporating some rudimentary forecasting into a modified priority list, which actually reduces the gap to 22%. This is thus an approach to find an upper bound for how much a linear program possibly underestimates the costs of a real energy system in Germany in regard to imperfect forecasting. We also find that the two approaches differ mainly in the dimensioning and operation of energy storage. The priority list yields 63% less batteries, 73% less thermal storage and 54% more hydrogen storage. The use of renewables and other components in the system is very similar.

This research aims to determine the effect of the REACT learning strategy assisted by structured student worksheets on mathematical problem-solving ability. This study design employs a quasi-experiment with a posttest-only control group design. The sampling technique was carried out using purposive sampling and cluster random sampling. Students from classes X7 and X9 at SMA Negeri 3 Karawang were used for the research samples. The instrument in this research consisted of four description questions on linear program material that had been tested for validity and reliability. The results of hypothesis testing with an independent sample test (t-test) at the 5% significance level show that there is an effect of the implementation of the REACT learning strategy assisted by structured student worksheet on mathematical problem-solving ability

This paper proposes a new mathematical paradigm to analyze discrete-time meanfield games. It is shown that finding Nash equilibrium solutions for a general class of discretetime mean-field games is equivalent to solving an optimization problem with bounded variables and simple convex constraints, called MF-OMO. This equivalence framework enables finding multiple (and possibly all) Nash equilibrium solutions of mean-field games by standard algorithms. For instance, projected gradient descent is shown to be capable of retrieving all possible Nash equilibrium solutions when there are finitely many of them, with proper initializations. Moreover, analyzing mean-field games with linear rewards and mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This framework does not rely on the contractive and the monotone assumptions and the uniqueness of the Nash equilibrium. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The natural approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s-measure of patterns in graphs as needed for data mining. [ABSTRACT FROM AUTHOR]

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino's additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino's additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction. [ABSTRACT FROM AUTHOR]

The efficiency ranking of a decision making units (DMU) measures its relative position among a group of DMUs over sets of feasible virtual prices that characterize preferences for input and output variables. But the efficiency ranking of a DMU conveys no information about the gap between this DMU and those superior and peer DMUs. So we propose an alternative efficiency measure named buffered-ranking for efficiency analysis. The statement that the efficiency buffered-ranking of a DMU is k implies that its efficiency score reaches the average of the top k efficiency scores of all DMUs. The proposed buffered-ranking is monotone with the conventional ranking, and conveys more information about its relation with superior and peer DMUs. When the efficiency score is based on virtual profit, i.e. the difference between virtual revenue and virtual cost, the calculation of the best buffered-ranking is equivalent to a continuous linear program. We also study the worst buffered-ranking that is opposite to the best buffered-ranking. Experiments demonstrate the advantages of buffered-ranking over conventional ranking. [ABSTRACT FROM AUTHOR]

This paper generalizes the Sethi–Thompson model of cash balance dynamics to the case of multiple current and investment accounts, with the cash flows or demands incident on the current accounts. Cash transfers can occur between any pair of current–current or current–investment accounts, with transaction costs proportional to the amount transferred, always deducted from current accounts. Performance indices are defined and maximization of an index for the next instant (day), by suitable choice of cash transfers that satisfy desired constraints on account balances, defines the basic optimal control problem referred to as one step ahead optimal control. It is shown that this one step ahead optimal control can be written as a mixed integer linear program of small size, leading to an implementable real time strategy for the generalized cash balance problem. In addition, for the simple case of a single cash and investment account, the proposed strategy is derived analytically and compared with a strategy of Miller–Orr type, called a three‐level strategy. Omniscient optimal control over a horizon is defined as the globally optimal control strategy, assuming the demands over the entire horizon to be known: although computable a posteriori, it is not implementable a priori, and only serves as a benchmark for comparison. The proposed one step ahead optimal or myopic approach makes no assumptions about the distribution of cash demands, and examples show that it attains performance indices which are superior to those attained by three‐level control strategies, and compare favorably with the omniscient benchmark performance indices. [ABSTRACT FROM AUTHOR]

This article shows how to solve linear programs of the form minAx=b,x =0 cT x with n variables in time O * ((nω + n2.5-a/2 + n2+1/6) log(n/d)), where ω is the exponent of matrix multiplication, a is the dual exponent of matrix multiplication, and d is the relative accuracy. For the current value of ω ~ 2.37 and a ~ 0.31, our algorithm takes O * (nω log(n/d)) time. When ω = 2, our algorithm takes O * (n2+1/6 log(n/d)) time. Our algorithm utilizes several new concepts that we believe may be of independent interest: • We define a stochastic central path method. • We show how to maintain a projection matrix v WAT (AWAT) -1A v W in sub-quadratic time under l2 multiplicative changes in the diagonal matrixW. [ABSTRACT FROM AUTHOR]

ABSTRACT: An artificial insemination (AI) company seeks to allocate semen units globally by balancing perceived demand with uncertain product supply, in what is an arduous subjective process. This study aimed to objectivize this process by providing a user-friendly linear programming model to allocate bulls' semen units to regions for the next trimester sales period based on maximum revenue, and to describe the features and outcomes of this model when applied to a sample bull herd and global demand scenario reflective of a leading AI company. The objective function of maximizing revenue was calculated by summing the product of units allocated by bull and region with purchase prices assigned by bull and region. Constraints considered were regional demand for overall units, regional preferences for specific genetic traits, bulls' production capacity, and percentage of bulls' units allocated to a single region. A sensitivity analysis was performed to identify the effects of variables and constraints on total revenue. Production, sales, and bull demographic data from 2018 to 2021 from a leading AI company were used to establish base values and build a sample herd of 61 bulls and 5 global regions. The case study provided a maximum revenue of $8,287,197 in semen sales per trimester, with 634,700 units allocated. Of the 61 bulls in the case study, 9 were not allocated to any region. The most limiting constraint was regional demand, which resulted in a surplus of 274,564 units not allocated. A sensitivity analysis confirmed this finding, with the largest shadow prices assigned to regional demands, and indicated that a single unit increase in regional demand would add up to $14.84 in total revenue.

An artificial insemination (AI) company seeks to allocate semen units globally by balancing perceived demand with uncertain product supply, in what is an arduous subjective process. This study aimed to objectivize this process by providing a user-friendly linear programming model to allocate bulls' semen units to regions for the next trimester sales period based on maximum revenue, and to describe the features and outcomes of this model when applied to a sample bull herd and global demand scenario reflective of a leading AI company. The objective function of maximizing revenue was calculated by summing the product of units allocated by bull and region with purchase prices assigned by bull and region. Constraints considered were regional demand for overall units, regional preferences for specific genetic traits, bulls' production capacity, and percentage of bulls' units allocated to a single region. A sensitivity analysis was performed to identify the effects of variables and constraints on total revenue. Production, sales, and bull demographic data from 2018 to 2021 from a leading AI company were used to establish base values and build a sample herd of 61 bulls and 5 global regions. The case study provided a maximum revenue of $8,287,197 in semen sales per trimester, with 634,700 units allocated. Of the 61 bulls in the case study, 9 were not allocated to any region. The most limiting constraint was regional demand, which resulted in a surplus of 274,564 units not allocated. A sensitivity analysis confirmed this finding, with the largest shadow prices assigned to regional demands, and indicated that a single unit increase in regional demand would add up to $14.84 in total revenue. [ABSTRACT FROM AUTHOR]

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost c ij of traveling from city i to city j, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results. [ABSTRACT FROM AUTHOR]

This study aims to describe the process of developing the device and producing a good quality guided inquiry model mathematics learning tool on linear program material for class XI SMA, and to describe the effectiveness of guided inquiry model mathematics learning which can train students' critical thinking skills on linear program material. This type of research is development research (RnD). The learning tools developed in this study are the Learning Implementation Plan (RPP), Students Worksheet (LKPD), and Critical Thinking Ability Test (TKBK) are developed using a 4-D development model which consists of four stages, namely the define stage, the design stage, the develop stage, and the disseminate stage. The research subjects for the trial class were 13 students of class XI MIPA 3 and the research subjects for the implementation class were 17 students of class XI MIPA 1. Based on the results of descriptive analysis, it was found that the learning tools developed were of good quality because they met valid, practical, and effective criteria. The learning device is said to be valid because all validators give a minimum score of 3 for each aspect of the assessment on a scale of 1-4 and the critical thinking ability test questions meet the valid, reliable, and sensitive criteria. The learning device is said to be practical because the teacher's activities in managing learning meet good criteria and the activities of students meet the active criteria. Learning devices are said to be effective because students 'responses to learning devices and learning activities meet the positive category, guided inquiry mathematics learning model to train students' critical thinking skills is achieved.

The probability box (P-box) model is an effective quantification tool that can deal with aleatory and epistemic uncertainties and can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box ones. This paper proposes a new structural reliability analysis method with the non-parameterized P-box uncertainty, through which bounds of the failure probability can be obtained efficiently. For the convenience of calculation, the reliability analysis problems are divided into the univariate and multivariate ones. Firstly, structural failure probability bound analysis for the univariate problem is converted into solving two linear programming models by discretizing the cumulative distribution function (CDF) of the P-box variable, which can be solved efficiently by the simplex algorithm. Secondly, an iterative technique is used to decompose the multivariate problem into a series of univariate problems, in which only one non-parameterized P-box's CDF is optimized and the remaining counterparts are fixed. Hence, the failure probability bounds can be obtained by solving a series of linear programming problems. Finally, the effectiveness of the proposed method is demonstrated by investigating three numerical examples. [ABSTRACT FROM AUTHOR]

In the capacitated facility location problem, we are given a set F of potential facilities and a set D of clients, where each facility has a capacity and an open cost, and each client has a demand to be served by the facilities with service costs. The goal is to open some facilities in F and assign all clients in D to these open facilities such that the total cost is minimum. Based on the natural integer programming formulation, Levi et al. [8] presented an LP-based 5-approximation algorithm for this problem under the assumption that the facility costs are uniform. Based on the same integer programming formulation, we remove the uniformity assumption and present an (R + R 2 + 8 R 2 + 3) -approximation algorithm for the capacitated facility location problem, where R is the upper bound of the ratio between facility costs. Our result is a slight extension of the corresponding result in [8] , as when R = 1 the worst-case ratio of our algorithm is R + R 2 + 8 R 2 + 3 = 5. [ABSTRACT FROM AUTHOR]

Cloud computing is an emerging paradigm that provides hardware, platform and software resources as services based on pay-as-you-go model. It is being increasingly used for hosting and executing service-based business processes. However, business processes are subject to dynamic evolution during their life-cycle due to the highly dynamic evolution of the cloud environment. Therefore, to efficiently manage them according to the autonomic computing paradigm, service-based business processes can be associated with autonomic managers. Autonomic managers monitor these processes, analyze monitoring data, plan configuration actions, and execute these actions on these processes. The main objective of cloud computing is to improve the performance level while minimizing operating costs. Thus, due to the diversity of business processes requirements and the heterogeneity of cloud resources, discovering the optimal management cost of a business process in the cloud becomes a highly challenging problem. For this purpose, we propose an approach based on an Integer Linear Program to find out the optimal allocation of cloud resources that meet customers' requirements and resources' constraints. Besides, to validate our approach under realistic conditions and inputs, we propose an extension of the CloudSim simulator to analyze the cloud resources consumed by an autonomic business process. Experiments conducted on two real datasets highlight the effectiveness and performance of our approach. [ABSTRACT FROM AUTHOR]

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.

Recently, coded blockchain systems have been proposed to encode blockchain into coded fragments and distributively store them. These fragments can be collected and decoded to obtain the original blockchain only when needed. This reduces the storage requirement of blockchains and makes it possible to incorporate blockchain in wireless Internet-of-Things (IoT) systems. However, transmitting such coded fragments consumes nonnegligible resource in wireless networks. Hence, this article studies the storage and transmission tradeoff for coded blockchains, and formulates the coded fragments assignment using an integer linear program (ILP). In particular, a $Q$ -hop localization property is proposed to ensure that any device is able to collect sufficient coded fragments for decoding within $Q$ -hop neighbors. This article then proposes an efficient heuristic algorithm that is built upon the solution to the relaxed ILP. Apart from these, this article studies regrowing blockchains, where nodes dynamically join and leave the networks, and proposes an algorithm to adjust the coded fragments assignments. Simulation results show that the performance of the proposed heuristic algorithm is close to that of the ILP, and only a small portion of nodes need to recalculate their assignments when using the proposed adjustment algorithm in the regrowing blockchains. [ABSTRACT FROM AUTHOR]

In the k -means problem with penalties, we are given a data set $${\cal D} \subseteq \mathbb{R}^\ell $$ of n points where each point $$j \in {\cal D}$$ is associated with a penalty cost p j and an integer k. The goal is to choose a set $${\rm{C}}S \subseteq {{\cal R}^\ell }$$ with |CS| ≤ k and a penalized subset $${{\cal D}_p} \subseteq {\cal D}$$ to minimize the sum of the total squared distance from the points in D / D p to CS and the total penalty cost of points in D p , namely $$\sum\nolimits_{j \in {\cal D}\backslash {{\cal D}_p}} {d^2}(j,{\rm{C}}S) + \sum\nolimits_{j \in {{\cal D}_p}} {p_j}$$. We employ the primal-dual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ ε) for the k -means problem with penalties, improving the previous best approximation ratio 19.849+ ∊ for this problem given by Feng et al. in Proceedings of FAW (2019). [ABSTRACT FROM AUTHOR]

This study aimed to describe the conceptual and procedural comprehension to solve linear program story problems in students who are an extrovert and an introvert. This was qualitative study with a case study method. The subjects were two students who are an extrovert and an introvert. Data collection included personality questionnaires, question tests, and interviews. Validity test of the data used time triangulation. Data analysis was conducted based on indicators of conceptual and procedural comprehension, which include data reduction, data presentation, and conclusion drawing. The results showed that the extroverted subject was able to meet all indicators of conceptual and procedural comprehension. This was reflected from the way the subject solved the questions properly according to the existing procedures. In contrast, the introverted student was also able to meet the procedural comprehension indicators, but did not meet the conceptual comprehension indicator. This was reflected from the mistakes that the subject made in comprehending the questions and the errors in interpreting the questions into mathematical model.

Good distribution network management is a very important competitive advantage for a company. The distribution that is not right with the wrong time will also have a big impact on all aspects, especially company profits. The exact number and timing are crucial points in the distribution. The distribution and transportation system must be designed optimally so that the minimum cost is obtained. Perum Bulog, West Java Regional Division, is the government's representative in distributing rice evenly and distributing rice, which is a staple food commodity for Indonesian people in general. Of course, it must pay attention to optimal distribution patterns. In carrying out the operational process, the West Java Regional Division of Perum Bulog will be assisted by 7 Regional Sub-Divisions scattered throughout the West Java region who will handle rice in their respective working areas. This study aims to determine the planning path and the optimum amount of rice distribution from the West Java Regional Division to districts and cities that can minimize distribution costs so that the costs incurred will reach their lowest point using the Linear Programming method. The analysis of this research was assisted by the LINDO software version 7.0 for Windows 10.0. From the results of this research, the optimization of rice distribution at Perum Bulog Divre West Java, with the optimum total distribution cost is IDR 6,374,025 360. [ABSTRACT FROM AUTHOR]

Influence maximization is an important research topic in social networks that has different applications such as analyzing spread of rumors, interest, adoption of innovations, and feed ranking. The goal is to select a limited size subset of vertices (called a seed-set) in a Social Graph, so that upon their activation, a maximum number of vertices of the graph become activated, due to the influence of the vertices on each other. The linear threshold model is one of two classic stochastic propagation models that describe the spread of influence in a network. We present a new approach called MLPR (matrix multiplication, linear programming, randomized rounding) with linear programming used as its core in order to solve the influence maximization problem in the linear threshold model. Experiments on four real data sets have shown the efficiency of the MLPR method in solving the influence maximization problem in the linear threshold model. The spread of the output seed-sets is as large as when the state-of-the-art algorithms are used; however, unlike most of the existing algorithms, the runtime of our method is independent of the seed size and does not increase with it. [ABSTRACT FROM AUTHOR]

This research aims to analyze student’s error types in solving linear programming problems based on Newman’s error analysis viewed from Adversity Quotient (AQ). This research approach is qualitative descriptive. Subjects in this research are 6 students in class X TKR 3 of SMKN 2 Jember. There are 2 climber students, 2 camper students, and 2 quitter students. Instruments that were used in this research to collect the data are ARP questionnaire, linear programming problem, interview guide, and validation sheets. Based on the result of this research, the climber students are able to do comprehension error, process skill error, and encoding error. The camper students are able to do comprehension error, transformation error, process skill error, and encoding error. The quitter students are able to do reading error, comprehension error, transformation error, process skill error, and encoding error.

This study aims to obtain a description of the errors of high school students on linear program topics by using the Newman Error Analysis. This type of research is a descriptive study with a qualitative approach. This research was conducted by giving a test to participants consisting of a three-word problem on the topic of a linear program then conducting interviews as a data collection technique. Participants in this study were five female students of class XI in one of the senior high schools in Bandung, including four people who were students majoring in Sciences studies and one person who was a student majoring in Social studies. Based on the results of a research according to the Newman Error Analysis, all participants made several types of errors on the topic of a linear program. Errors made by the participants include transformation errors made by three students, the process skill errors made by two students, and writing error answers made by two students.

Clustering is one of the essential tools for data mining since it reveals the natural structures of the unlabeled data. Many clustering algorithms have been proposed in the last decades. However, few of them are designed to adapt prior knowledge that is available in many real applications, such as the sizes of clusters. In this paper, we propose a novel iterative clustering algorithm that can impose the constraints on the sizes of clusters. Given an unordered set of cluster size constraints, the proposed method minimizes the mean squared error (MSE) while simultaneously considers the size constraints. Each iteration of the proposed method consists of two steps, namely an assignment step and an update step. In the assignment step, the observations are assigned into clusters under the size constraints. The assignment task is modeled as an integer linear programming (ILP) problem. We prove that part of the constraint matrix of this ILP problem is total unimodular. Therefore, the integer constraints on most of the variables can be omitted so that the problem would become a mixed integer programming (MILP) problem which is much easier to solve. In the update step, new cluster centroids will be updated as the centers of the observations in the corresponding clusters. Experiments on UCI data sets indicate that (1) imposing the size constraints as proposed could improve the clustering performance; (2) compared with the state-of-the-art size constrained clustering methods, the proposed method could efficiently derive better clustering results.

Problem solving skills can not be separated from teaching and learning activities. Problem solving skills require logical, critical and systematic thinking and can be developed in the process of learningmathematics. This research aims to find out the mathematical problem-solving abilities of students on linear program materials. The study was conducted at Sma Negeri 2 Lais. The sample in this study was taken with a simple random sampling technique, namely class XI IPA 1 which amounted to 34 students. The instrument used in this study is a test in the form of a description of linear program material. The data analysis method used in this study is a quantitative desktiptive method. From the results of data analysis and discussion, it can be concluded that students' mathematical problem solving skills from four indicators include: understanding the problem 56.62%, creating / compiling a mathematical model of 65.81%, choosing and developing a 60.29% solving strategy, and re-examining the correctness of the answers obtained from solving the problem 50.49%. Overall, the average percentage of students' mathematical problem-solving skills was 58.30%.

[Title: The Effect of Open-Ended Problems on Mathematics Problem toward Students' Ability in Solving Linear Program Problems]. The purpose of this study is to determine whether the provision of linear program mathematical problems in the form of open-ended problems can affect students' problem-solving abilities. This research is an experiment with one sample group, 28 students of class XI IPA-2 in SMA Negeri 7 Mataram. Data was collected through tests and interviews that were statistically analyzed both descriptive and inferential. The validity of mathematical problems is based on expert judgment while the reliability is tested using product-moment correlation. Pre-test and post-test data have been tested both homogeneous and normally distributed. The homogeneity test uses the F-test statistics and the normality test uses the interpretation of skewness and kurtosis. The influence test is performed using one-party t-test statistics. Student problem-solving performance was assessed using a holistic rubric. All data is processed using data analysis tools on Microsoft Excel. This experiment showed success by obtaining an average test score of students when the pre-test was 39.58 which then increased when the post-test became 79.76. This increase was statistically significant as evidenced by the one-party t-test where tcount = 37.33> ttable = 1.67 at α = 0.05, which means that Ha was accepted. So it can be concluded that there is an effect of the treatment given a mathematical problem in the form of open-ended problems to the ability of students to solve linear program problems.

In this paper, a large-scale linear programming problem including several parameters such as labor cost, raw material cost, machine and other cost have been formulated. Then the formulated problem has been solved by using Benders' Decomposition Method. The formulated large model is divided into master and small sub problem. In order to validate and calibrate the model, real data from a soap industry named Mega Sornali Soap and Cosmetics Industry have been collected. Soap industry is one of the most feasible business options owing to the straightforward manufacturing process involved starting a soap and detergent manufacturing business in Bangladesh. These models are solved by using AMPL. To find out the significant parameters of the model, the sensitivity analysis of different cost parameters such as labor cost, raw material cost and machine cost have been be considered. From the sensitivity analysis, the decision makers of the factory would able to find out the ranges of cost coefficients and all the resources. As a result, the company could able to see how any change can affect the profit or loss of the factory. From the numerical results, the most profitable product of the company is found to be Sornali Soap and Mega Extra Powder. On the contrary, Mega SornaliSobiMarka Soap and Mega Washing Powder are not more profitable. Further, raw material cost is the most significant sensitive cost. If the raw material cost can be decreased the profit could also beincreased. Finally, the result of the optimal solution has been represented in tabular and graphs. [ABSTRACT FROM AUTHOR]

Facility location problem is a well established research area within Operations Research. Capacitated facility location problem is one of the most important variants, in which each facility has an upper bound on the demand, i.e., capacity. Moreover, the integrality gap of the natural linear program relaxation for the problem is infinite. Fortunately, the gap is finite when all opening costs for the facilities are the same. We consider a capacity facility location problem with penalties in which it is allowed some customers are not served by facilities and all opening costs are uniform. Based on LP-rounding framework, we propose a 5.732-approximation algorithm. [ABSTRACT FROM AUTHOR]

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.

Abstract Background The ab initio approaches to protein structure prediction usually employ the Monte Carlo technique to search the structural conformation that has the lowest energy. However, the widely-used energy functions are usually ineffective for conformation search. How to construct an effective energy function remains a challenging task. Results Here, we present a framework to construct effective energy functions for protein structure prediction. Unlike existing energy functions only requiring the native structure to be the lowest one, we attempt to maximize the attraction-basin where the native structure lies in the energy landscape. The underlying rationale is that each energy function determines a specific energy landscape together with a native attraction-basin, and the larger the attraction-basin is, the more likely for the Monte Carlo search procedure to find the native structure. Following this rationale, we constructed effective energy functions as follows: i) To explore the native attraction-basin determined by a certain energy function, we performed reverse Monte Carlo sampling starting from the native structure, identifying the structural conformations on the edge of attraction-basin. i i) To broaden the native attraction-basin, we smoothened the edge points of attraction-basin through tuning weights of energy terms, thus acquiring an improved energy function. Our framework alternates the broadening attraction-basin and reverse sampling steps (thus called BARS) until the native attraction-basin is sufficiently large. We present extensive experimental results to show that using the BARS framework, the constructed energy functions could greatly facilitate protein structure prediction in improving the quality of predicted structures and speeding up conformation search. Conclusion Using the BARS framework, we constructed effective energy functions for protein structure prediction, which could improve the quality of predicted structures and speed up conformation search as well.

Static traffic assignment aims to disclose the spatial distribution of vehicular flow over a transportation network subject to given traffic demands, and plays an essential role in transportation engineering. User-optimal pattern adheres the individual rationality of motorists, in which everyone chooses a route that minimizes his own travel cost, while considering congestion effects influenced by the aggregated movement of vehicles. User optimal traffic assignment, which is also known as the user equilibrium, entails solving an optimization problem with a strictly convex objective function and linear constraints. However, the performances of general-purpose solvers are quite disappointing. This paper proposes two highly efficient computation models for the user equilibrium problem. The first one exploits the second-order cone reformulation of a convex power function, resulting in a second-order cone program, and no approximation is incurred. The second one approximates the convex objective function using a piece-wise linear function, and comes down to a linear program. An adaptive path generation oracle is devised in order to circumvent path enumeration in problem setup. Case studies demonstrate that the proposed method can deal with large-scale transportation systems, and outperforms the most popular iterative algorithm in the literature.

Embung is a small reservoir which can reserve water exceeds during the rainy season and utilize it on dry season. It is utilized for many purposes, such as providing water for agricultural purposes, fishery, and household needs. Jinggring Weir which is located at Mojokerto Regency, East Java Province is planned to enhance as embung to be able to provide higher water demand services. An appropriate method of water demand optimization study is important for reservoir water management operation to estimate water supply reliability both used for irrigation as well as domestic water. The Mock method was used to analyze water availability, while irrigation, and domestic water requirement, global water balance, simulation of the reservoir operation was analyzed based on Standard Operating Rule (SOR) method. The linear program method is used to determine an appropriate amount of water released to reach the optimum value of water supply reliability. The result of the simulation of target released using SOR method showed that the embung reliability for irrigation and domestic purpose increased from 81.55% to 100% and 80.09% to 100%, respectively.

• We modelled the time when drivers start steering away to overtake a cyclist. • Four driver models were compared using test-track and naturalistic data. • Modelling inverse tau fitted the data better than modelling expansion rate. • The compared models have implications for evaluation of active safety systems. The improvement of advanced driver assistance systems (ADAS) and their safety assessment rely on the understanding of scenario-dependent driving behaviours, such as steering to avoid collisions. This study compares driver models that predict when a driver starts steering away to overtake a cyclist on rural roads. The comparison is among four models: a threshold model, an accumulator model, and two models inspired by a proportional-integral and proportional-integral-derivative controller. These models were tested and cross-applied using two different datasets: one from a naturalistic driving (ND) study and one from a test-track (TT) experiment. Two perceptual variables, expansion rate (the horizontal angular expansion rate of the image of the lead road user on the driver's retina) and inverse tau (the ratio between the image's expansion rate and its horizontal optical size), were tested as input to the models. A linear cost function is proposed that can obtain the optimal parameters of the models by computationally efficient linear programming. The results show that the models based on inverse tau fitted the data better than the models that included expansion rate. In general, the models fitted the ND data reasonably well, but not as well the TT data. For the ND data, the models including an accumulative component outperformed the threshold model. For the TT data, due to the poorer fit of the models, more analysis is required to determine the merit of the models. The models fitted to TT data captured the overall pattern of steering onsets in the ND data rather well, but with a persistent bias, probably due to the drivers employing a more cautious strategy in TT. The models compared in this paper may support the virtual safety assessment of ADAS so that driver behaviour may be considered in the design and evaluation of new safety systems. [ABSTRACT FROM AUTHOR]

Abstract: 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.

This research is motivated by the difficulty of students in expressing economic problems in verbal and linear program languages. It is important to develop a linear program teaching material through realistic mathematic education approach with problem solving strategies with national character. This study aims to describe the needs of students and lecturers on the linear program teaching materials. this teaching material applies a realistic mathematics education approach to problem solving strategies. problem in this study relates to national economic problems. This research is mixed type of research design. Research instruments in the form of questionnaires and interviews. Subject of research 225 students and 7 lecturers. The results showed that linear program teaching materials are very important for students and lecturers. They get teaching material from the internet. The material they need is short, clear and the evaluation is in the form of a description. They need economic-based linear program teaching materials through realistic Mathematics education approach with problem-solving strategies with the national character. Based on the needs of students, it is necessary to arrange linear program teaching materials. [ABSTRACT FROM AUTHOR]

In this paper we consider one of the most basic scheduling problems where jobs have their respective arrival times and deadlines. The goal is to schedule as many jobs as possible nonpreemptively by their respective deadlines on m identical parallel machines. For the last decade, the best approximation ratio known for the single-machine case (m = 1) has been 1 - 1/e-∈ ≈ 0.632 due to Chuzhoy, Ostrovsky, and Rabani [FOCS 2001] and [MOR 2006]. We break this barrier and give an improved 0.644-approximation. For the multiple-machine case, we give an algorithm whose approximation guarantee becomes arbitrarily close to 1 as the number of machines increases. This improves upon the previous best 1 - 1/(1+1/m)m approximation due to Bar-Noy et al. [STOC 1999] and [SICOMP 2009], which converges to 1 - 1/e as m goes to infinity. Our result for the multiple-machine case extends to the weighted throughput objective where jobs have different weights, and the goal is to schedule jobs with the maximum total weight. Our results show that the 1 - 1/e approximation factor widely observed in various coverage problems is not tight for the nonpreemptive maximum throughput scheduling problem. [ABSTRACT FROM AUTHOR]