Search results for: Mathematical programming problem

Authors: Muh. Hisjam, Nancy Oktyajati, Wakhid A. Jauhari, Wahyudi Sutopo

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This research is intended to develop a raw material allocation model in timber processing industry in Perum Perhutani Unit I, Central Java, Indonesia. The model can be used to determine the quantity of allocation of timber between chain in the supply chain to select supplier considering factors that are log price and the distance. In determining the quantity of allocation of timber between chains in the supply chain, the model considers the optimal inventory in each chain. Whilst the optimal inventory is determined based on demand forecast, the capacity and safety stock. Problem solving allocation is conducted by developing linear programming model that aims to minimize the total cost of the purchase, transportation cost and storage costs at each chain. The results of numerical examples show that the proposed model can generate savings of the purchase cost of 20.84% and select suppliers with mileage closer.

Keywords: Allocation model, linear programming, purchase costs, storage costs, suppliers, transportation costs.

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Authors: M. S. Osman, A. A. Tharwat, I. A. El-Khodary, A. G. Chalabi

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In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.

Keywords: Equity Markets, Future Scenarios, PortfolioSelection, Multiple Criteria Fuzzy Optimization

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Authors: Satjaporn Tungsong, Gun Srijuntongsiri

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This research seeks to investigate the frequency and profitability of index arbitrage opportunities involving the SET50 futures, SET50 component stocks, and the ThaiDEX SET50 ETF (ticker symbol: TDEX). In particular, the frequency and profit of arbitrage are measured in the following three arbitrage tests: (1) SET50 futures vs. ThaiDEX SET50 ETF, (2) SET50 futures vs. SET50 component stocks, and (3) ThaiDEX SET50 ETF vs. SET50 component stocks are investigated. For tests (2) and (3), the problems involve conic optimization and quadratic programming as subproblems. This research is first to apply conic optimization and quadratic programming techniques in the context of index arbitrage and is first to investigate such index arbitrage in the Thai equity and derivatives markets. Thus, the contribution of this study is twofold. First, its results would help understand the contribution of the derivatives securities to the efficiency of the Thai markets. Second, the methodology employed in this study can be applied to other geographical markets, with minor adjustments.

Keywords: Conic optimization, Equity index arbitrage, Executionlags, Quadratic programming, SET50 index futures, ThaiDEX SET50ETF, Transaction costs

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Authors: Brajesh Kumar Jha, Neeru Adlakha, M. N. Mehta

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Mathematical and computational modeling of calcium signalling in nerve cells has produced considerable insights into how the cells contracts with other cells under the variation of biophysical and physiological parameters. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to understand the cell contraction. Main objective of this work is to study the effect of voltage gated (Operated) calcium channel (VOC) on calcium profile in the form of advection diffusion equation. A mathematical model is developed in the form of advection diffusion equation for the calcium profile. The model incorporates the important physiological parameter like diffusion coefficient etc. Appropriate boundary conditions have been framed. Finite volume method is employed to solve the problem. A program has been developed using in MATLAB 7.5 for the entire problem and simulated on an AMD-Turion 32-bite machine to compute the numerical results.

Keywords: Ca2+ Profile, Advection Diffusion, VOC, FVM.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

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This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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Authors: Luminita Dumitriu, Cristina Segal, Marian Craciun, Adina Cocu, Lucian P. Georgescu

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There are several approaches in trying to solve the Quantitative 1Structure-Activity Relationship (QSAR) problem. These approaches are based either on statistical methods or on predictive data mining. Among the statistical methods, one should consider regression analysis, pattern recognition (such as cluster analysis, factor analysis and principal components analysis) or partial least squares. Predictive data mining techniques use either neural networks, or genetic programming, or neuro-fuzzy knowledge. These approaches have a low explanatory capability or non at all. This paper attempts to establish a new approach in solving QSAR problems using descriptive data mining. This way, the relationship between the chemical properties and the activity of a substance would be comprehensibly modeled.

Keywords: association rules, classification, data mining, Quantitative Structure - Activity Relationship.

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Authors: C. Ardil

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A multiple-criteria decision support system is proposed for the best aircraft selection decision. Various strategic, economic, environmental, and risk-related factors can directly or indirectly influence this choice, and they should be taken into account in the decision-making process. The paper suggests a multiple-criteria analysis to aid in the airline management's decision-making process when choosing an appropriate aircraft. In terms of the suggested approach, an integrated entropic preference optimization programming (POP) for fleet modeling risk analysis is applied. The findings of the study of multiple criteria analysis indicate that the A321(neo) aircraft type is the best alternative in this particular optimization instance. The proposed methodology can be applied to other complex engineering problems involving multiple criteria analysis.

Keywords: Aircraft selection, decision making, multiple criteria decision making, preference optimization programming, POP, entropic weight method, TOPSIS, WSM, WPM

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Authors: G. Shojatalab

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In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.

Keywords: Integer, Programming, Operation Research, Variables of decision.

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Authors: Walid S. Abd El-hamid, Sherif S. El-Etriby, Mohiy M. Hadhoud

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Regression testing is a maintenance activity applied to modified software to provide confidence that the changed parts are correct and that the unchanged parts have not been adversely affected by the modifications. Regression test selection techniques reduce the cost of regression testing, by selecting a subset of an existing test suite to use in retesting modified programs. This paper presents the first general regression-test-selection technique, which based on code and allows selecting test cases for any programs written in any programming language. Then it handles incomplete program. We also describe RTSDiff, a regression-test-selection system that implements the proposed technique. The results of the empirical studied that performed in four programming languages java, C#, Cµ and Visual basic show that the efficiency and effective in reducing the size of test suit.

Keywords: Regression testing, testing, test selection, softwareevolution, software maintenance.

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

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Authors: Gaurav Kumar, Rakesh Kumar Bajaj

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The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), z_pqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree F_pq instead of  and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.

Keywords: Assignment problem, Interval-valued Intuitionistic Fuzzy Sets, Similarity Measures, score function.

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Authors: V.Sekar, T.G.Palanivelu, B.Revathi

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Electromagnetic interference (EMI) is one of the serious problems in most electrical and electronic appliances including fluorescent lamps. The electronic ballast used to regulate the power flow through the lamp is the major cause for EMI. The interference is because of the high frequency switching operation of the ballast. Formerly, some EMI mitigation techniques were in practice, but they were not satisfactory because of the hardware complexity in the circuit design, increased parasitic components and power consumption and so on. The majority of the researchers have their spotlight only on EMI mitigation without considering the other constraints such as cost, effective operation of the equipment etc. In this paper, we propose a technique for EMI mitigation in fluorescent lamps by integrating Frequency Modulation and Evolutionary Programming. By the Frequency Modulation technique, the switching at a single central frequency is extended to a range of frequencies, and so, the power is distributed throughout the range of frequencies leading to EMI mitigation. But in order to meet the operating frequency of the ballast and the operating power of the fluorescent lamps, an optimal modulation index is necessary for Frequency Modulation. The optimal modulation index is determined using Evolutionary Programming. Thereby, the proposed technique mitigates the EMI to a satisfactory level without disturbing the operation of the fluorescent lamp.

Keywords: Ballast, Electromagnetic interference (EMI), EMImitigation, Evolutionary programming (EP), Fluorescent lamp, Frequency Modulation (FM), Modulation index.

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Authors: Shyam S.N. Perera

Abstract:

The optimal control problem for the viscoelastic melt spinning process has not been reported yet in the literature. In this study, an optimal control problem for a mathematical model of a viscoelastic melt spinning process is considered. Maxwell-Oldroyd model is used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and the temperature of the quench air and the fiber length serve as control variables. A constrained optimization problem is derived and the first–order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. A computer program in MATLAB is developed for simulations.

Keywords: Fiber spinning, Maxwell-Oldroyd, Optimal control, First-order optimality system, Adjoint system

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Authors: Ons Sassi, Wahiba Ramdane Cherif-Khettaf, Ammar Oulamara

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In this paper, we consider the vehicle routing problem with mixed fleet of conventional and heterogenous electric vehicles and time dependent charging costs, denoted VRP-HFCC, in which a set of geographically scattered customers have to be served by a mixed fleet of vehicles composed of a heterogenous fleet of Electric Vehicles (EVs), having different battery capacities and operating costs, and Conventional Vehicles (CVs). We include the possibility of charging EVs in the available charging stations during the routes in order to serve all customers. Each charging station offers charging service with a known technology of chargers and time dependent charging costs. Charging stations are also subject to operating time windows constraints. EVs are not necessarily compatible with all available charging technologies and a partial charging is allowed. Intermittent charging at the depot is also allowed provided that constraints related to the electricity grid are satisfied. The objective is to minimize the number of employed vehicles and then minimize the total travel and charging costs. In this study, we present a Mixed Integer Programming Model and develop a Charging Routing Heuristic and a Local Search Heuristic based on the Inject-Eject routine with different insertion methods. All heuristics are tested on real data instances.

Keywords: charging problem, electric vehicle, heuristics, local search, optimization, routing problem.

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Authors: M. Zareiee, A. Dideban

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This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Nader A. Al Theeb, Zaid Abu Manneh, Ibrahim Al-Qadi

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Traveling salesman problem (TSP) is a combinatorial integer optimization problem that asks "What is the optimal route for a vehicle to traverse in order to deliver requests to a given set of customers?”. It is widely used by the package carrier companies’ distribution centers. The main goal of applying the TSP in courier organizations is to minimize the time that it takes for the courier in each trip to deliver or pick up the shipments during a day. In this article, an optimization model is constructed to create a new TSP variant to optimize the routing in a courier organization with a consideration of congestion in Amman, the capital of Jordan. Real data were collected by different methods and analyzed. Then, concert technology - CPLEX was used to solve the proposed model for some random generated data instances and for the real collected data. At the end, results have shown a great improvement in time compared with the current trip times, and an economic study was conducted afterwards to figure out the impact of using such models.

Keywords: Travel salesman problem, congestions, pick-up, integer programming, package carriers, service engineering.

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Authors: Loay A. Al-Zu'be, Asma A. Al-Tamimi, Thakir D. Al-Momani, Ayat J. Alkarala, Maryam A. Alzawahreh

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A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.

Keywords: Body Configurations, Equations of Motion, Mathematical Modeling, Movement Trajectories.

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Authors: Phakhapong Thanitakul, Worawat Sa-ngiamvibool, Apinan Aurasopon, Saravuth Pothiya

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This paper presents an improved ant colony optimization (IACO) for solving the reliability redundancy allocation problem (RAP) in order to maximize system reliability. To improve the performance of ACO algorithm, two additional techniques, i.e. neighborhood search, and re-initialization process are presented. To show its efficiency and effectiveness, the proposed IACO is applied to solve three RAPs. Additionally, the results of the proposed IACO are compared with those of the conventional heuristic approaches i.e. genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO). The experimental results show that the proposed IACO approach is comparatively capable of obtaining higher quality solution and faster computational time.

Keywords: Ant colony optimization, Heuristic algorithm, Mixed-integer nonlinear programming, Redundancy allocation problem, Reliability optimization.

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Authors: Zahra Khalid, Gul Muhammad Khan, Arbab Masood Ahmad

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Cartesian Genetic Programming (CGP) is explored to design an optimal circuit capable of early stage breast cancer detection. CGP is used to evolve simple multiplexer circuits for detection of malignancy in the Fine Needle Aspiration (FNA) samples of breast. The data set used is extracted from Wisconsins Breast Cancer Database (WBCD). A range of experiments were performed, each with different set of network parameters. The best evolved network detected malignancy with an accuracy of 99.14%, which is higher than that produced with most of the contemporary non-linear techniques that are computational expensive than the proposed system. The evolved network comprises of simple multiplexers and can be implemented easily in hardware without any further complications or inaccuracy, being the digital circuit.

Keywords: Breast cancer detection, cartesian genetic programming, evolvable hardware, fine needle aspiration (FNA).

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Authors: Chompunut Jantarasorn, Chutima Prommak

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The important issue considered in the widespread deployment of Wireless Sensor Networks (WSNs) is an efficiency of the energy consumption. In this paper, we present a study of the optimal relay station planning problems using Binary Integer Linear Programming (BILP) model to minimize the energy consumption in WSNs. Our key contribution is that the proposed model not only ensures the required network lifetime but also guarantees the radio connectivity at high level of communication quality. Specially, we take into account effects of noise, signal quality limitation and bit error rate characteristics. Numerical experiments were conducted in various network scenarios. We analyzed the effects of different sensor node densities and distribution on the energy consumption.

Keywords: Binary Integer Linear Programming, BILP, Energy consumption, Optimal node placement and Wireless sensor networks.

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Authors: Yu-Jen Chang, Yun Chen, Hei-Lam Wong

Abstract:

The Economic Lot Scheduling Problem (ELSP) is a valuable mathematical model that can support decision-makers to make scheduling decisions. The basic period approach is effective for solving the ELSP. The assumption for applying the basic period approach is that a product must use its maximum production rate to be produced. However, a product can lower its production rate to reduce the average total cost when a facility has extra idle time. The past researches discussed how a product adjusts its production rate under the common cycle approach. To the best of our knowledge, no studies have addressed how a product lowers its production rate under the basic period approach. This research is the first paper to discuss this topic. The research develops a simple fixed rate approach that adjusts the production rate of a product under the basic period approach to solve the ELSP. Our numerical example shows our approach can find a better solution than the traditional basic period approach. Our mathematical model that applies the fixed rate approach under the basic period approach can serve as a reference for other related researches.

Keywords: Economic Lot, Basic Period, Genetic Algorithm, Fixed Rate.

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Authors: Xiaoyuan Yan, Min Xu

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Truck platooning refers to a convoy of digitally connected automated trucks traveling safely with a small inter-vehicle gap. It has been identified as one of the most promising and applicable technologies towards automated and sustainable freight transportation. Although truck platooning delivers significant energy-saving benefits, it cannot be realized without good coordination of drivers’ shifts to lead the platoons subject to their mandatory breaks. Therefore, this study aims to route a fleet of trucks to their destinations using the least amount of fuel by maximizing platoon opportunities under the regulations of drivers’ mandatory breaks. We formulate this platoon coordination problem as a mixed-integer linear programming problem and solve it by CPLEX. Numerical experiments are conducted to demonstrate the effectiveness and efficiency of our proposed model. In addition, we also explore the impacts of drivers’ compulsory breaks on the fuel-savings performance. The results show a slight increase in the total fuel costs in the presence of drivers’ compulsory breaks, thanks to driving-while-resting benefit provided for the trailing trucks. This study may serve as a guide for the operators of automated freight transportation.

Keywords: Truck platooning, route optimization, compulsory breaks, energy saving.

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Authors: Chuan Li, Ming Liang, Qibing Yu

Abstract:

To improve the dynamics response of the vehicle passive suspension, a two-terminal mass is suggested to connect in parallel with the suspension strut. Three performance criteria, tire grip, ride comfort and suspension deflection, are taken into consideration to optimize the suspension parameters. However, the three criteria are conflicting and non-commensurable. For this reason, the Chebyshev goal programming method is applied to find the best tradeoff among the three objectives. A simulation case is presented to describe the multi-objective optimization procedure. For comparison, the Chebyshev method is also employed to optimize the design of a conventional passive suspension. The effectiveness of the proposed design method has been clearly demonstrated by the result. It is also shown that the suspension with a two-terminal mass in parallel has better performance in terms of the three objectives.

Keywords: Vehicle, passive suspension, two-terminal mass, optimization, Chebyshev goal programming

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Authors: Ding Guo-hao, Li Hua, Wang Wen-long

Abstract:

A parallel computational fluid dynamics code has been developed for the study of aerodynamic heating problem in hypersonic flows. The code employs the 3D Navier-Stokes equations as the basic governing equations to simulate the laminar hypersonic flow. The cell centered finite volume method based on structured grid is applied for spatial discretization. The AUSMPW+ scheme is used for the inviscid fluxes, and the MUSCL approach is used for higher order spatial accuracy. The implicit LU-SGS scheme is applied for time integration to accelerate the convergence of computations in steady flows. A parallel programming method based on MPI is employed to shorten the computing time. The validity of the code is demonstrated by comparing the numerical calculation result with the experimental data of a hypersonic flow field around a blunt body.

Keywords: Aerodynamic Heating, AUSMPW+, MPI, ParallelComputation

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Authors: Vichai Rungreunganaun, Chirawat Woarawichai

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The objective of this research is to calculate the optimal inventory lot-sizing for each supplier and minimize the total inventory cost which includes joint purchase cost of the products, transaction cost for the suppliers, and holding cost for remaining inventory. Genetic algorithms (GAs) are applied to the multi-product and multi-period inventory lot-sizing problems with supplier selection under storage space. Also a maximum storage space for the decision maker in each period is considered. The decision maker needs to determine what products to order in what quantities with which suppliers in which periods. It is assumed that demand of multiple products is known over a planning horizon. The problem is formulated as a mixed integer programming and is solved with the GAs. The detailed computation results are presented.

Keywords: Genetic Algorithms, Inventory lot-sizing, Supplier selection, Storage space.

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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Authors: K. Paisal

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The purposes of this research were (1) to create a learning activity for constructivism, (2) study the Mathematical Analysis courses learning achievement, and (3) study students’ attitude toward the learning activity for constructivism. The samples in this study were divided into 2 parts including 3 Mathematical Analysis courses instructors of Suan Sunandha Rajabhat University who provided basic information and attended the seminar and 17 Mathematical Analysis courses students who were studying in the academic and engaging in the learning activity for constructivism. The research instruments were lesson plans constructivism, subjective Mathematical Analysis courses achievement test with reliability index of 0.8119, and an attitude test concerning the students’ attitude toward the Mathematical Analysis courses learning activity for constructivism. The result of the research show that the efficiency of the Mathematical Analysis courses learning activity for constructivism is 73.05/72.16, which is more than expected criteria of 70/70. The research additionally find that the average score of learning achievement of students who engaged in the learning activities for constructivism are equal to 70% and the students’ attitude toward the learning activity for constructivism are at the medium level.

Keywords: Constructivism, learning management, Mathematical Analysis courses.

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Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

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In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modelling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: Plate heat exchanger, optimization, modeling, simulation.

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Authors: A. Yacob, N. Hj. Ali, M. H. Yusoff, M. Y. MohdSaman, W. M. A. F. W. Hamzah

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Personalized learning becomes increasingly popular which not be restricted by time, place or any other barriers. This study proposes an analysis of Personalized Learning using Item Response Theory which considers course material difficulty and learner ability.The study investigates twenty undergraduate students at TATI University College, who are taking programming subject. By using the IRT,it was found that, finding the most appropriate problem levels to each student include high and low level test items together is not a problem. Thus, the student abilities can be asses more accurately and fairly. Learners who experience more anxiety will affect a heavier cognitive load and receive lower test scores.Instructors are encouraged to provide a supportive learning environment to enhance learning effectiveness because Cognitive Load Theory concerns the limited capacity of the brain to absorb new information.

Keywords: Analysis, Cognitive Load Theory, Item Response Theory, Learning, Motivation, Performance.

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Authors: G. M. Arun Prasath, N. Arthi

Abstract:

This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.

Keywords: Fuzzy inventory model, warehouse location model, triangular fuzzy number, secondary warehouse, LINGO software.

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