Search results for: discrete location problems

Authors: Ahmed Osama, Hassan A. Mahdy, Khalid A. Kandil, Mohamed Elhabiby

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Automatic Vehicle Location systems (AVL) have been used worldwide for more than twenty years and have showed great success in public transportation management and monitoring. Cairo public bus service suffers from several problems such as unscheduled stops, unscheduled route deviations, and inaccurate schedules, which have negative impacts on service reliability. This research aims to study those problems for a selected bus route in Cairo using a prototype AVL system. Experimental trips were run on the selected route; and the locations of unscheduled stops, regions of unscheduled deviations, along with other trip time and speed data were collected. Data was analyzed to demonstrate the reliability of passengers on the unscheduled stops compared to the scheduled ones. Trip time was also modeled to assess the unscheduled stops’ impact on trip time, and to check the accuracy of the applied scheduled trip time. Moreover, frequency and length of the unscheduled route deviations, as well as their impact on the bus stops, were illustrated. Solutions were proposed for the bus service deficiencies using the AVL system. Finally, recommendations were proposed for further research.

Keywords: automatic vehicle location, public transportation, unscheduled stops, unscheduled route deviations, inaccurate schedule

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Authors: Karina C. Azzolin, Luis E. Kosteski, Alisson S. Milani, Raquel C. Zydeck

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This work aims to represent Numerically tests experimentally developed in reduced scale walls with horizontal and inclined cuts by using the Lattice Discrete Element Method (LDEM) implemented On de Abaqus/explicit environment. The cuts were performed with depths of 20%, 30%, and 50% On the walls subjected to centered and eccentric loading. The parameters used to evaluate the numerical model are its strength, the failure mode, and the in-plane and out-of-plane displacements.

Keywords: structural masonry, wall chases, small scale, numerical model, lattice discrete element method

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Authors: Tun Myat Aung, Ni Ni Hla

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This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: discrete logarithm problem, general attacks, elliptic curve, prime field, binary field

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Elham Taghizadeh, Mostafa Abedzadeh, Mostafa Setak

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Logistics network is expected that opened facilities work continuously for a long time horizon without any failure; but in real world problems, facilities may face disruptions. This paper studies a reliable joint inventory location problem to optimize cost of facility locations, customers’ assignment, and inventory management decisions when facilities face failure risks and doesn’t work. In our model we assume when a facility is out of work, its customers may be reassigned to other operational facilities otherwise they must endure high penalty costs associated with losing service. For defining the model closer to real world problems, the model is proposed based on p-median problem and the facilities are considered to have limited capacities. We define a new binary variable (Z_is) for showing that customers are not assigned to any facilities. Our problem involve a bi-objective model; the first one minimizes the sum of facility construction costs and expected inventory holding costs, the second one function that mention for the first one is minimizes maximum expected customer costs under normal and failure scenarios. For solving this model we use NSGAII and MOSS algorithms have been applied to find the pareto- archive solution. Also Response Surface Methodology (RSM) is applied for optimizing the NSGAII Algorithm Parameters. We compare performance of two algorithms with three metrics and the results show NSGAII is more suitable for our model.

Keywords: joint inventory-location problem, facility location, NSGAII, MOSS

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Authors: Ashish Ashish

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In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

Procedia PDF Downloads 133

Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, a hybrid blind digital watermarking system using Discrete Wavelet Transform (DWT) and Contourlet Transform (CT) has been implemented and tested. The implemented combined digital watermarking system has been tested against five common types of image attacks. The performance evaluation shows improved results in terms of imperceptibility, robustness, and high tolerance against these attacks; accordingly, the system is very effective and applicable.

Keywords: discrete wavelet transform (DWT), contourlet transform (CT), digital image watermarking, copyright protection, geometric attack

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Authors: A. S. Mousa, F. Shoman

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We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: coherent strategy, split strategy, pure strategy, mixed strategy, Nash equilibrium, game theory

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

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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, 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. Although the literature survey on facility location models is quite large, it is surprising that there are only few studies which handle together ATMs location and cash management problem. In order to fulfill the gap, 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: Samvel H. Sargsyan

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Together with the study of electron-optical properties of nanostructures and proceeding from experiment-based data, the study of the mechanical properties of nanostructures has become quite actual. For the study of the mechanical properties of fullerene, carbon nanotubes, graphene and other nanostructures one of the crucial issues is the construction of their adequate mathematical models. Among all mathematical models of graphene or carbon nano-tubes, this so-called discrete-continuous model is specifically important. It substitutes the interactions between atoms by elastic beams or springs. The present paper demonstrates the construction of the discrete-continual beam model for carbon nanotubes or graphene, where the micropolar beam model based on the theory of moment elasticity is accepted. With the account of the energy balance principle, the elastic moment constants for the beam model, expressed by the physical and geometrical parameters of carbon nanotube or graphene, are determined. By switching from discrete-continual beam model to the continual, the models of micropolar elastic cylindrical shell and micropolar elastic plate are confirmed as continual models for carbon nanotube and graphene respectively.

Keywords: carbon nanotube, discrete-continual, elastic, graphene, micropolar, plate, shell

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Authors: Blair D. Macdonald

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After nearly one hundred years of its origin, foundational quantum mechanics remains one of the greatest unexplained mysteries in physicists today. Within this time, chaos theory and its geometry, the fractal, has developed. In this paper, the propagation behaviour with an iteration of a simple fractal, the Koch Snowflake, was described and analysed. From an arbitrary observation point within the fractal set, the fractal propagates forward by oscillation—the focus of this study and retrospectively behind by exponential growth from a point beginning. It propagates a potentially infinite exponential oscillating sinusoidal wave of discrete triangle bits sharing many characteristics of light and quantum entities. The model's wave speed is potentially constant, offering insights into the perception and a direction of time where, to an observer, when travelling at the frontier of propagation, time may slow to a stop. In isolation, the fractal is a superposition of component bits where position and scale present a problem of location. In reality, this problem is experienced within fractal landscapes or fields where 'position' is only 'known' by the addition of information or markers. The quantum' measurement problem', 'uncertainty principle,' 'entanglement,' and the classical-quantum interface are addressed; these are a problem of scale invariance associated with isolated fractality. Dual forward and retrospective perspectives of the fractal model offer the opportunity for unification between quantum mechanics and cosmological mathematics, observations, and conjectures. Quantum and cosmological problems may be different aspects of the one fractal geometry.

Keywords: measurement problem, observer, entanglement, unification

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Authors: Serhat Tüzün, Tufan Demirel

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The objective of the present study is to select the most suitable location for a wind power plant station through Choquet integral method. The problem of selecting the location for a wind power station was considered as a multi-criteria decision-making problem. The essential and sub-criteria were specified and location selection was expressed in a hierarchic structure. Among the main criteria taken into account in this paper are wind potential, technical factors, social factors, transportation, and costs. The problem was solved by using different approaches of Choquet integral and the best location for a wind power station was determined. Then, the priority weights obtained from different Choquet integral approaches are compared and commented on.

Keywords: multi-criteria decision making, choquet integral, fuzzy sets, location of a wind power plant

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Authors: Badrun Taman

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This study aims to review the use of the Bengkulu Provincial Government Mess as the location of rukyatul hilal because its determination has not been carried out scientifically. There are three things that will be analyzed, namely geographical-astronomical conditions, the suitability of the location with ideal criteria, and the determination of the location of rukyatul hilal in accordance with regional conditions based on the results of the study. The research method used is qualitative with an astronomical geographical approach. The results showed that the factor that strengthened the disturbance from the weather aspect was the western sky horizon in the form of the Indian Ocean sea level. The potential for geographical disturbances on this horizon is high sea waves, relatively high sea breezes, and more seawater vapor due to sea surface temperatures and high air humidity. This study found new criteria for determining the location of the observation crescent. The criteria is the western horizon is not sea level (especially the Indian Ocean).

Keywords: criteria, location, Rukyatul Hilal, tropics, Indian ocean

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Authors: Sumaya Ismail, Aijaz Ahmad Rehi

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Abstract The location tracking and positioning systems have technologically grown exponentially in recent decade. In particular, Global Position system (GPS) has become a universal norm to be a part of almost every software application directly or indirectly for the location based modules. However major drawback of GPS based system is their inability of working in indoor environments. Researchers are thus focused on the alternative technologies which can be used in indoor environments for a vast range of application domains which require indoor location tracking. One of the most popular technology used for indoor tracking is radio frequency identification (RFID). Due to its numerous advantages, including its cost effectiveness, it is considered as a technology of choice in indoor location tracking systems. To contribute to the emerging trend of the research, this paper proposes an application architecture of passive RFID tag based indoor location tracking system. For the proof of concept, a test bed will be developed to in this study. In addition, various indoor location tracking algorithms will be used to assess their appropriateness in the proposed application architecture.

Keywords: RFID, GPS, indoor location tracking, application architecture, passive RFID tag

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Usama Abdulwahab, Mohammed Wahab

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This paper presents the application of uncapacitated facility location problems (UFLP) and 1-median problems to support decision making in blood supply chain networks. A plethora of factors make blood supply-chain networks a complex, yet vital problem for the regional blood bank. These factors are rapidly increasing demand; criticality of the product; strict storage and handling requirements; and the vastness of the theater of operations. As in the UFLP, facilities can be opened at any of $m$ predefined locations with given fixed costs. Clients have to be allocated to the open facilities. In classical location models, the allocation cost is the distance between a client and an open facility. In this model, the costs are the allocation cost, transportation costs, and inventory costs. In order to address this problem the median algorithm is used to analyze inventory, evaluate supply chain status, monitor performance metrics at different levels of granularity, and detect potential problems and opportunities for improvement. The Euclidean distance data for some Ontario cities (demand nodes) are used to test the developed algorithm. Sitation software, lagrangian relaxation algorithm, and branch and bound heuristics are used to solve this model. Computational experiments confirm the efficiency of the proposed approach. Compared to the existing modeling and solution methods, the median algorithm approach not only provides a more general modeling framework but also leads to efficient solution times in general.

Keywords: approximate dynamic programming, facility location, perishable product, inventory model, blood platelet, P-median problem

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Authors: Syarif Hidayat

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As millions of people with different backgrounds perform hajj every year in Saudi Arabia, it brings out several problems. Missing people is among many crucial problems need to be encountered. Some people might have had insufficient knowledge of using tracking system equipment. Other might become a victim of an accident, lose consciousness, or even died, prohibiting them to perform certain activity. For those reasons, people could not send proper SOS message. The major contribution of this paper is the application of the diverse alert method in pilgrims tracking system. It offers a simple yet robust solution to send SOS message by pilgrims during Hajj. Knowledge of context aware computing is assumed herein. This study presents four methods that could be utilized by pilgrims to send SOS. The first method is simple mobile application contains only a button. The second method is based on behavior analysis based off GPS location movement anomaly. The third method is by introducing pressing pattern to smartwatch physical button as a panic button. The fourth method is by identifying certain accelerometer pattern recognition as a sign of emergency situations. Presented method in this paper would be an important part of pilgrims tracking system. The discussion provided here includes easy to use design whilst maintaining tracking accuracy, privacy, and security of its users.

Keywords: context aware computing, emergency alert system, GPS, hajj pilgrim tracking, location-based services

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Authors: Gurmail Singh

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Effective supply chain is the main priority of every organization which is the outcome of strategic corporate investments with deliberate management action. Value-driven supply chain is defined through development, procurement and by configuring the appropriate resources, metrics and processes. However, responsiveness of the supply chain can be improved by proper coordination. So the Bullwhip effect (BWE) and Net stock amplification (NSAmp) values were anticipated and used for the control of inventory in organizations by both discrete wavelet transform-Artificial neural network (DWT-ANN) and Adaptive Network-based fuzzy inference system (ANFIS). This work presents a comparative methodology of forecasting for the customers demand which is non linear in nature for a multilevel supply chain structure using hybrid techniques such as Artificial intelligence techniques including Artificial neural networks (ANN) and Adaptive Network-based fuzzy inference system (ANFIS) and Discrete wavelet theory (DWT). The productiveness of these forecasting models are shown by computing the data from real world problems for Bullwhip effect and Net stock amplification. The results showed that these parameters were comparatively less in case of discrete wavelet transform-Artificial neural network (DWT-ANN) model and using Adaptive network-based fuzzy inference system (ANFIS).

Keywords: bullwhip effect, hybrid techniques, net stock amplification, supply chain flexibility

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Authors: Gabriel Wainer

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Modeling and Simulation methods have been used to better analyze the behavior of complex physical systems, and it is now common to use simulation as a part of the scientific and technological discovery process. M&S advanced thanks to the improvements in computer technology, which, in many cases, resulted in the development of simulation software using ad-hoc techniques. Formal M&S appeared in order to try to improve the development task of very complex simulation systems. Some of these techniques proved to be successful in providing a sound base for the development of discrete-event simulation models, improving the ease of model definition and enhancing the application development tasks; reducing costs and favoring reuse. The DEVS formalism is one of these techniques, which proved to be successful in providing means for modeling while reducing development complexity and costs. DEVS model development is based on a sound theoretical framework. The independence of M&S tasks made possible to run DEVS models on different environments (personal computers, parallel computers, real-time equipment, and distributed simulators) and middleware. We will present a historical perspective of discrete-event M&S methodologies, showing different modeling techniques. We will introduce DEVS origins and general ideas, and compare it with some of these techniques. We will then show the current status of DEVS M&S, and we will discuss a technological perspective to solve current M&S problems (including real-time simulation, interoperability, and model-centered development techniques). We will show some examples of the current use of DEVS, including applications in different fields. We will finally show current open topics in the area, which include advanced methods for centralized, parallel or distributed simulation, the need for real-time modeling techniques, and our view in these fields.

Keywords: modeling and simulation, discrete-event simulation, hybrid systems modeling, parallel and distributed simulation

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Authors: M. Zyczkowski, P. Markowski, M. Karol

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The security industry is making many efforts to lower the costs of system installation. However, the dominant technique is the application of fiber optic sensors. It is necessary to determine the location of the disorder of long optical fiber cables. For a number of years, many research centers developed their own solutions. The article presents the construction of the sensor systems with the possibility of disorder location. We present a methodology for determining location of the disorder. The aim of investigations is to answer the question of which of optical sensor configuration offer the best performance for location of the disorder.

Keywords: fiber optic sensor, security sensor, fiber cables, system instillation

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Authors: M. Pallikonda Rajasekaran, J. Joshapath, Abhishek Prasad Shaw

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Various techniques has been employed to find location such as GPS, GLONASS, Galileo, and Beidou (compass). This paper currently deals with finding location using the existing FM signals that operates between 88-108 MHz. The location can be determined based on the received signal strength of nearby existing FM stations by mapping the signal strength values using trilateration concept. Thus providing security to users data and maintains eco-friendly environment at zero installation cost as this technology already existing FM stations operating in commercial FM band 88-108 MHZ. Along with the signal strength based trilateration it also finds azimuthal angle of the transmitter by employing directional antenna like Yagi-Uda antenna at the receiver side.

Keywords: location, existing FM signals, received signal strength, trilateration, security, eco-friendly, direction, privacy, zero installation cost

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Authors: Michalis Linardakis, Vasilis Grammatikopoulos, Athanasios Gregoriadis, Kalliopi Trouli

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Discrete choice models belong to the family of Conjoint analysis that are applied on the preferences of the respondents towards a set of scenarios that describe alternative choices. The scenarios have been pre-designed to cover all the attributes of the alternatives that may affect the choices. In this study, we examine how preschool educators integrate physical activities into their everyday teaching practices through the use of discrete choice models. One of the advantages of discrete choice models compared to other more traditional data collection methods (e.g. questionnaires and interviews that use ratings) is that the respondent is called to select among competitive and realistic alternatives, rather than objectively rate each attribute that the alternatives may have. We present the effort to construct and choose representative attributes that would cover all possible choices of the respondents, and the scenarios that have arisen. For the purposes of the study, we used a sample of 50 preschool educators in Greece that responded to 4 scenarios (from the total of 16 scenarios that the orthogonal design resulted), with each scenario having three alternative teaching practices. Seven attributes of the alternatives were used in the scenarios. For the analysis of the data, we used multinomial logit model with random effects, multinomial probit model and generalized mixed logit model. The conclusions drawn from the estimated parameters of the models are discussed.

Keywords: conjoint analysis, discrete choice models, educational data, multivariate statistical analysis

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Authors: Iqbal Felani

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A Coal-Fired Power Plant has some integrated facilities to handle coal from three separated coal yards to eight units power plant’s bunker. But nowadays the facilities are not reliable enough for supporting the system. Management planned to invest some facilities to increase the reliability. They also had a plan to make single spesification of coal used all of the units, called Single Quality Coal (SQC). This simulation would compare before and after improvement with two scenarios i.e First In First Out (FIFO) and Last In First Out (LIFO). Some parameters like stay time, reorder point and safety stock is determined by the simulation. Discrete event simulation based software, Flexsim 5.0, is used to help the simulation. Based on the simulation, Single Quality Coal with FIFO scenario has the shortest staytime with 8.38 days.

Keywords: Coal Yard Management, Discrete event simulation First In First Out, Last In First Out.

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Authors: Mohamed Hassan Abdullahi

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Decomposition is used as a synthesis tool in several physical systems. It can also be used for tearing and restructuring, which is large-scale system analysis. On the other hand, the commutativity of series-connected systems has fascinated the interest of researchers, and its advantages have been emphasized in the literature. The presentation looks into the necessary conditions for decomposing any third-order discrete-time linear time-varying system into a commutative pair of first- and second-order systems. Additional requirements are derived in the case of nonzero initial conditions. MATLAB simulations are used to verify the findings. The work is unique and is being published for the first time. It is critical from the standpoints of synthesis and/or design. Because many design techniques in engineering systems rely on tearing and reconstruction, this is the process of putting together simple components to create a finished product. Furthermore, it is demonstrated that regarding sensitivity to initial conditions, some combinations may be better than others. The results of this work can be extended for the decomposition of fourth-order discrete-time linear time-varying systems into lower-order commutative pairs, as two second-order commutative subsystems or one first-order and one third-order commutative subsystems.

Keywords: commutativity, decomposition, discrete time-varying systems, systems

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Authors: Anders Schou Simonsen, Thomas Condra, Kim Sørensen

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Various processes are modelled using a discrete phase, where particles are seeded from a source. Such particles can represent liquid water droplets, which are affecting the continuous phase by exchanging thermal energy, momentum, species etc. Discrete phases are typically modelled using parcel, which represents a collection of particles, which share properties such as temperature, velocity etc. When coupling the phases, the exchange rates are integrated over the cell, in which the parcel is located. This can cause spikes and fluctuating exchange rates. This paper presents an alternative method of coupling a discrete and a continuous plug flow phase. This is done using triangular parcels, which span between nodes following the dynamics of single droplets. Thus, the triangular parcels are propagated using the corner nodes. At each time step, the exchange rates are spatially integrated over the surface of the triangular parcels, which yields a smooth continuous exchange rate to the continuous phase. The results shows that the method is more stable, converges slightly faster and yields smooth exchange rates compared with the steam tube approach. However, the computational requirements are about five times greater, so the applicability of the alternative method should be limited to processes, where the exchange rates are important. The overall balances of the exchanged properties did not change significantly using the new approach.

Keywords: CFD, coupling, discrete phase, parcel

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Authors: Raed Alnajjar, Mohd Zakree, Ahmad Nazri

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In this study, we apply Discrete Group Search Optimizer (DGSO) for solving Traveling Salesman Problem (TSP). The DGSO is a nature inspired optimization algorithm that imitates the animal behavior, especially animal searching behavior. The proposed DGSO uses a vector representation and some discrete operators, such as destruction, construction, differential evolution, swap and insert. The TSP is a well-known hard combinatorial optimization problem, which seeks to find the shortest path among numbers of cities. The performance of the proposed DGSO is evaluated and tested on benchmark instances which listed in LIBTSP dataset. The experimental results show that the performance of the proposed DGSO is comparable with the other methods in the state of the art for some instances. The results show that DGSO outperform Ant Colony System (ACS) in some instances whilst outperform other metaheuristic in most instances. In addition to that, the new results obtained a number of optimal solutions and some best known results. DGSO was able to obtain feasible and good quality solution across all dataset.

Keywords: discrete group search optimizer (DGSO); Travelling salesman problem (TSP); Variable neighborhood search(VNS)

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Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Hooman Dabirmanesh, Attila M. Zsaki

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Traditionally, rock slope stability is carried out using limit equilibrium analysis when investigating toppling failure. In these equilibrium methods, internal forces exerted between columns are not clearly defined, and to the authors’ best knowledge, there is no consensus in literature with respect to the results of analysis. A discrete element method-based numerical model was developed and applied to simulate the behavior of rock layers subjected to toppling failure. Based on this calibrated numerical model, a study of the location and distribution of internal forces that result in equilibrium was carried out. The sum of side forces was applied at a point on a block which properly represents the force to determine the inter-column force distribution. In terms of the side force distribution coefficient, the result was compared to those obtained from laboratory centrifuge tests. The results of the simulation show the suitable criteria to select the correct position for the internal exerted force between rock layers. In addition, the numerical method demonstrates how a theoretical method could be reliable by considering the interaction between the rock layers.

Keywords: contact bond, discrete element, force distribution, limit equilibrium, tensile stress

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Authors: Saltanat Zhilkibayeva, Muratulla Utenov, Nurzhan Utenov

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The distributed inertia forces of complex nature appear in links of rod mechanisms within the motion process. Such loads raise a number of problems, as the problems of destruction caused by a large force of inertia; elastic deformation of the mechanism can be considerable, that can bring the mechanism out of action. In this work, a new analytical approach for the definition of internal forces in links of robotic systems and mechanisms with statically indeterminate and determinate structures taking into account the distributed inertial and concentrated forces is proposed. The relations between the intensity of distributed inertia forces and link weight with geometrical, physical and kinematic characteristics are determined in this work. The distribution laws of inertia forces and dead weight make it possible at each position of links to deduce the laws of distribution of internal forces along the axis of the link, in which loads are found at any point of the link. The approximation matrixes of forces of an element under the action of distributed inertia loads with the trapezoidal intensity are defined. The obtained approximation matrixes establish the dependence between the force vector in any cross-section of the element and the force vector in calculated cross-sections, as well as allow defining the physical characteristics of the element, i.e., compliance matrix of discrete elements. Hence, the compliance matrixes of an element under the action of distributed inertial loads of trapezoidal shape along the axis of the element are determined. The internal loads of each continual link are unambiguously determined by a set of internal loads in its separate cross-sections and by the approximation matrixes. Therefore, the task is reduced to the calculation of internal forces in a final number of cross-sections of elements. Consequently, it leads to a discrete model of elastic calculation of links of rod mechanisms. The discrete model of the elements of mechanisms and robotic systems and their discrete model as a whole are constructed. The dynamic equilibrium equations for the discrete model of the elements are also received in this work as well as the equilibrium equations of the pin and rigid joints expressed through required parameters of internal forces. Obtained systems of dynamic equilibrium equations are sufficient for the definition of internal forces in links of mechanisms, which structure is statically definable. For determination of internal forces of statically indeterminate mechanisms (in the way of determination of internal forces), it is necessary to build a compliance matrix for the entire discrete model of the rod mechanism, that is reached in this work. As a result by means of developed technique the programs in the MAPLE18 system are made and animations of the motion of the fourth class mechanisms of statically determinate and statically indeterminate structures with construction on links the intensity of cross and axial distributed inertial loads, the bending moments, cross and axial forces, depending on kinematic characteristics of links are obtained.

Keywords: distributed inertial forces, internal forces, statically determinate mechanisms, statically indeterminate mechanisms

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