Search results for: Resource Scheduling.

Authors: Javier Roca, Etienne Pugnaghi, Gaëtan Libert

Abstract:

We introduce an extended resource leveling model that abstracts real life projects that consider specific work ranges for each resource. Contrary to traditional resource leveling problems this model considers scarce resources and multiple objectives: the minimization of the project makespan and the leveling of each resource usage over time. We formulate this model as a multiobjective optimization problem and we propose a multiobjective genetic algorithm-based solver to optimize it. This solver consists in a two-stage process: a main stage where we obtain non-dominated solutions for all the objectives, and a postprocessing stage where we seek to specifically improve the resource leveling of these solutions. We propose an intelligent encoding for the solver that allows including domain specific knowledge in the solving mechanism. The chosen encoding proves to be effective to solve leveling problems with scarce resources and multiple objectives. The outcome of the proposed solvers represent optimized trade-offs (alternatives) that can be later evaluated by a decision maker, this multi-solution approach represents an advantage over the traditional single solution approach. We compare the proposed solver with state-of-art resource leveling methods and we report competitive and performing results.

Keywords: Intelligent problem encoding, multiobjective decision making, evolutionary computing, RCPSP, resource leveling.

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Authors: Bella Llego

Abstract:

This study on “The relationship between human resource practices and Firm Performance is a speculative investigation research. The purpose of this research are (1) to provide and to understand of HRM history and current HR practices in the Philippines (2) to examine the extent of HRM practice among its Philippine firms effectively; (3) to investigate the relationship between HRM practice and firm performance in the Philippines. The survey was done to 233 companies in the Philippines. The questionnaire is divided into three parts a) to gathers information on the profile of respondent, b) to measures the extent to which human resource practices are being practiced in their organization c) to measure the organizations performance as perceived by human resource managers and top executives as compared with their competitors in the same industry. As a result an interesting finding was that almost 50 percent of firm performance is affected by the extent of implementation of HR practices in the firm. These results show that HR practices that are in line with the organization’s strategic goals are important for future performance.

Keywords: Economic Growth, Firm performance, Human Resource Practices, Management.

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Authors: V. K. Bansal

Abstract:

Geographic Information System (GIS) is a computerbased tool used extensively to solve various engineering problems related to spatial data. In spite of growing popularity of GIS, its complete potential to construction industry has not been realized. In this paper, the summary of up-to-date work on spatial applications of GIS technologies in construction industry is presented. GIS technologies have the potential to solve space related problems of construction industry involving complex visualization, integration of information, route planning, E-commerce, cost estimation, etc. GISbased methodology to handle time and space issues of construction projects scheduling is developed and discussed in this paper.

Keywords: Construction, GIS in construction, Scheduling, Project Management.

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Authors: Sangsuree Vasupongayya

Abstract:

To provide a better understanding of fair share policies supported by current production schedulers and their impact on scheduling performance, A relative fair share policy supported in four well-known production job schedulers is evaluated in this study. The experimental results show that fair share indeed reduces heavy-demand users from dominating the system resources. However, the detailed per-user performance analysis show that some types of users may suffer unfairness under fair share, possibly due to priority mechanisms used by the current production schedulers. These users typically are not heavy-demands users but they have mixture of jobs that do not spread out.

Keywords: Fair share, Parallel job scheduler, Backfill, Measures

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Authors: J. Kaabi, Y. Harrath

Abstract:

This paper studied the flow shop scheduling problem under machine availability constraints. The machines are subject to flexible preventive maintenance activities. The nonresumable scenario for the jobs was considered. That is, when a job is interrupted by an unavailability period of a machine it should be restarted from the beginning. The objective is to minimize the total tardiness time for the jobs and the advance/tardiness for the maintenance activities. To solve the problem, a genetic algorithm was developed and successfully tested and validated on many problem instances. The computational results showed that the new genetic algorithm outperforms another earlier proposed algorithm. 

Keywords: Flow shop scheduling, maintenance, genetic algorithm, priority rules.

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Authors: Xiaoming Jiang, Jinqiao Shi, Qingfeng Tan, Wentao Zhang, Xuebin Wang, Muqian Chen

Abstract:

Nowadays, big companies such as Google, Microsoft, which have adequate proxy servers, have perfectly implemented their web crawlers for a certain website in parallel. But due to lack of expensive proxy servers, it is still a puzzle for researchers to crawl large amounts of information from a single website in parallel. In this case, it is a good choice for researchers to use free public proxy servers which are crawled from the Internet. In order to improve efficiency of web crawler, the following two issues should be considered primarily: (1) Tasks may fail owing to the instability of free proxy servers; (2) A proxy server will be blocked if it visits a single website frequently. In this paper, we propose Proxisch, an optimization approach of large-scale unstable proxy servers scheduling, which allow anyone with extremely low cost to run a web crawler efficiently. Proxisch is designed to work efficiently by making maximum use of reliable proxy servers. To solve second problem, it establishes a frequency control mechanism which can ensure the visiting frequency of any chosen proxy server below the website’s limit. The results show that our approach performs better than the other scheduling algorithms.

Keywords: Proxy server, priority queue, optimization approach, distributed web crawling.

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Authors: Yu-Jen Chang, Shih-Chieh Chen, Yu-Wei Kuo

Abstract:

In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the reworked products. In this paper, we formulate a mathematical model for the ELSP with reworks using the basic period approach. In order to solve this problem, we propose a search algorithm to find the cyclic multiplier ki of each product that can be cyclically produced for every ki basic periods. This research also uses two heuristics to search for the optimal production sequence of all lots and the optimal time length of the basic period so as to minimize the average total cost. This research uses a numerical example to show the effectiveness of our approach.

Keywords: Economic lot, reworks, inventory, basic period.

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Authors: Vijay Kumar, Jagdev Singh, Yaduvir Singh, Sanjay Sood

Abstract:

In a practical power system, the power plants are not located at the same distance from the center of loads and their fuel costs are different. Also, under normal operating conditions, the generation capacity is more than the total load demand and losses. Thus, there are many options for scheduling generation. In an interconnected power system, the objective is to find the real and reactive power scheduling of each power plant in such a way as to minimize the operating cost. This means that the generator’s real and reactive powers are allowed to vary within certain limits so as to meet a particular load demand with minimum fuel cost. This is called optimal power flow problem. In this paper, Economic Load Dispatch (ELD) of real power generation is considered. Economic Load Dispatch (ELD) is the scheduling of generators to minimize total operating cost of generator units subjected to equality constraint of power balance within the minimum and maximum operating limits of the generating units. In this paper, genetic algorithms are considered. ELD solutions are found by solving the conventional load flow equations while at the same time minimizing the fuel costs.

Keywords: ELD, Equality constraints, Genetic algorithms, Strings.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

Abstract:

A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

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This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: Bus scheduling problem, decision support system, genetic algorithm, operation planning, shortest path, transportation.

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Authors: Tadeusz Witkowski, Paweł Antczak, Arkadiusz Antczak

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In the paper we discuss the influence of the route flexibility degree, the open rate of operations and the production type coefficient on makespan. The flexible job-open shop scheduling problem FJOSP (an extension of the classical job shop scheduling) is analyzed. For the analysis of the production process we used a hybrid heuristic of the GRASP (greedy randomized adaptive search procedure) with simulated annealing algorithm. Experiments with different levels of factors have been considered and compared. The GRASP+SA algorithm has been tested and illustrated with results for the serial route and the parallel one.

Keywords: Makespan, open shop, route flexibility, serial and parallel route, simulation modeling, type of production.

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Authors: S. Padmapriya, M. Tamilarasi

Abstract:

Femtocells are regarded as a milestone for next generation cellular networks. As femtocells are deployed in an unplanned manner, there is a chance of assigning same resource to neighboring femtocells. This scenario may induce co-channel interference and may seriously affect the service quality of neighboring femtocells. In addition, the dominant transmit power of a femtocell will induce co-tier interference to neighboring femtocells. Thus to jointly handle co-tier and co-channel interference, we propose an interference-free power and resource block allocation (IFPRBA) algorithm for closely located, closed access femtocells. Based on neighboring list, inter-femto-base station distance and uplink noise power, the IFPRBA algorithm assigns non-interfering power and resource to femtocells. The IFPRBA algorithm also guarantees the quality of service to femtouser based on the knowledge of resource requirement, connection type, and the tolerable delay budget. Simulation result shows that the interference power experienced in IFPRBA algorithm is below the tolerable interference power and hence the overall service success ratio, PRB efficiency and network throughput are maximum when compared to conventional resource allocation framework for femtocell (RAFF) algorithm.

Keywords: Co-channel interference, co-tier interference, femtocells, guaranteed QoS, power optimization, resource assignment.

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Authors: Yessine Hadj Kacem, Adel Mahfoudhi, Hedi Tmar, Mohamed Abid

Abstract:

Unified Modeling Language (UML) extensions for real time embedded systems (RTES) co-design, are taking a growing interest by a great number of industrial and research communities. The extension mechanism is provided by UML profiles for RTES. It aims at improving an easily-understood method of system design for non-experts. On the other hand, one of the key items of the co- design methods is the Hardware/Software partitioning and scheduling tasks. Indeed, it is mandatory to define where and when tasks are implemented and run. Unfortunately the main goals of co-design are not included in the usual practice of UML profiles. So, there exists a need for mapping used models to an execution platform for both schedulability test and HW/SW partitioning. In the present work, test schedulability and design space exploration are performed at an early stage. The proposed approach adopts Model Driven Engineering MDE. It starts from UML specification annotated with the recent profile for the Modeling and Analysis of Real Time Embedded systems MARTE. Following refinement strategy, transformation rules allow to find a feasible schedule that satisfies timing constraints and to define where tasks will be implemented. The overall approach is experimented for the design of a football player robot application.

Keywords: MDE, UML profile, scheduling analysis, HW/SW partitioning.

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Authors: Jerome T. Tolentino, Ma. Victoria Rejuso, Jara Kaye Villanueva, Loureal Camille Inocencio, Ma. Rosario Concepcion O. Ang

Abstract:

Wind energy is rapidly emerging as the primary source of electricity in the Philippines, although developing an accurate wind resource model is difficult. In this study, Weather Research and Forecasting (WRF) Model, an open source mesoscale Numerical Weather Prediction (NWP) model, was used to produce a 1-year atmospheric simulation with 4 km resolution on the Ilocos Region of the Philippines. The WRF output (netCDF) extracts the annual mean wind speed data using a Python-based Graphical User Interface. Lastly, wind resource assessment was produced using a GIS software. Results of the study showed that it is more flexible to use Python scripts than using other post-processing tools in dealing with netCDF files. Using WRF Model, Python, and Geographic Information Systems, a reliable wind resource map is produced.

Keywords: Wind resource assessment, Weather Research and Forecasting (WRF) Model, python, GIS software.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper introduces a framework based on the collaboration of multi agent and hyper-heuristics to find a solution of the real single machine production problem. There are many techniques used to solve this problem. Each of it has its own advantages and disadvantages. By the collaboration of multi agent system and hyper-heuristics, we can get more optimal solution. The hyper-heuristics approach operates on a search space of heuristics rather than directly on a search space of solutions. The proposed framework consists of some agents, i.e. problem agent, trainer agent, algorithm agent (GPHH, GAHH, and SAHH), optimizer agent, and solver agent. Some low level heuristics used in this paper are MRT, SPT, LPT, EDD, LDD, and MON

Keywords: Hyper-heuristics, multi-agent systems, scheduling problem.

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Authors: Wen-Shan Lin, Shu-Lu Hsu

Abstract:

Environmental concern and consumer rights have entailed e-tailers to adopt better strategies to facilitate product returns from customers. As the demand for reverse logistics (RL) continues to grow, little is known about what motivates e-tailers to enhance their RL capabilities and about the role RL capabilities plays in enabling e-tailers to achieve better customer satisfaction and economic performance. Based on resource-based theory and institutional theory, this article proposes that the following factors play a critical role in influencing the RL capability of e-tailers: (a) Financial resource commitment to RL, (b) managerial resource commitment to RL, and (c) institutional pressure to implement RL. Based on the role of these factors, the study provides a framework and propositions that serve to guide future research addressing the link among resources, institutional pressure, and RL capability.

Keywords: Reverse logistics, e-tailing, resource-based theory, institutional theory.

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Authors: Muhammad Abrar, Xiang Gui, Amal Punchihewa

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In this paper we study the resource allocation problem for an OFDMA based cooperative two-way relaying (TWR) network. We focus on amplify and forward (AF) analog network coding (ANC) protocol. An optimization problem for two basic resources namely, sub-carrier and power is formulated for multi-user TWR networks. A joint optimal optimization problem is investigated and two-step low complexity sub-optimal resource allocation algorithm is proposed for multi-user TWR networks with ANC protocol. The proposed algorithm has been evaluated in term of total achievable system sum-rate and achievable individual sum-rate for each userpair. The good tradeoff between system sum-rate and fairness is observed in the two-step proportional resource allocation scheme.

Keywords: Relay Network, Relay Protocols, Resource Allocation, Two –way relaying.

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Authors: M. J. Lengare, R. H. Chile, L. M. Waghmare, Bhavesh Parmar

Abstract:

One of the most basic functions of control engineers is tuning of controllers. There are always several process loops in the plant necessitate of tuning. The auto tuned Proportional Integral Derivative (PID) Controllers are designed for applications where large load changes are expected or the need for extreme accuracy and fast response time exists. The algorithm presented in this paper is used for the tuning PID controller to obtain its parameters with a minimum computing complexity. It requires continuous analysis of variation in few parameters, and let the program to do the plant test and calculate the controller parameters to adjust and optimize the variables for the best performance. The algorithm developed needs less time as compared to a normal step response test for continuous tuning of the PID through gain scheduling.

Keywords: Auto tuning; gain scheduling; MIMO Processes; Optimization; PID controller; Process Control.

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Authors: Ahmad Thanyan Al-Sultan

Abstract:

The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: Airport terminal, Integer programming, Scheduling, Simulation.

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Authors: M. Heck, H. Vettiger

Abstract:

Small and medium-sized enterprises (SME) are the backbone of central Europe’s economies and have a significant contribution to the gross domestic product. Production planning and scheduling (PPS) is still a crucial element in manufacturing industries of the 21^st century even though this area of research is more than a century old. The topic of PPS is well researched especially in the context of large enterprises in the manufacturing industry. However the implementation of PPS methodologies within SME is mostly unobserved. This work analyzes how PPS is implemented in SME with the geographical focus on Switzerland and its vicinity. Based on restricted resources compared to large enterprises, SME have to face different challenges. The real problem areas of selected enterprises in regards of PPS are identified and evaluated. For the identified real-life problem areas of SME clear and detailed recommendations are created, covering concepts and best practices and the efficient usage of PPS. Furthermore the economic and entrepreneurial value for companies is lined out and why the implementation of the introduced recommendations is advised.

Keywords: Central Europe, PPS, Production Planning, SME.

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Authors: A. Eui Koog Ahn, B. Gi-Nam Wang, C. Sang C. Park

Abstract:

Higher productivity and less cost in the ship manufacturing process are required to maintain the international competitiveness of morden manufacturing industries. In shipbuilding, however, the Engineering To Order (ETO) production method and production process is very difficult. Thus, designs change frequently. In accordance with production, planning should be set up according to scene changes. Therefore, fixed production planning is very difficult. Thus, a scheduler must first make sketchy plans, then change the plans based on the work progress and modifications. Thus, data sharing in a shipbuilding block assembly shop is very important. In this paper, we proposed to scheduling method applicable to the shipbuilding industry and decision making support system through web based visualization system.

Keywords: Shipbuilding, Monitoring, Block assembly shop, Visualization

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Authors: Sanjay Kumar Parjapati, Ajai Jain

Abstract:

This paper presents optimization of makespan for ‘n’ jobs and ‘m’ machines flexible job shop scheduling problem with sequence dependent setup time using genetic algorithm (GA) approach. A restart scheme has also been applied to prevent the premature convergence. Two case studies are taken into consideration. Results are obtained by considering crossover probability (pc = 0.85) and mutation probability (pm = 0.15). Five simulation runs for each case study are taken and minimum value among them is taken as optimal makespan. Results indicate that optimal makespan can be achieved with more than one sequence of jobs in a production order.

Keywords: Flexible Job Shop, Genetic Algorithm, Makespan, Sequence Dependent Setup Times.

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Authors: Fatemeh Dadkhah, Hossein Ali Akbarpour

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This paper considers a scheduling problem in flexible flow shops environment with the aim of minimizing two important criteria including makespan and cumulative tardiness of jobs. Since the proposed problem is known as an Np-hard problem in literature, we have to develop a meta-heuristic to solve it. We considered general structure of Genetic Algorithm (GA) and developed a new version of that based on Data Envelopment Analysis (DEA). Two objective functions assumed as two different inputs for each Decision Making Unit (DMU). In this paper we focused on efficiency score of DMUs and efficient frontier concept in DEA technique. After introducing the method we defined two different scenarios with considering two types of mutation operator. Also we provided an experimental design with some computational results to show the performance of algorithm. The results show that the algorithm implements in a reasonable time.

Keywords: Data envelopment analysis, Efficiency, Flexible flow shops, Genetic algorithm

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Authors: J. Kluabwang

Abstract:

An economic operation scheduling problem of a hydro-thermal power generation system has been properly solved by the proposed multipath adaptive tabu search algorithm (MATS). Four reservoirs with their own hydro plants and another one thermal plant are integrated to be a studied system used to formulate the objective function under complicated constraints, eg water managements, power balance and thermal generator limits. MATS with four subsearch units (ATSs) and two stages of discarding mechanism (DM), has been setting and trying to solve the problem through 25 trials under function evaluation criterion. It is shown that MATS can provide superior results with respect to single ATS and other previous methods, genetic algorithms (GA) and differential evolution (DE).

Keywords: Hydro-thermal scheduling problem, economic dispatch, adaptive tabu search, multipath adaptive tabu search

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Authors: František Bozek, Alexandr Bozek, Alena Bumbova, Eduard Bakos, Jiri Dvorak

Abstract:

The article deals with the classification of alternative water resources in terms of potential risks which is the prerequisite for incorporating these water resources to the emergency plans. The classification is based on the quantification of risks resulting from possible damage, disruption or total destruction of water resource caused by natural and anthropogenic hazards, assessment of water quality and availability, traffic accessibility of the assessed resource and finally its water yield. The aim is to achieve the development of an integrated rescue system, which will be capable of supplying the population with drinking water on the whole stricken territory during the states of emergency.

Keywords: Classification, Emergency Supply, Risk, Water Standby Resource.

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Authors: Volker Heierhoff, Aurilla Aurelie Bechina Arntzen, Gerrit Muller

Abstract:

It well recognized that one feature that makes a successful company is its ability to successfully align its business goals with its information communication technologies platform. Enterprise Resource Planning (ERP) systems contribute to achieve better performance by integrating various business functions and providing support for information flows. However, the technological systems complexity is known to prevent the business users to exploit in an efficient way the Enterprise Resource Planning Systems (ERP). This paper aims to investigate the role of training in improving the usage of ERP systems. To this end, we have designed an instrument survey to employees of a Norwegian multinational global provider of technology solutions. Based on the analysis of collected data, we have delineated a training model that could be high relevance for both researchers and practitioners as a step towards a better understanding of ERP system implementation.

Keywords: Business User Training, Enterprise resource planning system, Global consulting company, Role and responsibilities

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Authors: N. Ravi Kumar, R. Kamalakannan

Abstract:

The advancement of hybrid energy resources such as solar and wind power leading to the emergence of customer owned grid. It provides an opportunity to regulars to obtain low energy costs as well as enabling the power supplier to regulate the utility grid. There is a need to develop smart systems that will automatically submit energy demand schedule and monitors energy price signals in real-time without the prompt of customers. In this paper, a demand side energy management for a grid connected household and also smart preparation of electrical appliance have been presented. It also reduces electricity bill for the consumers in the grid. In addition to this, when production is high, the surplus energy fashioned in the customer owned grid is given to main grid or neighboring micro grids. The simulation of the entire system is presented using LabVIEW software.

Keywords: Distributed renewable energy resource, power storage devices, scheduling, smart meters, smart micro grid, electric vehicle.

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Authors: Vijay Shankar, C.S.P. Ojha, K.S. Hari Prasad

Abstract:

Maize and Indian mustard are significant crops in semi-arid climate zones of India. Improved water management requires precise scheduling of irrigation, which in turn requires an accurate computation of daily crop evapotranspiration (ETc). Daily crop evapotranspiration comes as a product of reference evapotranspiration (ET0) and the growth stage specific crop coefficients modified for daily variation. The first objective of present study is to develop crop coefficients Kc for Maize and Indian mustard. The estimated values of Kc for maize at the four crop growth stages (initial, development, mid-season, and late season) are 0.55, 1.08, 1.25, and 0.75, respectively, and for Indian mustard the Kc values at the four growth stages are 0.3, 0.6, 1.12, and 0.35, respectively. The second objective of the study is to compute daily crop evapotranspiration from ET0 and crop coefficients. Average daily ETc of maize varied from about 2.5 mm/d in the early growing period to > 6.5 mm/d at mid season. The peak ETc of maize is 8.3 mm/d and it occurred 64 days after sowing at the reproductive growth stage when leaf area index was 4.54. In the case of Indian mustard, average ETc is 1 mm/d at the initial stage, >1.8 mm/d at mid season and achieves a peak value of 2.12 mm/d on 56 days after sowing. Improved schedules of irrigation have been simulated based on daily crop evapo-transpiration and field measured data. Simulation shows a close match between modeled and field moisture status prevalent during crop season.

Keywords: Crop coefficient, Crop evapotranspiration, Field moisture, Irrigation Scheduling

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Authors: Frantisek Bozek, Alexandr Bozek, Eduard Bakos, Jiri Dvorak, Alena Bumbova, Lenka Jesonkova

Abstract:

The case study deals with the semi-quantitative risk assessment of water resource earmarked for the emergency supply of population with drinking water. The risk analysis has been based on previously identified hazards/sensitivities of the elements of hydrogeological structure and technological equipment of ground water resource as well as on the assessment of the levels of hazard, sensitivity and criticality of individual resource elements in the form of point indexes. The following potential sources of hazard have been considered: natural disasters caused by atmospheric and geological changes, technological hazards, and environmental burdens. The risk analysis has proved that the assessed risks are acceptable and the water resource may be integrated into a crisis plan of a given region.

Keywords: Crisis, emergency, frequency, ground water, hazard, point index, risk, sensitivity, water supply.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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