Search results for: Discrete ill-posed problem

Authors: Yung-Chien Sun, O. Grant Clark

Abstract:

In this paper, the implementation of a rule-based intuitive reasoner is presented. The implementation included two parts: the rule induction module and the intuitive reasoner. A large weather database was acquired as the data source. Twelve weather variables from those data were chosen as the “target variables" whose values were predicted by the intuitive reasoner. A “complex" situation was simulated by making only subsets of the data available to the rule induction module. As a result, the rules induced were based on incomplete information with variable levels of certainty. The certainty level was modeled by a metric called "Strength of Belief", which was assigned to each rule or datum as ancillary information about the confidence in its accuracy. Two techniques were employed to induce rules from the data subsets: decision tree and multi-polynomial regression, respectively for the discrete and the continuous type of target variables. The intuitive reasoner was tested for its ability to use the induced rules to predict the classes of the discrete target variables and the values of the continuous target variables. The intuitive reasoner implemented two types of reasoning: fast and broad where, by analogy to human thought, the former corresponds to fast decision making and the latter to deeper contemplation. . For reference, a weather data analysis approach which had been applied on similar tasks was adopted to analyze the complete database and create predictive models for the same 12 target variables. The values predicted by the intuitive reasoner and the reference approach were compared with actual data. The intuitive reasoner reached near-100% accuracy for two continuous target variables. For the discrete target variables, the intuitive reasoner predicted at least 70% as accurately as the reference reasoner. Since the intuitive reasoner operated on rules derived from only about 10% of the total data, it demonstrated the potential advantages in dealing with sparse data sets as compared with conventional methods.

Keywords: Artificial intelligence, intuition, knowledge acquisition, limited certainty.

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Authors: S. J. Arif

Abstract:

In the presented technique, a simple method is given for accurate measurement and control of power frequency deviation. The sinusoidal signal for which the frequency deviation measurement is required is transformed to a low voltage level and passed through a zero crossing detector to convert it into a pulse train. Another stable square wave signal of 10 KHz is obtained using a crystal oscillator and decade dividing assemblies (DDA). These signals are combined digitally and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded to make them equally suitable for both control applications and display units. The developed circuit using discrete components has a resolution of 0.5 Hz and completes measurement within 20 ms. The realized circuit is simulated and synthesized using Verilog HDL and subsequently implemented on FPGA. The results of measurement on FPGA are observed on a very high resolution logic analyzer. These results accurately match the simulation results as well as the results of same circuit implemented with discrete components. The proposed system is suitable for accurate measurement and control of power frequency deviation.

Keywords: Digital encoder for frequency measurement, frequency deviation measurement, measurement and control systems, power systems.

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Authors: M. Erol Genevois, D. Celik, H. Z. Ulukan

Abstract:

Automated Teller Machines (ATMs) can be considered among one of the most important service facilities in the banking industry. The investment in ATMs and the impact on the banking industry is growing steadily in every part of the world. The banks take into consideration many factors like safety, convenience, visibility, and cost in order to determine the optimum locations of ATMs. Today, ATMs are not only available in bank branches but also at retail locations. Another important factor is the cash management in ATMs. A cash demand model for every ATM is needed in order to have an efficient cash management system. This forecasting model is based on historical cash demand data which is highly related to the ATMs location. So, the location and the cash management problem should be considered together. This paper provides a general review on studies, efforts and development in ATMs location and cash management problem.

Keywords: ATM location problem, cash management problem, ATM cash replenishment problem, literature review in ATMs.

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: M. Ismail, Cao Yihua, Zhao Ming

Abstract:

Heavy rainfall greatly affects the aerodynamic performance of the aircraft. There are many accidents of aircraft caused by aerodynamic efficiency degradation by heavy rain. In this Paper we have studied the heavy rain effects on the aerodynamic efficiency of NACA 64-210 & NACA 0012 airfoils. For our analysis, CFD method and preprocessing grid generator are used as our main analytical tools, and the simulation of rain is accomplished via two phase flow approach-s Discrete Phase Model (DPM). Raindrops are assumed to be non-interacting, non-deforming, non-evaporating and non-spinning spheres. Both airfoil sections exhibited significant reduction in lift and increase in drag for a given lift condition in simulated rain. The most significant difference between these two airfoils was the sensitivity of the NACA 64-210 to liquid water content (LWC), while NACA 0012 performance losses in the rain environment is not a function of LWC . It is expected that the quantitative information gained in this paper will be useful to the operational airline industry and greater effort such as small scale and full scale flight tests should put in this direction to further improve aviation safety.

Keywords: airfoil, discrete phase modeling, heavy rain, Reynolds number

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Authors: B. Özlük, A. Karaaslan

Abstract:

This study has been conducted as a supplementary and relationship seeking study with the purpose of measuring the tendency and success of support among peers amid nursing students studying at university in solving interpersonal problems. The population of the study (N:279) is comprised of nursing students who are studying at one state and one private university in the province of Konya, while its sample is comprised of 231 nursing students who agreed to take part in the study voluntarily. As a result of this study, it has been determined that the peer support and interpersonal problem solving characteristics among students were at medium levels and that the interpersonal problem solving skills of students studying in the third year were higher than those of first and second year students. While the interpersonal problem solving characteristics of students who are aged 20 and over were found to be higher, no difference could be determined in terms of the interpersonal problem solving skills and tendencies among students, based on their gender and where they reside. A positive – to a medium degree – and significant relationship was determined between peer support and interpersonal problem solving skills, and it is possible to say that as peer support increases, so do the skills and tendencies to solve problems.

Keywords: Interpersonal problem, nursing students, peer support, problem solving.

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Authors: Amir Farkhonde

Abstract:

The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: P.L.D.N.M. de Silva, S.G. Edirisinghe, R. Weerasuriya

Abstract:

High Peak-to-Average Power Ratio (PAPR) is a concern of Orthogonal Frequency Division Multiplexing (OFDM) based Visible Light Communication (VLC) systems. Discrete Fourier Transform spread (DFT-s) OFDM is an alternative single carrier modulation scheme which would address this concern. Employing channel coding techniques is another mechanism to reduce the PAPR. In this study, the improvement which can be harnessed by hybridizing these two techniques for VLC system is being studied. Within the study, efficient techniques such as Hamming coding and Convolutional coding have been studied. Thus, we present the impact of the hybrid of DFT-s OFDM and Channel coding (Hamming coding and Convolutional coding) on PAPR in VLC systems, using MATLAB simulations.

Keywords: Convolutional Coding, Discrete Fourier Transform spread Orthogonal Frequency Division Multiplexing (DFT-s OFDM), Hamming Coding, Peak-to-Average Power Ratio (PAPR), Visible Light Communications (VLC).

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Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

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This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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Authors: Takayuki Shiina

Abstract:

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: Emad Alenany, M. Adel El-Baz

Abstract:

In this paper, the flow of different classes of patients into a hospital is modelled and analyzed by using the queueing network analyzer (QNA) algorithm and discrete event simulation. Input data for QNA are the rate and variability parameters of the arrival and service times in addition to the number of servers in each facility. Patient flows mostly match real flow for a hospital in Egypt. Based on the analysis of the waiting times, two approaches are suggested for improving performance: Separating patients into service groups, and adopting different service policies for sequencing patients through hospital units. The separation of a specific group of patients, with higher performance target, to be served separately from the rest of patients requiring lower performance target, requires the same capacity while improves performance for the selected group of patients with higher target. Besides, it is shown that adopting the shortest processing time and shortest remaining processing time service policies among other tested policies would results in, respectively, 11.47% and 13.75% reduction in average waiting time relative to first come first served policy.

Keywords: Queueing network, discrete-event simulation, health applications, SPT.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: M. Rezki, A. Belaidi

Abstract:

This paper deals with a method of learning to solve a real problem in biomedical engineering from a technical study of muscle fatigue. Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles (viewpoint: anatomical and physiological). EMG is used as a diagnostics tool for identifying neuromuscular diseases, assessing low-back pain and muscle fatigue in general. In order to study the EMG signal for detecting fatigue in a muscle, we have taken a real problem which touches the tramway conductor the handle bar. For the study, we have used a typical autonomous platform in order to get signals at real time. In our case study, we were confronted with complex problem to do our experiments in a tram. This type of problem is recurring among students. To teach our students the method to solve this kind of problem, we built a similar system. Through this study, we realized a lot of objectives such as making the equipment for simulation, the study of detection of muscle fatigue and especially how to manage a study of biomedical looking.

Keywords: EMG, health platform, conductor’s tram, muscle fatigue.

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Authors: Shang-Lin Hsieh, Lung-Yao Hsu, I-Ju Tsai

Abstract:

This paper proposes a copyright protection scheme for color images using secret sharing and wavelet transform. The scheme contains two phases: the share image generation phase and the watermark retrieval phase. In the generation phase, the proposed scheme first converts the image into the YCbCr color space and creates a special sampling plane from the color space. Next, the scheme extracts the features from the sampling plane using the discrete wavelet transform. Then, the scheme employs the features and the watermark to generate a principal share image. In the retrieval phase, an expanded watermark is first reconstructed using the features of the suspect image and the principal share image. Next, the scheme reduces the additional noise to obtain the recovered watermark, which is then verified against the original watermark to examine the copyright. The experimental results show that the proposed scheme can resist several attacks such as JPEG compression, blurring, sharpening, noise addition, and cropping. The accuracy rates are all higher than 97%.

Keywords: Color image, copyright protection, discrete wavelet transform, secret sharing, watermarking.

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Authors: Hossain Aziz, Rinku Mukherjee

Abstract:

A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface" boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface" boundary condition Kelvin-s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Keywords: Aerodynamics, Airfoils, Configuration, Unsteady.

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Authors: Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid

Abstract:

Deoxyribonucleic Acid or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science and mathematics. Thus, in this paper, the possibility of DNA-based computing to solve an absolute 1-center problem by molecular manipulations is presented. This is truly the first attempt to solve such a problem by DNA-based computing approach. Since, part of the procedures involve with shortest path computation, research works on DNA computing for shortest path Traveling Salesman Problem, in short, TSP are reviewed. These approaches are studied and only the appropriate one is adapted in designing the computation procedures. This DNA-based computation is designed in such a way that every path is encoded by oligonucleotides and the path-s length is directly proportional to the length of oligonucleotides. Using these properties, gel electrophoresis is performed in order to separate the respective DNA molecules according to their length. One expectation arise from this paper is that it is possible to verify the instance absolute 1-center problem using DNA computing by laboratory experiments.

Keywords: DNA computing, operation research, 1-center problem.

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Authors: Wen-Haw Chen

Abstract:

This paper proposes a method to improve the shortest path problem on a NURBS (Non-uniform rational basis spline) surfaces. It comes from an application of the theory in classic differential geometry on surfaces and can improve the distance problem not only on surfaces but in the Euclidean 3-space R3 .

Keywords: shortest paths, geodesic-like method, NURBS surfaces.

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Authors: Lee Yih Rou, Hishammuddin Asmuni

Abstract:

Flexible Job Shop Problem (FJSP) is an extension of classical Job Shop Problem (JSP). The FJSP extends the routing flexibility of the JSP, i.e assigning machine to an operation. Thus it makes it more difficult than the JSP. In this study, Cooperative Coevolutionary Genetic Algorithm (CCGA) is presented to solve the FJSP. Makespan (time needed to complete all jobs) is used as the performance evaluation for CCGA. In order to test performance and efficiency of our CCGA the benchmark problems are solved. Computational result shows that the proposed CCGA is comparable with other approaches.

Keywords: Co-evolution, Genetic Algorithm (GA), Flexible JobShop Problem(FJSP)

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Authors: Kouamana Bousson, Paulo Machado

Abstract:

The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials.

Keywords: Pseudospectral Methods, Trajectory Optimization, 4DTrajectories

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.

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Authors: Tirthankar Ghosh, Dilip Roy, Nimai Kumar Chandra

Abstract:

Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

Keywords: Discretization, Reversed Hazard Rate, Exponential distribution, reliability approximation, engineering item.

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Authors: Xu LiYun, Briand Florent, Fan GuoLiang

Abstract:

The loop-layout design problem (LLDP) aims at optimizing the sequence of positioning of the machines around the cyclic production line. Traffic congestion is the usual criteria to minimize in this type of problem, i.e. the number of additional cycles spent by each part in the network until the completion of its required routing sequence of machines. This paper aims at applying several improvements mechanisms such as a positioned-based crossover operator for the Genetic Algorithm (GA) called a Two Points Crossover (TPC) and an offspring selection process. The performance of the improved GA is measured using well-known examples from literature and compared to other evolutionary algorithms. Good results show that GA can still be competitive for this type of problem against more recent evolutionary algorithms.

Keywords: Crossover, genetic algorithm, layout design problem, loop-layout, manufacturing optimization.

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Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: Economic dispatch, optimization, quadratic programming, MATLAB.

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Authors: Mhand Hifi, Hedi Mhalla

Abstract:

In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

Abstract:

A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Stephen C. H. Leung, Defu Zhang

Abstract:

This paper addresses a stock-cutting problem with rotation of items and without the guillotine cutting constraint. In order to solve the large-scale problem effectively and efficiently, we propose a simple but fast heuristic algorithm. It is shown that this heuristic outperforms the latest published algorithms for large-scale problem instances.

Keywords: Combinatorial optimization, heuristic, large-scale, stock-cutting.

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Authors: R. Rama Kishore, Sunesh

Abstract:

This paper presents an optimized, robust, and secured watermarking technique. The methodology used in this work is the combination of entropy and chaotic grid map. The proposed methodology incorporates Discrete Cosine Transform (DCT) on the host image. To improve the imperceptibility of the method, the host image DCT blocks, where the watermark is to be embedded, are further optimized by considering the entropy of the blocks. Chaotic grid is used as a key to reorder the DCT blocks so that it will further increase security while selecting the watermark embedding locations and its sequence. Without a key, one cannot reveal the exact watermark from the watermarked image. The proposed method is implemented on four different images. It is concluded that the proposed method is giving better results in terms of imperceptibility measured through PSNR and found to be above 50. In order to prove the effectiveness of the method, the performance analysis is done after implementing different attacks on the watermarked images. It is found that the methodology is very strong against JPEG compression attack even with the quality parameter up to 15. The experimental results are confirming that the combination of entropy and chaotic grid map method is strong and secured to different image processing attacks.

Keywords: Digital watermarking, discrete cosine transform, chaotic grid map, entropy.

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Authors: Barıs Kocer, Ahmet Arslan

Abstract:

Travelling salesman problem (TSP) is a combinational optimization problem and solution approaches have been applied many real world problems. Pure TSP assumes the cities to visit are fixed in time and thus solutions are created to find shortest path according to these point. But some of the points are canceled to visit in time. If the problem is not time crucial it is not important to determine new routing plan but if the points are changing rapidly and time is necessary do decide a new route plan a new approach should be applied in such cases. We developed a route plan transfer method based on transfer learning and we achieved high performance against determining a new model from scratch in every change.

Keywords: genetic algorithms, transfer learning, travellingsalesman problem

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Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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