Search results for: optimization model

Authors: P. Pongsumpun

Abstract:

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

Keywords: Age structural model, Herpes zoster, local stability, Numerical solution.

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Authors: Jan Erik Stellet

Abstract:

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.

Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.

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Authors: Seyed Habib A. Rahmati

Abstract:

During last decades, developing multi-objective evolutionary algorithms for optimization problems has found considerable attention. Flexible job shop scheduling problem, as an important scheduling optimization problem, has found this attention too. However, most of the multi-objective algorithms that are developed for this problem use nonprofessional approaches. In another words, most of them combine their objectives and then solve multi-objective problem through single objective approaches. Of course, except some scarce researches that uses Pareto-based algorithms. Therefore, in this paper, a new Pareto-based algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our considered objectives are makespan, critical machine work load, and total work load of machines. The proposed algorithm is also compared with one the best Pareto-based algorithms of the literature on some multi-objective criteria, statistically.

Keywords: Scheduling, Flexible job shop scheduling problem, controlled elitism non-dominated sorting genetic algorithm

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Authors: Mohd Shahrom Ismail, B.T. Hang Tuah Baharudin, K.K.B. Hon

Abstract:

In this paper, a methodology of a model based on predicting the tool forces oblique machining are introduced by adopting the orthogonal technique. The applied analytical calculation is mostly based on Devries model and some parts of the methodology are employed from Amareggo-Brown model. Model validation is performed by comparing experimental data with the prediction results on machining titanium alloy (Ti-6Al-4V) based on micro-cutting tool perspective. Good agreements with the experiments are observed. A detailed friction form that affected the tool forces also been examined with reasonable results obtained.

Keywords: dynamics machining, micro cutting tool, Tool forces

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Authors: M. Rychlik, R. Roszak, M. Morzynski, M. Nowak, H. Hausa, K. Kotecki

Abstract:

Article presents the geometry and structure reconstruction procedure of the aircraft model for flatter research (based on the I22-IRYDA aircraft). For reconstruction the Reverse Engineering techniques and advanced surface modeling CAD tools are used. Authors discuss all stages of data acquisition process, computation and analysis of measured data. For acquisition the three dimensional structured light scanner was used. In the further sections, details of reconstruction process are present. Geometry reconstruction procedure transform measured input data (points cloud) into the three dimensional parametric computer model (NURBS solid model) which is compatible with CAD systems. Parallel to the geometry of the aircraft, the internal structure (structural model) are extracted and modeled. In last chapter the evaluation of obtained models are discussed.

Keywords: computer modeling, numerical simulation, Reverse Engineering, structural model

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Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

Abstract:

 A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: Forecasting model, Steel demand uncertainty, Hierarchical Bayesian framework, Exponential smoothing method.

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Authors: Prashant P. Bedekar, Sudhir R. Bhide, Vijay S. Kale

Abstract:

Overcurrent (OC) relays are the major protection devices in a distribution system. The operating time of the OC relays are to be coordinated properly to avoid the mal-operation of the backup relays. The OC relay time coordination in ring fed distribution networks is a highly constrained optimization problem which can be stated as a linear programming problem (LPP). The purpose is to find an optimum relay setting to minimize the time of operation of relays and at the same time, to keep the relays properly coordinated to avoid the mal-operation of relays. This paper presents two phase simplex method for optimum time coordination of OC relays. The method is based on the simplex algorithm which is used to find optimum solution of LPP. The method introduces artificial variables to get an initial basic feasible solution (IBFS). Artificial variables are removed using iterative process of first phase which minimizes the auxiliary objective function. The second phase minimizes the original objective function and gives the optimum time coordination of OC relays.

Keywords: Constrained optimization, LPP, Overcurrent relaycoordination, Two-phase simplex method.

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Authors: M. A. Serag-Eldin

Abstract:

The paper presents the results of simple measurements conducted on a model of a wind-driven venturi-type room ventilator. The ventilator design is new and was developed employing mathematical modeling. However, the computational model was not validated experimentally for the particular application considered. The paper presents the performance of the ventilator model under laboratory conditions, for five different wind tunnel speeds. The results are used to both demonstrate the effectiveness of the new design and to validate the computational model employed to develop it.

Keywords: Venturi-flow, ventilation, Wind-energy, Wind flow.

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Authors: D. Tedesco, G. Feletti, P. Trucco

Abstract:

The present study aims to develop a Decision Support System (DSS) to support operational decisions in Emergency Medical Service (EMS) systems regarding the assignment of medical emergency requests to Emergency Departments (ED). This problem is called “hospital selection” and concerns the definition of policies for the selection of the ED to which patients who require further treatment are transported by ambulance. The employed research methodology consists of a first phase of review of the technical-scientific literature concerning DSSs to support the EMS management and, in particular, the hospital selection decision. From the literature analysis, it emerged that current studies mainly focused on the EMS phases related to the ambulance service and consider a process that ends when the ambulance is available after completing a mission. Therefore, all the ED-related issues are excluded and considered as part of a separate process. Indeed, the most studied hospital selection policy turned out to be proximity, thus allowing to minimize the travelling time and to free-up the ambulance in the shortest possible time. The purpose of the present study consists in developing an optimization model for assigning medical emergency requests to the EDs also considering the expected time performance in the subsequent phases of the process, such as the case mix, the expected service throughput times, and the operational capacity of different EDs in hospitals. To this end, a Discrete Event Simulation (DES) model was created to compare different hospital selection policies. The model was implemented with the AnyLogic software and finally validated on a realistic case. The hospital selection policy that returned the best results was the minimization of the Time To Provider (TTP), considered as the time from the beginning of the ambulance journey to the ED at the beginning of the clinical evaluation by the doctor. Finally, two approaches were further compared: a static approach, based on a retrospective estimation of the TTP, and a dynamic approach, focused on a predictive estimation of the TTP which is determined with a constantly updated Winters forecasting model. Findings reveal that considering the minimization of TTP is the best hospital selection policy. It allows to significantly reducing service throughput times in the ED with a negligible increase in travel time. Furthermore, an immediate view of the saturation state of the ED is produced and the case mix present in the ED structures (i.e., the different triage codes) is considered, as different severity codes correspond to different service throughput times. Besides, the use of a predictive approach is certainly more reliable in terms on TTP estimation, than a retrospective approach. These considerations can support decision-makers in introducing different hospital selection policies to enhance EMSs performance.

Keywords: Emergency medical services, hospital selection, discrete event simulation, forecast model.

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Authors: Ali Taee Zade, Siamak Rasulzadeh, Reza Torkashvan

Abstract:

Although Model Driven Architecture has taken successful steps toward model-based software development, this approach still faces complex situations and ambiguous questions while applying to real world software systems. One of these questions - which has taken the most interest and focus - is how model transforms between different abstraction levels, MDA proposes. In this paper, we propose an approach based on Story Driven Modeling and Aspect Oriented Programming to ease these transformations. Service Oriented Architecture is taken as the target model to test the proposed mechanism in a functional system. Service Oriented Architecture and Model Driven Architecture [1] are both considered as the frontiers of their own domain in the software world. Following components - which was the greatest step after object oriented - SOA is introduced, focusing on more integrated and automated software solutions. On the other hand - and from the designers' point of view - MDA is just initiating another evolution. MDA is considered as the next big step after UML in designing domain.

Keywords: SOA, MDA, SDM, Model Transformation, Middleware Transparency, Aspects and Jini.

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Authors: Azlina Abu Bakar, Abdul Fatah Wan Sidek

Abstract:

Well-being has been given special emphasis in quality of life. It involves living a meaningful, life satisfaction, stability and happiness in life. Well-being also concerns the satisfaction of physical, psychological, social needs and demands of an individual. The purpose of this study was to validate three-factor measurement model of well-being using structural equation modeling (SEM). The conceptions of well-being measured such dimensions as physical, psychological and social well-being. This study was done based on a total sample of 650 adolescents from east-coast of peninsular Malaysia. The Well-Being Scales which was adapted from [1] was used in this study. The items were hypothesized a priori to have nonzero loadings on all dimensions in the model. The findings of the SEM demonstrated that it is a good fitting model which the proposed model fits the driving theory; (x2df = 1.268; GFI = .994; CFI = .998; TLI= .996; p = .255; RMSEA = .021). Composite reliability (CR) was .93 and average variance extracted (AVE) was 58%. The model in this study fits with the sample of data and well-being is important to bring sustainable development to the mainstream.

Keywords: Adolescence, Structural Equation Modeling, Sustainable Development, Well-Being.

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Authors: A. Shayeghi, H. Eimani Kalasar, H. Shayeghi

Abstract:

This paper emphasizes on the application of genetic algorithm (GA) to optimize the parameters of the TMD for achieving the best results in the reduction of the building response under earthquake excitations. The Integral of the Time multiplied Absolute value of the Error (ITAE) based on relative displacement of all floors in the building is taken as a performance index of the optimization criterion. The problem of robustly TMD controller design is formatted as an optimization problem based on the ITAE performance index to be solved using GA that has a story ability to find the most optimistic results. An 11–story realistic building, located in the city of Rasht, Iran is considered as a test system to demonstrate effectiveness of the proposed GA based TMD (GATMD) controller without specifying which mode should be controlled. The results of the proposed GATMD controller are compared with the uncontrolled structure through timedomain simulation and some performance indices. The results analysis reveals that the designed GA based TMD controller has an excellent capability in reduction of the seismically excited example building and the ITAE performance, that is so for remains as unknown, can be introduced a new criteria - method for structural dynamic design.

Keywords: Tuned Mass Damper, Genetic Algorithm, TallBuildings, Structural Dynamics.

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Authors: Ksenija Dumičić, Anita Čeh Časni, Berislav Žmuk

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The aim of this paper is to select the most accurate forecasting method for predicting the future values of the unemployment rate in selected European countries. In order to do so, several forecasting techniques adequate for forecasting time series with trend component, were selected, namely: double exponential smoothing (also known as Holt`s method) and Holt-Winters` method which accounts for trend and seasonality. The results of the empirical analysis showed that the optimal model for forecasting unemployment rate in Greece was Holt-Winters` additive method. In the case of Spain, according to MAPE, the optimal model was double exponential smoothing model. Furthermore, for Croatia and Italy the best forecasting model for unemployment rate was Holt-Winters` multiplicative model, whereas in the case of Portugal the best model to forecast unemployment rate was Double exponential smoothing model. Our findings are in line with European Commission unemployment rate estimates.

Keywords: European Union countries, exponential smoothing methods, forecast accuracy unemployment rate.

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Authors: Lenka Krulikovská, Jaroslav Polec

Abstract:

In this paper we present a modification to existed model of threshold for shot cut detection, which is able to adapt itself to the sequence statistics and operate in real time, because it use for calculation only previously evaluated frames. The efficiency of proposed modified adaptive threshold scheme was verified through extensive test experiment with several similarity metrics and achieved results were compared to the results reached by the original model. According to results proposed threshold scheme reached higher accuracy than existed original model.

Keywords: Abrupt cut, shot cut detection, adaptive threshold.

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Authors: Oscar Javier Herrera Ochoa, Ivan Dario Romero Fonseca

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This paper presents a design of a model for planning the distribution logistics operation. The significance of this work relies on the applicability of this fact to the analysis of small and medium enterprises (SMEs) of dry freight in Bogotá. Two stages constitute this implementation: the first one is the place where optimal planning is achieved through a hybrid model developed with mixed integer programming, which considers the transhipment operation based on a combined load allocation model as a classic transshipment model; the second one is the specific routing of that operation through the heuristics of Clark and Wright. As a result, an integral model is obtained to carry out the step by step planning of the distribution of dry freight for SMEs in Bogotá. In this manner, optimum assignments are established by utilizing transshipment centers with that purpose of determining the specific routing based on the shortest distance traveled.

Keywords: Transshipment model, mixed integer programming, saving algorithm, dry freight transportation.

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Authors: Supunmali Ahangama, Danny Chiang Choon Poo

Abstract:

Health analytics (HA) is used in healthcare systems for effective decision making, management and planning of healthcare and related activities. However, user resistances, unique position of medical data content and structure (including heterogeneous and unstructured data) and impromptu HA projects have held up the progress in HA applications. Notably, the accuracy of outcomes depends on the skills and the domain knowledge of the data analyst working on the healthcare data. Success of HA depends on having a sound process model, effective project management and availability of supporting tools. Thus, to overcome these challenges through an effective process model, we propose a HA process model with features from rational unified process (RUP) model and agile methodology.

Keywords: Agile methodology, health analytics, unified process model, UML.

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Authors: H. Zabiri, N. Mazuki

Abstract:

Several valve stiction models have been proposed in the literature to help understand and study the behavior of sticky valves. In this paper, an alternative black-box modeling approach based on Neural Network (NN) is presented. It is shown that with proper network type and optimum model structures, the performance of the developed NN stiction model is comparable to other established method. The resulting NN model is also tested for its robustness against the uncertainty in the stiction parameter values. Predictive mode operation also shows excellent performance of the proposed model for multi-steps ahead prediction.

Keywords: Control valve stiction, neural network, modeling.

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Authors: A. Amar, O. Hemeda

Abstract:

A study of the structure of the nucleus with the analogy by solid-state physics has been developed. We have used binding energy to calculate R (a parameter that is proportional to the radius of the nucleus) for deuteron, alpha, and ⁸Be. The calculated parameter r calculated from solid state physics produces a probe for calculation the nuclear radii. ⁸Be has special attention as it is radioactive nucleus and the latest nucleus to be calculated from crystalline model approach. The distribution of nucleons inside the nucleus is taken to be tetrahedral for ¹⁶O. The model has failed to expect the radius of ⁹Be which is an impression about the modification should be done on the model at near future. A comparison between our calculations and those from literature has been made, and a good agreement has been obtained.

Keywords: The structure of the nucleus, binding energy, crystalline model approach, nuclear radii, tetrahedral for 16O.

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Authors: Indar Chaerah Gunadin, Adi Soeprijanto, Ontoseno Penangsang

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This paper will discuss about an active power generator scheduling method in order to increase the limit level of steady state systems. Some power generator optimization methods such as Langrange, PLN (Indonesian electricity company) Operation, and the proposed Z-Thevenin-based method will be studied and compared in respect of their steady state aspects. A method proposed in this paper is built upon the thevenin equivalent impedance values between each load respected to each generator. The steady state stability index obtained with the REI DIMO method. This research will review the 500kV-Jawa-Bali interconnection system. The simulation results show that the proposed method has the highest limit level of steady state stability compared to other optimization techniques such as Lagrange, and PLN operation. Thus, the proposed method can be used to create the steady state stability limit of the system especially in the peak load condition.

Keywords: generation scheduling, steady-state stability limit, REI Dimo, margin stability

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Authors: M. Palanivel, R. Uthayakumar

Abstract:

In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous Weibull distribution deteriorating items with power demand pattern is presented. In this model, the holding cost per unit of the item per unit time is assumed to be an increasing linear function of time spent in storage. Here the retailer is allowed a trade-credit offer by the supplier to buy more items. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimizing the total inventory cost by finding the optimal time interval and finding the optimal order quantity. The optimal solution of the model is illustrated with the help of numerical examples. Finally sensitivity analysis and graphical representations are given to demonstrate the model.

Keywords: Power demand pattern, Partial backlogging, Time dependent holding cost, Trade credit, Weibull deterioration.

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Authors: Heung Sun Yoon, Jong Tae Kim

Abstract:

In this paper, we present an activity diagram model for double-loop control self-adaptive braking system. Since activity diagram helps to improve visibility of self-adaption. We can easily find where improvement is needed on double-loop control. Double-loop control is adopted since the design conditions and actual conditions can be different. The system is reconfigured in runtime by using double-loop control. We simulated to verify and validate our model by using MATLAB. We compared single-loop control model with double-loop control model. Simulation results show that double-loop control provides more consistent brake power control than single-loop control.

Keywords: Activity diagram, automotive, braking system, double-loop, Self-adaptive, UML, vehicle.

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Authors: M. A. Badr, M.N. El Kordy, A. N. Mohib, M. M. Ibrahim

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The basic objective of the research is to study the effect of hybrid wind energy on the cost of generated electricity considering the cost of reduction CO₂ emissions. The system consists of small wind turbine(s), storage battery bank and a diesel generator (W/D/B). Using an optimization software package, different system configurations are investigated to reach optimum configuration based on the net present cost (NPC) and cost of energy (COE) as economic optimization criteria. The cost of avoided CO₂ is taken into consideration. The system is intended to supply the electrical load of a small community (gathering six families) in a remote Egyptian area. The investigated system is not connected to the electricity grid and may replace an existing conventional diesel powered electric supply system to reduce fuel consumption and CO₂ emissions. The simulation results showed that W/D energy system is more economic than diesel alone. The estimated COE is 0.308$/kWh and extracting the cost of avoided CO₂, the COE reached 0.226 $/kWh which is an external benefit of wind turbine, as there are no pollutant emissions through operational phase.

Keywords: Hybrid wind turbine systems, remote areas electrification, simulation of hybrid energy systems, techno-economic study.

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Authors: N. Arslanoglu

Abstract:

This paper deals with the optimum tilt angle for the solar collector in order to collect the maximum solar radiation. The optimum angle for tilted surfaces varying from 0^◦ to 90^◦ in steps of 1^◦ was computed. In present study, a theoretical model is used to predict the global solar radiation on a tilted surface and to obtain the optimum tilt angle for a solar collector in Bursa, Turkey. Global solar energy radiation on the solar collector surface with an optimum tilt angle is calculated for specific periods. It is determined that the optimum slope angle varies between 0^◦ (June) and 59^◦ (December) throughout the year. In winter (December, January, and February) the tilt should be 55^◦, in spring (March, April, and May) 19.6^◦, in summer (June, July, and August) 5.6^◦, and in autumn (September, October, and November) 44.3^◦. The yearly average of this value was obtained to be 31.1^◦ and this would be the optimum fixed slope throughout the year.

Keywords: Optimum tilt angle, global solar radiation, tilted surface.

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Authors: Mehdi Kheradmand, Mehdi Azhdary Moghaddam, Abdolreza Zahiri, Khalil Ghorbani

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This research compares results of major methods of determining the flow discharge using experimental relationships with results from the M5 decision tree model in meandering compound sections in several laboratory channels. It was found that the M5 decision tree model enjoyed greater accuracy of statistical parameters compared to methods to the said methods. This suggested that the M5 decision tree model has highly improved the calculated accuracy of the flow discharge in meandering compound channels.

Keywords: Stage-discharge relationship, M5 decision tree model, compound section, meandering compound channel.

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Authors: T.C.Manjunath, C. Ardil

Abstract:

This paper deals with the development of a Jacobean model for a 4-axes indigenously developed scara robot arm in the laboratory. This model is used to study the relation between the velocities and the forces in the robot while it is doing the pick and place operation.

Keywords: SCARA, Jacobean, Tool Configuration Vector, Computer Control , Visual Basic , Interfacing , Drivers,

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Authors: Liu Shu, Dong Shangjia

Abstract:

Our goal is to effectively increase the number of boats in the river during a six month period. The main factors of determining the number of boats are duration and “select the priority trip". In the microcosmic simulation model, the best result is 4 to 24 nights with DSCF, and the number of boats is 812 with an increasing ratio of 9.0% related to the second best result. However, the number of boats is related to 31.6% less than the best one in 6 to 18 nights with FCFS. In the discrete duration model, we get from 6 to 18 nights, the numbers of boats have increased to 848 with an increase ratio of 29.7% than the best result in model I for the same time range. Moreover, from 4 to 24 nights, the numbers of boats have increase to 1194 with an increase ratio of 47.0% than the best result in model I for the same time range.

Keywords: Discrete duration model, “select the priority trip”, microcosmic simulation model.

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Authors: M. S. Reza, M. Hamdi, A.S. Hadi

Abstract:

The operating control parameters of injection flushing type of electrical discharge machining process on stainless steel 304 workpiece with copper tools are being optimized according to its individual machining characteristic i.e. material removal rate (MRR). Lower MRR during EDM machining process may decrease its- machining productivity. Hence, the quality characteristic for MRR is set to higher-the-better to achieve the optimum machining productivity. Taguchi method has been used for the construction, layout and analysis of the experiment for each of the machining characteristic for the MRR. The use of Taguchi method in the experiment saves a lot of time and cost of preparing and machining the experiment samples. Therefore, an L18 Orthogonal array which was the fundamental component in the statistical design of experiments has been used to plan the experiments and Analysis of Variance (ANOVA) is used to determine the optimum machining parameters for this machining characteristic. The control parameters selected for this optimization experiments are polarity, pulse on duration, discharge current, discharge voltage, machining depth, machining diameter and dielectric liquid pressure. The result had shown that the higher the discharge voltage, the higher will be the MRR.

Keywords: ANOVA, EDM, Injection Flushing, L18 OrthogonalArray, MRR, Stainless Steel 304

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Authors: Sunita Dhingra, Satinder Bal Gupta, Ranjit Biswas

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Multiprocessor task scheduling is a NP-hard problem and Genetic Algorithm (GA) has been revealed as an excellent technique for finding an optimal solution. In the past, several methods have been considered for the solution of this problem based on GAs. But, all these methods consider single criteria and in the present work, minimization of the bi-criteria multiprocessor task scheduling problem has been considered which includes weighted sum of makespan & total completion time. Efficiency and effectiveness of genetic algorithm can be achieved by optimization of its different parameters such as crossover, mutation, crossover probability, selection function etc. The effects of GA parameters on minimization of bi-criteria fitness function and subsequent setting of parameters have been accomplished by central composite design (CCD) approach of response surface methodology (RSM) of Design of Experiments. The experiments have been performed with different levels of GA parameters and analysis of variance has been performed for significant parameters for minimisation of makespan and total completion time simultaneously.

Keywords: Multiprocessor task scheduling, Design of experiments, Genetic Algorithm, Makespan, Total completion time.

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Authors: Muh. Hisjam, Nancy Oktyajati, Wakhid A. Jauhari, Wahyudi Sutopo

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This research is intended to develop a raw material allocation model in timber processing industry in Perum Perhutani Unit I, Central Java, Indonesia. The model can be used to determine the quantity of allocation of timber between chain in the supply chain to select supplier considering factors that are log price and the distance. In determining the quantity of allocation of timber between chains in the supply chain, the model considers the optimal inventory in each chain. Whilst the optimal inventory is determined based on demand forecast, the capacity and safety stock. Problem solving allocation is conducted by developing linear programming model that aims to minimize the total cost of the purchase, transportation cost and storage costs at each chain. The results of numerical examples show that the proposed model can generate savings of the purchase cost of 20.84% and select suppliers with mileage closer.

Keywords: Allocation model, linear programming, purchase costs, storage costs, suppliers, transportation costs.

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