Search results for: modifiable areal unit problem (MAUP)

Authors: A. Mohammadi, M. Moghimi, S. Mohammadi

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Engineers need computational methods which could provide solutions less sensitive to the environmental effects, so the techniques should be used which take the uncertainty to account to control and minimize the risk associated with design and operation. In order to consider uncertainty in engineering problem, the optimization problem should be solved for a suitable range of the each uncertain input variable instead of just one estimated point. Using deterministic optimization problem, a large computational burden is required to consider every possible and probable combination of uncertain input variables. Several methods have been reported in the literature to deal with problems under uncertainty. In this paper, different methods presented and analyzed.

Keywords: uncertainty, Monte Carlo simulated, stochastic programming, scenario method

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang

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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.

Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation

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Authors: Harshit Garg, Shakshi Gupta

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One of the major problems in today’s world is the growing pollution. The cause for all environmental problems is the increasing pollution rate. Looking upon the statistics, one can find out that most of the pollution is caused by the vehicular pollution which is more than 70 % of the total pollution, effecting the environment as well as human health proportionally. One is aware of the fact that vehicles run on roads so why not having the roads which could adsorb that pollution, not only once but a number of times. Every problem has a solution which can be solved by the state of art of technology, that is one can use the innovative ideas and thoughts to make technology as a solution to the problem of vehicular pollution on roads. Solving the problem up to a certain limit/ percentage can be formulated into a new term called ECO ROADS.

Keywords: environment, pollution, roads, sustainibility

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Authors: Tarek S. Jamil, Ahmed M. Shaban, Eman S. Mansor, Ahmed A. Karim, Azza M. Abdel Aty

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In this manuscript, 35 m³/d NF unit was designed and applied for surface water treatment of river Nile water. Intake of Embaba drinking water treatment plant was selected to install that unit at since; it has the lowest water quality index value through the examined 6 sites in greater Cairo area. The optimized operating conditions were feed and permeate flow, 40 and 7 m³/d, feed pressure 2.68 bar and flux rate 37.7 l/m2.h. The permeate water was drinkable according to Egyptian Ministerial decree 458/2007 for the tested parameters (physic-chemical, heavy metals, organic, algal, bacteriological and parasitological). Single and double sand filters were used as pretreatment for NF membranes, but continuous clogging for sand filters moved us to use UF membrane as pretreatment for NF membrane.

Keywords: River Nile, NF membrane, pretreatment, UF membrane, water quality

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Authors: Graham Brooks, Belaisha Bin Belaisha, Hakkyong Kim

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The problem of preventing and/or reducing corruption is a major international problem. This paper, however, specifically focuses on how organisations in Dubai are tackling the problem of money laundering. This research establishes that Dubai has a clear international anti-money laundering framework but suffers from some national weaknesses such as diverse anti-money laundering working practice, lack of communication, sharing information and disparate organisational vested self-interest.

Keywords: corruption, governance, money laundering, prevention, strategies

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Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

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In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: Lucas Paganin, Viliam Makis

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With the advent of globalization, the market competition has become a major issue for most companies. One of the main strategies to overcome this situation is the quality improvement of the product at a lower cost to meet customers’ expectations. In order to achieve the desired quality of products, it is important to control the process to meet the specifications, and to implement the optimal maintenance policy for the machines and the production lines. Thus, the overall objective is to reduce process variation and the production and maintenance costs. In this paper, an integrated model involving Statistical Process Control (SPC) and maintenance is developed to achieve this goal. Therefore, the main focus of this paper is to develop the jointly optimal maintenance and statistical process control policy minimizing the total long run expected average cost per unit time. In our model, the production process can go out of control due to either the deterioration of equipment or other assignable causes. The equipment is also subject to failures in any of the operating states due to deterioration and aging. Hence, the process mean is controlled by an Xbar control chart using equidistant sampling epochs. We assume that the machine inspection epochs are the times when the control chart signals an out-of-control condition, considering both true and false alarms. At these times, the production process will be stopped, and an investigation will be conducted not only to determine whether it is a true or false alarm, but also to identify the causes of the true alarm, whether it was caused by the change in the machine setting, by other assignable causes, or by both. If the system is out of control, the proper actions will be taken to bring it back to the in-control state. At these epochs, a maintenance action can be taken, which can be no action, or preventive replacement of the unit. When the equipment is in the failure state, a corrective maintenance action is performed, which can be minimal repair or replacement of the machine and the process is brought to the in-control state. SMDP framework is used to formulate and solve the joint control problem. Numerical example is developed to demonstrate the effectiveness of the control policy.

Keywords: maintenance, semi-Markov decision process, statistical process control, Xbar control chart

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Authors: Amjad Naveed

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This study analysed the role of structural change in the process of labour productivity convergence at country and regional levels. Many forms of structural changes occurred within the European Union (EU) countries i.e. variation in sectoral employment share, changes in demand for products, variations in trade patterns and advancement in technology which may have an influence on the process of convergence. Earlier studies on convergence have neglected the role of structural changes which can have resulted in different conclusion on the nature of convergence. The contribution of this study is to examine the role of structural change in testing labour productivity convergence at various levels. For the empirical purpose, the data of 19 EU countries, 259 regions and 6 industries is used for the period of 1991-2009. The results indicate that convergence varies across regional and country levels for different industries when considered the role of structural change.

Keywords: labor produvitivty, convergence, structural change, panel unit root

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Authors: Chandra Gupt Porwal, Preeti C. Porwal

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Transient data reveals much about the machine's condition that steady-state data cannot. New technologies make this information much more available for evaluating the mechanical integrity of a machine train. Recent surveys at various stations indicate that simplicity is preferred over completeness in machine audits throughout the power generation industry. This is most clearly shown by the number of rotating machinery predictive maintenance programs in which only steady-state vibration amplitude is trended while important transient vibration data is not even acquired. Efforts have been made to explain what transient data is, its importance, the types of plots used for its display, and its effective utilization for analysis. In order to demonstrate the value of measuring transient data and its practical application in rotating machinery for resolving complex and persistent issues with turbine generators, the author presents a few case studies that highlight the presence of rotor instabilities due to the shaft moving towards the bearing centre in a 100 MM LMZ unit located in the Northern Capital Region (NCR), heavy misalignment noticed—especially after 2993 rpm—caused by loose coupling bolts, which prevented the machine from being synchronized for more than four months in a 250 MW KWU unit in the Western Region (WR), and heavy preload noticed at Intermediate pressure turbine (IPT) bearing near HP- IP coupling, caused by high points on coupling faces at a 500 MW KWU unit in the Northern region (NR), experienced at Indian power plants.

Keywords: transient data, steady-state-data, intermediate -pressure-turbine, high-points

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Authors: C. E. Nugraheni, L. Abednego

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This paper is concerned with minimization of mean tardiness and flow time in a real single machine production scheduling problem. Two variants of genetic algorithm as meta-heuristic are combined with hyper-heuristic approach are proposed to solve this problem. These methods are used to solve instances generated with real world data from a company. Encouraging results are reported.

Keywords: hyper-heuristics, evolutionary algorithms, production scheduling, meta-heuristic

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Authors: Dimitri Golenko-Ginzburg

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A CPM network project with deterministic activity durations, in which activities require homogenous resources with fixed capacities, is considered. The problem is to determine the optimal schedule of starting times for all network activities within their maximal allowable limits (in order not to exceed the network's critical time) to minimize the maximum required resources for the project at any point in time. In case when a non-critical activity may start only at discrete moments with the pregiven time span, the problem becomes NP-complete and an optimal solution may be obtained via a look-over algorithm. For the case when a look-over requires much computational time an approximate algorithm is suggested. The algorithm's performance ratio, i.e., the relative accuracy error, is determined. Experimentation has been undertaken to verify the suggested algorithm.

Keywords: resource smoothing problem, CPM network, lookover algorithm, lexicographical order, approximate algorithm, accuracy estimate

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Authors: Prateek Chharia, Biswa Bhusan Ghosh

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Graph coloring is one of the prominent concepts in graph coloring. It can be defined as a coloring of the various regions of the graph such that all the constraints are fulfilled. In this paper various graphs coloring approaches like greedy coloring, Heuristic search for maximum independent set and graph coloring using edge table is described. Graph coloring can be used in various real time applications like student time tabling generation, Sudoku as a graph coloring problem, GSM phone network.

Keywords: graph coloring, greedy coloring, heuristic search, edge table, sudoku as a graph coloring problem

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Authors: Jelena Popović, Andrijana Mićanović

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Officially, 60% of Montenegrin territory is covered in forests, but they are continually being destroyed by illegal cutting, concession politics and wildfires. Montenegrin Ecologists Society started the first dendrochronology lab in Montenegro, and data collection began in the Summer of 2021. The cores were taken from 3 localities around the peak Lisac on the mt. Prekornica, where biggest P.heldreichii forests existed until recent huge wildfires. This research is the first step towards comprehensive dendrochronology research in Montenegro. It will show how old certain forest stands of Pinus heldreichii on mountain Prekornica are, that were not destroyed in huge wildfires from the recent years. It will also show how do they correlate between each other. Per locality 15 trees were sampled. Electric sanders (150 - 2000) were used for preparation. Cores were scanned, then measured in CooRecorder. Analysis is done in Cofecha. Process will be repeated with Lintab 6 and TSAP (Time Series Analysis and Presentation for Dendrochronology and Related Applications) - Win Scientific software by Rinntech. Since this is the first dendrochronology research entirely done in Montenegro it is a foundation for the dendroclimatology research. Besides, it’ll contribute to the understanding of the life of these forests in this part of its areal, and in designing good management practices.

Keywords: dendrochronology, bosnian pine, pinus heldreichii, montenegro, forests

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Authors: Miklos Taliga

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In the present case study we examined the development and testing methods of systems that contain safety-critical elements in different industrial fields. Consequentially, we observed the classical object-oriented development and testing environment, as both medical technology and automobile industry approaches the development of safety critical elements that way. Subsequently, we examined model-based development. We introduce the quality parameters that define development and testing. While taking modern agile methodology (scrum) into consideration, we examined whether and to what extent the methodologies we found fit into this environment.

Keywords: safety-critical elements, quality managent, unit verification, model base testing, agile methods, scrum, metamodel, object-oriented programming, field specific modelling, sprint, user story, UML Standard

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Authors: Ahmed Atef, Mohamed Alhasheem, Eman Beshr

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In this paper, an enhanced DC microgrid design is proposed using the DAB converter as a conversion unit in order to harvest the maximum power from the PV array. Each connected DAB converter is controlled with an enhanced control strategy. The controller is based on the artificial intelligence (AI) technique to regulate the terminal PV voltage through the phase shift angle of each DAB converter. In this manner, no need for a Maximum Power Point Tracking (MPPT) unit to set the reference of the PV terminal voltage. This strategy overcomes the stability issues of the DC microgrid as the response of converters is superior compared to the conventional strategies. The proposed PV interface system is modelled and simulated using MATLAB/SIMULINK. The simulation results reveal an accurate and fast response of the proposed design in case of irradiance changes.

Keywords: DC microgrid, DAB converter, parallel operation, artificial intelligence, fast response

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Authors: Afy Syahidan ACHMAD, Astin NURDIANA, SURYANTINI

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In volcanic arc environment we can find multiple volcanic deposits which overlapped with another volcanic deposit so it will complicates source and distribution determination. This problem getting more difficult when we can not trace any deposit border evidences in field especially in high vegetation volcanic area, or overlapped deposit with same characteristics. Main purpose of this study is to solve complex volcanostratigraphy mapping problems trough ridge, valley, and river continuity. This method application carried out in Old Sunda Volcanic, West Java, Indonesia. Using 1:100.000 and 1:50.000 topographic map, and regional geology map, old sunda volcanic deposit was differentiated in regional level and detail level. Final product of this method is volcanostratigraphy unit determination in reconnaissance stage to simplify mapping process.

Keywords: volcanostratigraphy, study, method, volcanic deposit

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

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This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm

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Authors: K. Djellabi, M. E. H. Latreche

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The induction heating phenomenon depends on various factors, making the problem highly nonlinear. The mathematical analysis of this problem in most cases is very difficult and it is reduced to simple cases. Another knowledge of induction heating systems is generated in production environments, but these trial-error procedures are long and expensive. The numerical models of induction heating problem are another approach to reduce abovementioned drawbacks. This paper deals with the simulation model of induction heating problem. The simulation model of induction heating system in COMSOL Multiphysics is created. In this work we present results of numerical simulations of induction heating process in pieces of cylindrical shapes, in an inductor with four coils. The modeling of the inducting heating process was made with the software COMSOL Multiphysics Version 4.2a, for the study we present the temperature charts.

Keywords: induction heating, electromagnetic field, inductor, numerical simulation, finite element

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Authors: M. S. Annie Christi

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Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: best candidate method, centroid ranking technique, fuzzy transportation problem, robust ranking technique, transportation problem

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Authors: N. Varsamis, M. Gerasimou, P. Christodoulou, S. Mantzoukis, G. Kolliopoulou, N. Zotos

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Purpose: Body fluids (pleural, peritoneal, synovial, pericardial, cerebrospinal) are an important element in the detection of microorganisms. For this reason, it is important to examine them in the Intensive Care Unit (ICU) patients. Material and Method: Body fluids are transported through sterile containers and enriched as soon as possible with Tryptic Soy Broth (TSB). After one day of incubation, the broth is poured into selective media: Blood, Mac Conkey No. 2, Chocolate, Mueller Hinton, Chapman and Saboureaud agar. The above selective media are incubated directly for 2 days. After this period, if any number of microbial colonies are detected, gram staining is performed. After that, the isolated organisms are identified by biochemical techniques in the automated Microscan system (Siemens) and followed by a sensitivity test on the same system using the minimum inhibitory concentration MIC technique. The sensitivity test is verified by Kirby Bauer-based plate test. Results: In 2017 the Laboratory of Microbiology received 60 samples of body fluids from the ICU. More specifically the Microbiology Department received 6 peritoneal fluid specimens, 18 pleural fluid specimens and 36 cerebrospinal fluid specimens. 36 positive cultures were tested. S. epidermidis was identified in 18 specimens, S. haemolyticus in 6, and E. faecium in 12. Conclusions: The results show low detection of microorganisms in body fluid cultures.

Keywords: body fluids, culture, intensive care unit, microorganisms

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Authors: Min-Tsai Lai, Taqwa Hariguna

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This paper presents a periodical replacement model for a system, considering the concept of single and cumulative repair cost limits simultaneously. The failures are divided into two types. Minor failure can be corrected by minimal repair and serious failure makes the system breakdown completely. When a minor failure occurs, if the repair cost is less than a single repair cost limit L1 and the accumulated repair cost is less than a cumulative repair cost limit L2, then minimal repair is executed, otherwise, the system is preventively replaced. The system is also replaced at time T or at serious failure. The optimal period T minimizing the long-run expected cost per unit time is verified to be finite and unique under some specific conditions.

Keywords: repair-cost limit, cumulative repair-cost limit, minimal repair, periodical replacement policy

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Authors: Sungho Kim, Dae Shik Kim, Jong Min Lee

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Fluid catalytic cracking (FCC) process is one of the most important process in modern refinery indusrty. This paper focuses on the fluid catalytic cracking (FCC) process. As the FCC process is difficult to model well, due to its nonlinearities and various interactions between its process variables, rigorous process modeling of whole FCC plant is demanded for control and plant-wide optimization of the plant. In this study, a process design for the FCC plant includes riser reactor, main fractionator, and gas processing unit was developed. A reactor model was described based on four-lumped kinetic scheme. Main fractionator, gas processing unit and other process units are designed to simulate real plant data, using a process flowsheet simulator, Aspen PLUS. The custom reactor model was integrated with the process flowsheet simulator to develop an integrated process model.

Keywords: fluid catalytic cracking, simulation, plant data, process design

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Authors: Mohanad Al-Behadili, Djamila Ouelhadj

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In this paper, a specific type of vehicle routing problem under stochastic demand (SVRP) is considered. This problem is of great importance because it models for many of the real world vehicle routing applications. This paper used a robust optimisation model to solve the problem along with the novel Simulation-Particle Swarm Optimisation (Sim-PSO) approach. The proposed Sim-PSO approach is based on the hybridization of the Monte Carlo simulation technique with the PSO algorithm. A comparative study between the proposed model and the Sim-PSO approach against other solution methods in the literature has been given in this paper. This comparison including the Analysis of Variance (ANOVA) to show the ability of the model and solution method in solving the complicated SVRP. The experimental results show that the proposed model and Sim-PSO approach has a significant impact on the obtained solution by providing better quality solutions comparing with well-known algorithms in the literature.

Keywords: stochastic vehicle routing problem, robust optimisation model, Monte Carlo simulation, particle swarm optimisation

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Authors: Weiwei Xie, Yichao Li

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The initial installation of the umbilical can affect the subsequent installation process and final installation. Meanwhile, the design of both ends of the ultra-deep water dynamic umbilical (UDWDU), as well as the design of the surface unit and the subsea production system connected by UDWDU,], varies in different oil and gas fields. To optimize the installation process of UDWDU, on the basis of the summary and analysis of the surface-end and the subsea-end design of UDWDU and the mainstream construction resources, the method of initial installation from the surface unit side or the subsea production system side of UDWDU is studied, and each initiation installation method is pointed out if some difficulties that may be encountered.

Keywords: dynamic umbilical, ultra-deep-water, initial installation, installation process

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Authors: Ahmed Tarek, Ahmed Alveed

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Vehicle routing problem is a well-known re-search avenue in computing. Modern vehicle routing is more focused with the GPS-based coordinate system, as the state-of-the-art vehicle, and trucking systems are equipped with digital navigation. In this paper, a new two dimensional coordinate-based algorithm for addressing the vehicle routing problem for a supply chain network is proposed and explored, and the algorithm is compared with other available, and recently devised heuristics. For the algorithms discussed, which includes the pro-posed coordinate-based search heuristic as well, the advantages and the disadvantages associated with the heuristics are explored. The proposed algorithm is studied from the stand point of a small supermarket chain delivery network that supplies to its stores in four different states around the East Coast area, and is trying to optimize its trucking delivery cost. Minimizing the delivery cost for the supply network of a supermarket chain is important to ensure its business success.

Keywords: coordinate-based optimal routing, Hamiltonian Circuit, heuristic algorithm, traveling salesman problem, vehicle routing problem

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Authors: Ramesh Chandra Majhi

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Saturation flow is a very important input variable for the design of signalized intersections. Saturation flow measurement is well established for homogeneous traffic. However, saturation flow measurement and modeling is a challenging task in heterogeneous characterized by multiple vehicle types and non-lane based movement. Present study focuses on proposing a field procedure for Saturation flow measurement and the effect of typical mixed traffic behavior at the signal as far as non-lane based traffic movement is concerned. Data collected during peak and off-peak hour from five intersections with varying approach width is used for validating the saturation flow model. The insights from the study can be used for modeling saturation flow and delay at signalized intersection in heterogeneous traffic conditions.

Keywords: optimization, passenger car unit, saturation flow, signalized intersection

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Authors: Sa-Kil Kim, Jang-Soo Lee

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On March 31, 1993, a severe fire accident took place in a nuclear power plant located in Narora in North India. The event involved a major fire in the turbine building of NAPS unit-1 and resulted in a total loss of power to the unit for 17 hours. In addition, there was a heavy ingress of smoke in the control room, mainly through the intake of the ventilation system, forcing the operators to vacate the control room. The Narora fire accident provides us lessons indicating that operators could lose their mind and predictable behaviors during a fire. After the Fukushima accident, which resulted from a natural disaster, unanticipated external events are also required to be prepared and controlled for the ultimate safety of nuclear power plants. From last year, our research team has developed a test and evaluation facility that can simulate external events such as an earthquake and fire based on the operators’ real-sense. As one of the results of the project, we proposed a unit real-sense-based facility that can simulate fire events in a control room for utilizing a test-bed of human factor validation. The test-bed has the operator’s workstation shape and functions to simulate fire conditions such as smoke, heat, and auditory alarms in accordance with the prepared fire scenarios. Furthermore, the test-bed can be used for the operators’ training and experience.

Keywords: human behavior in fire, human factors validation, nuclear power plants, real-sense-based fire simulation

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Authors: Abeer Tariq, Mohammed S. Aljawad, Khaldoun S. Alfarisi

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This paper aimed to estimate the petrophysical properties (porosity, permeability, and fluid saturation) of the Ajeel well (Aj-1) Shale reservoir. Petrophysical properties of the Naokelekan Formation at Ajeel field are determined from the interpretation of open hole log data of one well which penetrated the source rock reservoir. However, depending on these properties, it is possible to divide the Formation which has a thickness of approximately 28-34 m, into three lithological units: A is the upper unit (thickness about 9 to 13 m) consisting of dolomitized limestones; B is a middle unit (thickness about 13 to 20 m) which is composed of dolomitic limestone, and C is a lower unit (>22 m thick) which consists of shale-rich and dolomitic limestones. The results showed that the average formation water resistivity for the formation (Rw = 0.024), the average resistivity of the mud filtration (Rmf = 0.46), and the Archie parameters were determined by the picket plot method, where (m) value equal to 1.86, (n) value equal to 2 and (a) value equal to 1. Also, this reservoir proved to be economical for future developments to increase the production rate of the field by dealing with challenging reservoirs. In addition, Porosity values and water saturation Sw were calculated along with the depth of the composition using Interactive Petrophysics (IP) V4.5 software. The interpretation of the computer process (CPI) showed that the better porous zone holds the highest amount of hydrocarbons in the second and third zone. From the flow zone indicator FZI method, there are two rock types in the studied reservoir.

Keywords: petrophysical properties, porosity, permeability, ajeel field, Naokelekan formation, Jurassic sequences, carbonate reservoir, source rock

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Ebrahim Asadi-Gangraj

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Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems.

Keywords: hybrid flow shop, mixed integer linear programming, Benders decomposition, makespan

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