Search results for: cycle time minimization

Authors: Kalpana Dahiya

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This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: global optimization, hierarchical optimization, transportation problem, concave minimization

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Authors: Kanate Pantusavase, Jaramporn Hassamontr

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This research aims to develop an algorithm to generate a schedule of multiple cranes that will maximize load throughputs in anodizing operation. The algorithm proposed utilizes an enumerative strategy to search for constant time between successive loads and crane covering range over baths. The computer program developed is able to generate a near-optimal crane schedule within reasonable times, i.e. within 10 minutes. Its results are compared with existing solutions from an aluminum extrusion industry. The program can be used to generate crane schedules for mixed products, thus allowing mixed-model line balancing to improve overall cycle times.

Keywords: crane scheduling, anodizing operations, cycle time minimization

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Authors: Ekta Jain, Kalpana Dahiya, Vanita Verma

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This paper discusses a priority based imbalanced time minimization assignment problem dealing with the allocation of n jobs to m < n persons in which the project is carried out in two stages, viz. Stage-I and Stage-II. Stage-I consists of n1 ( < m) primary jobs and Stage-II consists of remaining (n-n1) secondary jobs which are commenced only after primary jobs are finished. Each job is to be allocated to exactly one person, and each person has to do at least one job. It is assumed that nature of the Stage-I jobs is such that one person can do exactly one primary job whereas a person can do more than one secondary job in Stage-II. In a particular stage, all persons start doing the jobs simultaneously, but if a person is doing more than one job, he does them one after the other in any order. The aim of the proposed study is to find the feasible assignment which minimizes the total time for the two stage execution of the project. For this, an iterative algorithm is proposed, which at each iteration, solves a constrained imbalanced time minimization assignment problem to generate a pair of Stage-I and Stage-II times. For solving this constrained problem, an algorithm is developed in the current paper. Later, alternate combinations based method to solve the priority based imbalanced problem is also discussed and a comparative study is carried out. Numerical illustrations are provided in support of the theory.

Keywords: assignment, imbalanced, priority, time minimization

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Authors: Youn-Sung Kim, Jin-Ho Jo, Mi-Sung Kim, Jae-Kun Lee

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Accelerated life cycle test is applied to various products or components in order to reduce the time of life cycle test in industry. It must be considered for many test conditions according to the product characteristics for the test and the selection of acceleration parameter is especially very important. We have carried out the general life cycle test and the accelerated life cycle test by applying the acceleration factor (AF) considering the characteristics of brushless DC (BLDC) motor for washing machine. The final purpose of this study is to verify the validity by analyzing the results of the general life cycle test and the accelerated life cycle test. It will make it possible to reduce the life test time through the reasonable accelerated life cycle test.

Keywords: accelerated life cycle test, reliability test, motor for washing machine, brushless dc motor test

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Authors: Youn-Sung Kim, Mi-Sung Kim, Jae-Kun Lee

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This paper deals with the accelerated life cycle test method of the motor for home appliances that demand high reliability. Life Cycle of parts in home appliances also should be 10 years because life cycle of the home appliances such as washing machine, refrigerator, TV is at least 10 years. In case of washing machine, the life cycle test method of motor is advanced for 3000 cycle test (1cycle = 2hours). However, 3000 cycle test incurs loss for the time and cost. Objectives of this study are to reduce the life cycle test time and the number of test samples, which could be realized by using acceleration factor for the test time and reduction factor for the number of sample.

Keywords: accelerated life cycle test, motor reliability test, motor for washing machine, BLDC motor

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Authors: Alirıza Kaleli, M. Akif Ceviz, Erdoğan Güner, Köksal Erentürk

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The cyclic variations in spark ignition engines occurring especially under specific engine operating conditions make the maximum pressure variable for successive in-cylinder pressure cycles. Minimization of cyclic variations has a great importance in effectively operating near to lean limit, or at low speed and load. The cyclic variations may reduce the power output of the engine, lead to operational instabilities, and result in undesirable engine vibrations and noise. In this study, spark timing is controlled in order to reduce the cyclic variations in spark ignition engines. Firstly, an ARMAX model has developed between spark timing and maximum pressure using system identification techniques. By using this model, the maximum pressure of the next cycle has been predicted. Then, self-tuning minimum variance controller has been designed to change the spark timing for consecutive cycles of the first cylinder of test engine to regulate the in-cylinder maximum pressure. The performance of the proposed controller is illustrated in real time and experimental results show that the controller has a reliable effect on cycle to cycle variations of maximum cylinder pressure when the engine works under low speed conditions.

Keywords: cyclic variations, cylinder pressure, SI engines, self tuning controller

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: Qazi Salman Khalid, Muhammad Khalid, Shahid Maqsood

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This paper presents a solution for optimizing the cycle time in an assembly line with human-robot collaboration and diverse operators. A genetic algorithm with tailored parameters is used to address the assembly line balancing problem in the automobile sector. A mathematical model is developed, depicting the problem. Currently, the firm runs on the largest candidate rule; however, it causes a lag in orders, which ultimately gets penalized. The results of the study show that the proposed GA is effective in providing efficient solutions and that the cycle time has significantly impacted productivity.

Keywords: line balancing, cycle time, genetic algorithm, productivity

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Authors: N. Gayathri Devi, K. Batri

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The advent of technology has increased the traffic hazards and the road accidents take place. Collision detection system in automobile aims at reducing or mitigating the severity of an accident. This project aims at avoiding Vehicle head on collision by means of collision detection algorithm. This collision detection algorithm predicts the collision and the avoidance or minimization have to be done within few seconds on confirmation. Under critical situation collision minimization is made possible by turning the vehicle to the desired turn radius so that collision impact can be reduced. In order to avoid the collision completely, the turning of the vehicle should be achieved at reduced speed in order to maintain the stability.

Keywords: collision avoidance system, time to collision, time to turn, turn radius

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Authors: Reza Lotfalian, Sudarshan Martins, Peter Radziszewski

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The effect of reliability on life-cycle cost, including initial and maintenance cost of a system is studied. The failure probability of a component is used to calculate the average maintenance cost during the operation cycle of the component. The standard deviation of the life-cycle cost is also calculated as an error measure for the average life-cycle cost. As a numerical example, the model is used to study the average life cycle cost of an electric motor.

Keywords: initial cost, life-cycle cost, maintenance cost, reliability

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: Tarek Aboueldahab, Hanan Farag

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Cost minimization of Multiple Vehicle Routing Problem becomes a critical issue in the field of transportation because it is NP-hard optimization problem and the search space is complex. Many researches use the hybridization of artificial intelligence (AI) models to solve this problem; however, it can not guarantee to reach the best solution due to the difficulty of searching the whole search space. To overcome this problem, we introduce the hybrid model of Discrete Particle Swarm Optimization (DPSO) with a passive congregation which enable searching the whole search space to compromise between both local and global search. The practical experiment shows that our model obviously outperforms other hybrid models in cost minimization.

Keywords: cost minimization, multi-vehicle routing problem, passive congregation, discrete swarm, passive congregation

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Authors: I. O. Nascimento, J. T. Manzi

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The drying process is an important operation in the chemical industry and it is widely used in the food, grain industry and fertilizer industry. However, for demanding a considerable consumption of energy, such a process requires a deep energetic analysis in order to reduce operating costs. This paper deals with thermodynamic optimization applied to rotary dryers based on the entropy production minimization, aiming at to reduce the energy consumption. To do this, the mass, energy and entropy balance was used for developing a relationship that represents the rate of entropy production. The use of the Second Law of Thermodynamics is essential because it takes into account constraints of nature. Since the entropy production rate is minimized, optimals conditions of operations can be established and the process can obtain a substantial gain in energy saving. The minimization strategy had been led using classical methods such as Lagrange multipliers and implemented in the MATLAB platform. As expected, the preliminary results reveal a significant energy saving by the application of the optimal parameters found by the procedure of the entropy minimization It is important to say that this method has shown easy implementation and low cost.

Keywords: thermodynamic optimization, drying, entropy minimization, modeling dryers

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Authors: Tarek Aboueldahab, Hanan Farag

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Parallel Job Shop Scheduling Problem (JSP) is a multi-objective and multi constrains NP- optimization problem. Traditional Artificial Intelligence techniques have been widely used; however, they could be trapped into the local minimum without reaching the optimum solution, so we propose a hybrid Artificial Intelligence model (AI) with Discrete Breeding Swarm (DBS) added to traditional Artificial Intelligence to avoid this trapping. This model is applied in the cost minimization of the Car Sequencing and Operator Allocation (CSOA) problem. The practical experiment shows that our model outperforms other techniques in cost minimization.

Keywords: parallel job shop scheduling problem, artificial intelligence, discrete breeding swarm, car sequencing and operator allocation, cost minimization

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Authors: Arakelian Vigen, Geng Jing, Le Baron Jean-Paul

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The paper deals with the design of parallel manipulators with balanced inertia forces and moments. The balancing of the resultant of the inertia forces of 3-RRR planar parallel manipulators is carried out through mass redistribution and centre of mass acceleration minimization. The proposed balancing technique is achieved in two steps: at first, optimal redistribution of the masses of input links is accomplished, which ensures the similarity of the end-effector trajectory and the manipulator’s common centre of mass trajectory, then, optimal trajectory planning of the end-effector by 'bang-bang' profile is reached. In such a way, the minimization of the magnitude of the acceleration of the centre of mass of the manipulator brings about a minimization of shaking force. To minimize the resultant of the inertia moments (shaking moment), the active balancing via inertia flywheel is applied. However, in this case, the active balancing is quite different from previous applications because it provides only a partial cancellation of the shaking moment due to the incomplete balancing of shaking force.

Keywords: dynamic balancing, inertia force minimization, inertia moment minimization, 3-RRR planar parallel manipulator

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Authors: Samad Jafarmadar, Amin Habibzadeh

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A power and cooling cycle, which combines the organic Rankine cycle and the ejector refrigeration cycle supplied by waste heat energy sources, is discussed in this paper. 13 working fluids including wet, dry, and isentropic fluids are studied in order to find their performances on the combined cycle. Various operating conditions’ effects on the proposed cycle are examined by fixing power/refrigeration ratio. According to the results, dry and isentropic fluids have better performance compared with wet fluids.

Keywords: combined power and refrigeration cycle, low temperature heat sources, organic rankine cycle, working fluids

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Authors: Tarek Fatouh, Chehab Elbelehy, Alaa Abdelsalam, Eman Elakkad, Alaa Abdelshafie

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This paper aims to explore the possibility of time compression in Engineer to Order production networks. A case study research method is used in a Norwegian shipbuilding project by implementing a value stream mapping lean tool with total cycle time as a unit of analysis. The analysis resulted in demonstrating the time deviations for the planned tasks in one of the processes in the shipbuilding project. So, authors developed a future state map by removing time wastes from value stream process.

Keywords: engineer to order, total cycle time, value stream mapping, shipbuilding

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Authors: Amin Eslami, Jafar Bolouri Bazaz

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Under active stress conditions, a rigid cantilever retaining wall tends to rotate about a pivot point located within the embedded depth of the wall. For purely granular and cohesive soils, a methodology was previously reported called minimization of moment ratio to determine the location of the pivot point of rotation. The usage of this new methodology is to estimate the rotational stability safety factor. Moreover, the degree of improvement required in a backfill to get a desired safety factor can be estimated by the concept of the shear strength demand. In this article, the accuracy of this method for another type of cantilever walls called Contiguous Bored Pile (CBP) retaining wall is evaluated by using physical modeling technique. Based on observations, the results of moment ratio minimization method are in good agreement with the results of the carried out physical modeling.

Keywords: cantilever retaining wall, physical modeling, minimization of moment ratio method, pivot point

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Authors: Apurv Kulkarni, Shreyas Badave, B. Rajiv

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Non-parametric reliability technique is useful for assessment of reliability of systems for which failure rates are not available. This is useful when detection of malfunctioning of any component is the key purpose during ongoing operation of the system. The main purpose of the Heat Exchanger Cycle discussed in this paper is to provide hot water at a constant temperature for longer periods of time. In such a cycle, certain components play a crucial role and this paper presents an effective way to predict the malfunctioning of the components by determination of system reliability. The method discussed in the paper is feasible and this is clarified with the help of various test cases.

Keywords: heat exchanger cycle, k-statistics, PID controller, system reliability

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Authors: Ashwini Umale

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Trajectory planning and optimization is a fundamental problem in articulated robotics. It is often viewed as a two phase problem of initial feasible path planning around obstacles and subsequent optimization of a trajectory satisfying dynamical constraints. An optimized trajectory of multi-axis robot is important and directly influences the Performance of the executing task. Optimal is defined to be the minimum time to transition from the current speed to the set speed. In optimization of trajectory through virtual environment explores the most suitable way to represent robot motion from virtual environment to real environment. This paper aims to review the research of trajectory optimization in virtual environment using simulation software Robcad. Improvements are to be expected in trajectory optimization to generate smooth and collision free trajectories with minimization of overall robot cycle time.

Keywords: trajectory optimization, forward kinematics and reverse kinematics, dynamic constraints, robcad simulation software

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Authors: V. Rashtchi, H. Bizhani, F. R. Tatari

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This paper presents a new online loss minimization for an induction motor drive. Among the many loss minimization algorithms (LMAs) for an induction motor, a particle swarm optimization (PSO) has the advantages of fast response and high accuracy. However, the performance of the PSO and other optimization algorithms depend on the accuracy of the modeling of the motor drive and losses. In the development of the loss model, there is always a trade off between accuracy and complexity. This paper presents a new online optimization to determine an optimum flux level for the efficiency optimization of the vector-controlled induction motor drive. An induction motor (IM) model in d-q coordinates is referenced to the rotor magnetizing current. This transformation results in no leakage inductance on the rotor side, thus the decomposition into d-q components in the steady-state motor model can be utilized in deriving the motor loss model. The suggested algorithm is simple for implementation.

Keywords: induction machine, loss minimization, magnetizing current, particle swarm optimization

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Authors: Busaba Phurksaphanrat

Abstract:

This research proposes a pre-emptive fuzzy goal programming model for multi-objective multi-mode resource constrained project scheduling problem. The objectives of the problem are minimization of the total time and the total cost of the project. Objective in a multi-mode resource-constrained project scheduling problem is often a minimization of make-span. However, both time and cost should be considered at the same time with different level of important priorities. Moreover, all elements of cost functions in a project are not included in the conventional cost objective function. Incomplete total project cost causes an error in finding the project scheduling time. In this research, pre-emptive fuzzy goal programming is presented to solve the multi-objective multi-mode resource constrained project scheduling problem. It can find the compromise solution of the problem. Moreover, it is also flexible in adjusting to find a variety of alternative solutions.

Keywords: multi-mode resource constrained project scheduling problem, fuzzy set, goal programming, pre-emptive fuzzy goal programming

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Authors: Vijay Sodhi, Charanjit Singh, Neelam Sodhi, Puneet P. S. Cheema, Reena Sharma, Mithilesh K. Jha

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The management and secure disposal of the biosludge generated from widely commercialized conventional activated sludge (CAS) treatments become a potential environmental issue. Thus, a sustainable technological upgradation to the CAS for sludge yield minimization has recently been gained serious attention of the scientific community. A number of recently reported studies effectively addressed the remedial technological advancements that in monopoly limited to the municipal wastewater. Moreover, the critical review of the literature signifies side-stream sludge minimization as a complex task to maintain. In this work, therefore, a hybrid moving bed biofilm reactor (MBBR) configuration (named as AMOMOX process) for in-situ minimization of the excess biosludge generated from high organic strength tannery wastewater has been demonstrated. The AMOMOX collectively stands for anoxic MBBR (as AM), aerobic MBBR (OM) and an oxic CAS (OX). The AMOMOX configuration involved a combined arrangement of an anoxic MBBR and oxic MBBR coupled with the aerobic CAS. The AMOMOX system was run in parallel with an identical CAS reactor. Both system configurations were fed with same influent to judge the real-time operational changes. For the AMOMOX process, the strict maintenance of operational strategies resulted about 95% removal of NH4-N and SCOD from tannery wastewater. Here, the nourishment of filamentous microbiota and purposeful promotion of cell-lysis effectively sustained sludge yield (Yobs) lowering upto 0.51 kgVSS/kgCOD. As a result, the volatile sludge scarcity apparent in the AMOMOX system succeeded upto 47% reduction of the excess biosludge. The corroborated was further supported by FE-SEM imaging and thermogravimetric analysis. However, the detection of microbial strains habitat underlying extended SRT (23-26 days) of the AMOMOX system would be the matter of further research.

Keywords: tannery wastewater, moving bed biofilm reactor, sludhe yield, sludge minimization, solids retention time

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Authors: Shin-Shin Kao, Hsiu-Chunj Pan

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Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3-ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered [1]. Furthermore, based on computer experimental results in [1], it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

Keywords: Hamiltonian cycle, 4-ordered, Chordal rings, 3-regular

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Authors: Farhat Hajer, Khir Tahar, Ammar Ben Brahim

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This work presents a study on the influence of the main operating variables on the gas turbine cycle. A numerical simulation of a gas turbine cycle is performed for a real net power of 100 MW. A calculation code is developed using EES software. The operating variables are taken in conformity with the local environmental conditions adopted by the Tunisian Society of Electricity and Gas. Results show that the increase of ambient temperature leads to an increase of Tpz and NO_x emissions rate and a decrease of cycle efficiency and UHC emissions. The CO emissions decrease with the raise of residence time, while NO_x emissions rate increases and UHC emissions rate decreases. Furthermore, both of cycle efficiency and NOx emissions increase with the increase of the pressure ratio.

Keywords: Carbon monoxide, Efficiency, Emissions, Gas Turbine, Nox, UHC

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Authors: Drago Jakovčević, Maja Mihelja Žaja

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This paper provides an analysis of the insurance cycle in the Republic of Croatia and whether they are affected by catastrophic losses on a global level. In general, it is considered that insurance cycles are particularly pronounced in periods of financial crisis, but are also affected by the growing number of catastrophic losses. They cause the change of insurance cycle and premium growth and intensification and narrowing of the coverage conditions, so these variables move in the same direction and these phenomena point to a new cycle. The main goal of this paper is to determine the existence of insurance cycle in the Republic of Croatia and investigate whether catastrophic losses have an influence on insurance cycles.

Keywords: catastrophic loss, insurance cycle, premium, Republic of Croatia

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Authors: Wajahat Ali, Shakeel Javaid

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In this study, we have developed a mathematical programming model for a solid transportation problem with three objective functions arranged in hierarchical order. The mathematical programming models with more than one objective function to be solved in hierarchical order is termed as a multi-level programming model. Our study explores a Multi-Level Solid Transportation Problem with Uncertain Parameters (MLSTPWU). The proposed MLSTPWU model consists of three objective functions, viz. minimization of transportation cost, minimization of total transportation time, and minimization of deterioration during transportation. These three objective functions are supposed to be solved by decision-makers at three consecutive levels. Three constraint functions are added to the model, restricting the total availability, total demand, and capacity of modes of transportation. All the parameters involved in the model are assumed to be uncertain in nature. A solution method based on fuzzy logic is also discussed to obtain the compromise solution for the proposed model. Further, a simulated numerical example is discussed to establish the efficiency and applicability of the proposed model.

Keywords: solid transportation problem, multi-level programming, uncertain variable, uncertain environment

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Authors: Haoshui Yu, Donghoi Kim, Truls Gundersen

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Low-temperature waste heat is abundant in the process industries, and large amounts of Liquefied Natural Gas (LNG) cold energy are discarded without being recovered properly in LNG terminals. Power generation is an effective way to utilize low-temperature waste heat and LNG cold energy simultaneously. Organic Rankine Cycles (ORCs) and CO₂ power cycles are promising technologies to convert low-temperature waste heat and LNG cold energy into electricity. If waste heat and LNG cold energy are utilized simultaneously in one system, the performance may outperform separate systems utilizing low-temperature waste heat and LNG cold energy, respectively. Low-temperature waste heat acts as the heat source and LNG regasification acts as the heat sink in the combined system. Due to the large temperature difference between the heat source and the heat sink, cascaded power cycle configurations are proposed in this paper. Cascaded power cycles can improve the energy efficiency of the system considerably. The cycle operating at a higher temperature to recover waste heat is called top cycle and the cycle operating at a lower temperature to utilize LNG cold energy is called bottom cycle in this study. The top cycle condensation heat is used as the heat source in the bottom cycle. The top cycle can be an ORC, transcritical CO₂ (tCO₂) cycle or supercritical CO₂ (sCO₂) cycle, while the bottom cycle only can be an ORC due to the low-temperature range of the bottom cycle. However, the thermodynamic path of the tCO₂ cycle and sCO₂ cycle are different from that of an ORC. The tCO₂ cycle and the sCO₂ cycle perform better than an ORC for sensible waste heat recovery due to a better temperature match with the waste heat source. Different combinations of the tCO₂ cycle, sCO₂ cycle and ORC are compared to screen the best configurations of the cascaded power cycles. The influence of the working fluid and the operating conditions are also investigated in this study. Each configuration is modeled and optimized in Aspen HYSYS. The results show that cascaded tCO₂/ORC performs better compared with cascaded ORC/ORC and cascaded sCO₂/ORC for the case study.

Keywords: LNG cold energy, low-temperature waste heat, organic Rankine cycle, supercritical CO₂ cycle, transcritical CO₂ cycle

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Authors: Anteneh Getachew Gebrie, Rabian Wangkeeree

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The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

Keywords: Hilbert Space, minimization problems, Moreau-Yosida approximate, split feasibility problem

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Authors: M. M. M. Jaradat

Abstract:

For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated.

Keywords: cycle space, minimum cycle basis, basis number, wreath product

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