Search results for: Initial value problem.

Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Taehan Lee

Abstract:

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: Integer programming, multicommodity network design, routing, shortest path.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: Gurung S., Yadav B. N., Budhathoki SS.

Abstract:

Problem based learning is one of the highly acclaimed learning methods in medical education since its first introduction at Mc-Master University in Canada in the 1960s. It has now been adopted as a teaching learning method in many medical colleges of Nepal. B.P. Koirala Institute of Health Sciences (BPKIHS), a health science deemed university is the second institute in Nepal to establish problem-based learning academic program and need-based teaching approach hence minimizing teaching through lectures since its inception. During the first two years of MBBS course, the curriculum is divided into various organ-systems incorporated with problem-based learning exercise each of one week duration.

Keywords: PBL, medical education.

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Authors: Kyungroul Lee, Kwangjin Bae, Kangbin Yim

Abstract:

This paper introduces a hardware solution to password exposure problem caused by direct accesses to the keyboard hardware interfaces through which a possible attacker is able to grab user-s password even where existing countermeasures are deployed. Several researches have proposed reasonable software based solutions to the problem for years. However, recently introduced hardware vulnerability problems have neutralized the software approaches and yet proposed any effective software solution to the vulnerability. Hardware approach in this paper is expected as the only solution to the vulnerability

Keywords: Keyboard sniff, password exposure, hardware vulnerability, privacy problem, insider security.

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Authors: Abdolsalam Ghaderi

Abstract:

In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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Authors: Prasanti Widyasih Sarli, Prayatni Soewondo

Abstract:

Greater access to sanitation in developing countries is urgent. However even though sanitation is crucial, overall budget for sanitation is limited. With this budget limitation, it is important to (1) allocate resources strategically to maximize impact and (2) take into account communal agency to potentially be a source for sanitation improvements. The Jodipan and Kesatrian Project in Malang, Indonesia is an interesting alternative for solving the sanitation problem in which resources were allocated strategically and communal agency was also observed. Although the projects initial goal was only to improve visually the situation in the slums, it became a new tourist destination, and the economic benefit that came with it had an effect also on the change of behavior of the residents and the government towards sanitation. It also grew from only including the Kesatrian Village to expanding to the Jodipan Village in the course of less than a year. To investigate the success of this project, in this paper a descriptive model will be used and data will be drawn from intensive interviews with the initiators of the project, residents affected by the project and government officials. In this research it is argued that three points mark the success of the project: (1) the strategic initial impact due to choice of location, (2) the influx of tourists that triggered behavioral change among residents and, (3) the direct economic impact which ensured its sustainability and growth by gaining government officials support and attention for more public spending in the area for slum development and sanitation improvement.

Keywords: Behavior change, sanitation, slum, strategic thinking.

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Authors: Tarek Aboueldah, Hanan Farag

Abstract:

Parallel Job Shop Scheduling Problem (JSSP) 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. Thus, we propose a hybrid Artificial Intelligence (AI) model with Discrete Breeding Swarm (DBS) added to traditional AI 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: X. Vecino, J. M. Cruz, A. Moldes

Abstract:

The disposal and the treatment of sewage sludge is an expensive and environmentally complex problem. In this work, a lipopeptide biosurfactant extracted from corn steep liquor was used as ecofriendly and cost-competitive alternative for the mobilization and bioremediation of fluorene in sewage sludge. Results have demonstrated that this biosurfactant has the capability to mobilize fluorene to the aqueous phase, reducing the amount of fluorene in the sewage sludge from 484.4 mg/Kg up to 413.7 mg/Kg and 196.0 mg/Kg after 1 and 27 days respectively. Furthermore, once the fluorene was extracted the lipopeptide biosurfactant contained in the aqueous phase allowed the biodegradation, up to 40.5% of the initial concentration of this polycyclic aromatic hydrocarbon.

Keywords: Fluorene, lipopeptide biosurfactant, mobilization, sewage sludge.

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Authors: Ajay Sharma, R.S. Jangid

Abstract:

Analytical seismic response of multi-story building supported on base isolation system is investigated under real earthquake motion. The superstructure is idealized as a shear type flexible building with lateral degree-of-freedom at each floor. The force-deformation behaviour of the isolation system is modelled by the bi-linear behaviour which can be effectively used to model all isolation systems in practice. The governing equations of motion of the isolated structural system are derived. The response of the system is obtained numerically by step-by-method under three real recorded earthquake motions and pulse motions associated in the near-fault earthquake motion. The variation of the top floor acceleration, interstory drift, base shear and bearing displacement of the isolated building is studied under different initial stiffness of the bi-linear isolation system. It was observed that the high initial stiffness of the isolation system excites higher modes in base-isolated structure and generate floor accelerations and story drift. Such behaviour of the base-isolated building especially supported on sliding type of isolation systems can be detrimental to sensitive equipment installed in the building. On the other hand, the bearing displacement and base shear found to reduce marginally with the increase of the initial stiffness of the initial stiffness of the isolation system. Further, the above behaviour of the base-isolated building was observed for different parameters of the bearing (i.e. post-yield stiffness and characteristic strength) and earthquake motions (i.e. real time history as well as pulse type motion).

Keywords: base isolation, base shear, bi-linear, earthquake, floor accelerations, inter-story drift, multi-story building, pulsemotion, stiffness ratio.

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Authors: Khalid S. Hashim, Andy Shaw, Rafid Alkhaddar, Montserrat Ortoneda Pedrola

Abstract:

A flow column has been innovatively used in the design of a new electrocoagulation reactor (ECR1) that will reduce the temperature of water being treated; where the flow columns work as a radiator for the water being treated. In order to investigate the performance of ECR1 and compare it to that of traditional reactors; 600 mL water samples with an initial temperature of 350C were pumped continuously through these reactors for 30 min at current density of 1 mA/cm2. The temperature of water being treated was measured at 5 minutes intervals over a 30 minutes period using a thermometer. Additional experiments were commenced to investigate the effects of initial temperature (15-350C), water conductivity (0.15 – 1.2 S) and current density (0.5 -3 mA/cm2) on the performance of ECR1. The results obtained demonstrated that the ECR1, at a current density of 1 mA/cm2 and continuous flow model, reduced water temperature from 350C to the vicinity of 280C during the first 15 minutes and kept the same level till the end of the treatment time. While, the temperature increased from 28.1 to 29.80C and from 29.8 to 31.90C in the batch and the traditional continuous flow models respectively. In term of initial temperature, ECR1 maintained the temperature of water being treated within the range of 22 to 280C without the need for external cooling system even when the initial temperatures varied over a wide range (15 to 350C). The influent water conductivity was found to be a significant variable that affect the temperature. The desirable value of water conductivity is 0.6 S. However, it was found that the water temperature increased rapidly with a higher current density.

Keywords: Water temperature, flow column, electrocoagulation.

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Authors: Phruksaphanrat B.

Abstract:

This research proposes a preemptive 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 makespan. 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, preemptive 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, Preemptive fuzzy goal programming.

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Authors: T. R. Alencar, P. T. Leite

Abstract:

Several optimization algorithms specifically applied to the problem of Operation Planning of Hydrothermal Power Systems have been developed and are used. Although providing solutions to various problems encountered, these algorithms have some weaknesses, difficulties in convergence, simplification of the original formulation of the problem, or owing to the complexity of the objective function. Thus, this paper presents the development of a computational tool for solving optimization problem identified and to provide the User an easy handling. Adopted as intelligent optimization technique, Genetic Algorithms and programming language Java. First made the modeling of the chromosomes, then implemented the function assessment of the problem and the operators involved, and finally the drafting of the graphical interfaces for access to the User. The program has managed to relate a coherent performance in problem resolution without the need for simplification of the calculations together with the ease of manipulating the parameters of simulation and visualization of output results.

Keywords: Energy, Optimization, Hydrothermal Power Systemsand Genetic Algorithms

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Authors: Waralak Vongdoiwang Siricharoen

Abstract:

One of object oriented software developing problem is the difficulty of searching the appropriate and suitable objects for starting the system. In this work, ontologies appear in the part of supporting the object discovering in the initial of object oriented software developing. There are many researches try to demonstrate that there is a great potential between object model and ontologies. Constructing ontology from object model is called ontology engineering can be done; On the other hand, this research is aiming to support the idea of building object model from ontology is also promising and practical. Ontology classes are available online in any specific areas, which can be searched by semantic search engine. There are also many helping tools to do so; one of them which are used in this research is Protégé ontology editor and Visual Paradigm. To put them together give a great outcome. This research will be shown how it works efficiently with the real case study by using ontology classes in travel/tourism domain area. It needs to combine classes, properties, and relationships from more than two ontologies in order to generate the object model. In this paper presents a simple methodology framework which explains the process of discovering objects. The results show that this framework has great value while there is possible for expansion. Reusing of existing ontologies offers a much cheaper alternative than building new ones from scratch. More ontologies are becoming available on the web, and online ontologies libraries for storing and indexing ontologies are increasing in number and demand. Semantic and Ontologies search engines have also started to appear, to facilitate search and retrieval of online ontologies.

Keywords: Software Developing, Ontology, Ontology Library, Artificial Intelligent, Protégé, Object Model.

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Authors: John Tarus, Zhendong Niu, Bakhti Khadidja

Abstract:

In recent years, e-learning recommender systems has attracted great attention as a solution towards addressing the problem of information overload in e-learning environments and providing relevant recommendations to online learners. E-learning recommenders continue to play an increasing educational role in aiding learners to find appropriate learning materials to support the achievement of their learning goals. Although general recommender systems have recorded significant success in solving the problem of information overload in e-commerce domains and providing accurate recommendations, e-learning recommender systems on the other hand still face some issues arising from differences in learner characteristics such as learning style, skill level and study level. Conventional recommendation techniques such as collaborative filtering and content-based deal with only two types of entities namely users and items with their ratings. These conventional recommender systems do not take into account the learner characteristics in their recommendation process. Therefore, conventional recommendation techniques cannot make accurate and personalized recommendations in e-learning environment. In this paper, we propose a recommendation technique combining collaborative filtering and ontology to recommend personalized learning materials to online learners. Ontology is used to incorporate the learner characteristics into the recommendation process alongside the ratings while collaborate filtering predicts ratings and generate recommendations. Furthermore, ontological knowledge is used by the recommender system at the initial stages in the absence of ratings to alleviate the cold-start problem. Evaluation results show that our proposed recommendation technique outperforms collaborative filtering on its own in terms of personalization and recommendation accuracy.

Keywords: Collaborative filtering, e-learning, ontology, recommender system.

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Authors: Thorsten Herrmann, Alexander Laukemann, Hansgeorg Binz, Daniel Roth

Abstract:

For the analysis of already identified and existing problems, the pertinent literature provides a comprehensive collection of approaches as well as methods in order to analyze the problems in detail. But coming up with problems, which are assets worth pursuing further, is often challenging. However, the importance of well-formulated problem ideas and their influence of subsequent creative processes are incontestable and proven. In order to meet the covered challenges, the Institute for Engineering Design and Industrial Design (IKTD) developed the Emoji Method. This paper presents the Emoji Method, which support designers to generate problem ideas in a structured way. Considering research findings from knowledge management and innovation management, research into emojis and emoticons reveal insights by means of identifying and formulating problem ideas within the early design phase. The simple application and the huge supporting potential of the Emoji Method within the early design phase are only few of the many successful results of the conducted evaluation. The Emoji Method encourages designers to identify problem ideas and describe them in a structured way in order to start focused with generating solution ideas for the revealed problem ideas.

Keywords: Emojis, problem ideas, innovation management, knowledge management.

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Authors: Agni Stylianou-Georgiou, Eliza Pitri

Abstract:

This study is a design narrative that discusses researchers’ new learning based on changes made in pedagogies and learning opportunities in the context of a Cognitive Psychology and an Art History undergraduate course. The purpose of this study was to investigate how to encourage creative problem-based play in tertiary education engaging instructors and student-teachers in designing educational games. Course instructors modified content to encourage flexible thinking during game design problem-solving. Qualitative analyses of data sources indicated that Thinking Birds’ questions could encourage flexible thinking as instructors engaged in creative problem-based play. However, student-teachers demonstrated weakness in adopting flexible thinking during game design problem solving. Further studies of student-teachers’ shifting perspectives during different instructional design tasks would provide insights for developing the Thinking Birds’ questions as tools for creative problem solving.

Keywords: Creative problem-based play, educational games, flexible thinking, tertiary education.

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Authors: S. B. Liu, K. M. Ng, H. L. Ong

Abstract:

This paper presents a new heuristic algorithm for the classical symmetric traveling salesman problem (TSP). The idea of the algorithm is to cut a TSP tour into overlapped blocks and then each block is improved separately. It is conjectured that the chance of improving a good solution by moving a node to a position far away from its original one is small. By doing intensive search in each block, it is possible to further improve a TSP tour that cannot be improved by other local search methods. To test the performance of the proposed algorithm, computational experiments are carried out based on benchmark problem instances. The computational results show that algorithm proposed in this paper is efficient for solving the TSPs.

Keywords: Local search, overlapped neighborhood, travelingsalesman problem.

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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: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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Authors: Julija Asmuss, Gunars Lauks, Viktors Zagorskis

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We consider the problem of bandwidth allocation in a substrate network as an optimization problem for the aggregate utility of multiple applications with diverse requirements and describe a simulation scheme for dynamically adaptive bandwidth allocation protocols. The proposed simulation model based on Coloured Petri Nets (CPN) is realized using CPN Tools.

Keywords: Bandwidth Allocation Problem, Coloured Petri Nets, CPN Tools, Simulation

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Authors: Wayan F. Mahmudy, Romeo M. Marian, Lee H. S. Luong

Abstract:

This paper and its companion (Part 2) deal with modeling and optimization of two NP-hard problems in production planning of flexible manufacturing system (FMS), part type selection problem and loading problem. The part type selection problem and the loading problem are strongly related and heavily influence the system-s efficiency and productivity. The complexity of the problems is harder when flexibilities of operations such as the possibility of operation processed on alternative machines with alternative tools are considered. These problems have been modeled and solved simultaneously by using real coded genetic algorithms (RCGA) which uses an array of real numbers as chromosome representation. These real numbers can be converted into part type sequence and machines that are used to process the part types. This first part of the papers focuses on the modeling of the problems and discussing how the novel chromosome representation can be applied to solve the problems. The second part will discuss the effectiveness of the RCGA to solve various test bed problems.

Keywords: Flexible manufacturing system, production planning, part type selection problem, loading problem, real-coded genetic algorithm

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Authors: Dariusz Barbucha, Piotr Jedrzejowicz

Abstract:

The paper proposes and validates a new method of solving instances of the vehicle routing problem (VRP). The approach is based on a multiple agent system paradigm. The paper contains the VRP formulation, an overview of the multiple agent environment used and a description of the proposed implementation. The approach is validated experimentally. The experiment plan and the discussion of experiment results follow.

Keywords: multi-agent systems, population-based methods, vehiclerouting problem.

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Authors: Wai-Sum Lee

Abstract:

This study investigates C-V and V-C co-articulation in Cantonese monosyllables of the CV, VC or CVC structure, with C = one of the three stop consonants [p, t, k] and V = one of the three corner vowels [i, a, u]. Five repetitions of each test syllable on a randomized list were elicited from Cantonese young adult speakers in their early-20s. A research tool, EMA AG500, was used to record the synchronized audio signals and articulatory data at three different locations of the tongue – tongue tip, tongue middle, and tongue back – and the positions of the upper and lower lips during the test syllables. The main findings based on the articulatory data collected from two male Cantonese speakers are as follows: (i) For the syllable-initial [p-], strong co-articulation is observed when [p-] preceding the high vowel [i] or [u], but not the low vowel [a]. As for the syllable-final [-p], it is strongly co-articulated with the preceding vowel, even when the vowel is [a]. (ii) The co-articulation between the initial [t-] and the following vowel of any type is weak. In the syllable-final position, the degree of co-articulatory resistance of [-t] is also large when following the vowel [u], but [-t] is largely co-articulated with the preceding vowel when the vowel is [i] or [a]. (iii) The strength of co-articulation differs when the initial [k-] precedes the different types of vowel. A stronger co-articulation between [k-] and [i] than between [k-] and [u], and the strength of co-articulation is much reduced between [k-] and [a]. However, in the syllable-final position, there is strong co-articulation between [-k] and the preceding vowel [a]. (iv) Among the three types of stop consonants in the syllable-initial position, the decreasing degree of co-articulatory resistance (CR) is [t-] > [k-] > [p-], and the degree of CR is reduced during all three types of stop in the syllable-final position. In general, the data on co-articulation between consonant and vowel in the Cantonese monosyllables are similar to those in other languages reported in previous studies.

Keywords: Cantonese, co-articulation, consonant, vowel.

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Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: Liang-Chien Lee, Chih-Hsiang Chang, Ying-Shu Tseng

Abstract:

Comparing with prior studies mainly focused on the effect of a certain event (it may be the initial announcement of bad news or the repeated announcements of identical bad news) on stock price, the aim of this study is to explore how investors react to subsequent bad news with identical content. Empirical results show that as a result of behavioral pitfalls, investors underreact to the initial announcement of the bad news (i.e., unknown bad news) and overreact to the repeated announcements of the identical bad news (i.e., known bad news).

Keywords: Subsequent bad news, Behavioral finance, Investors’ misreaction, Behavioral pitfalls.

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Authors: Pankaj Dutta, Debjani Chakraborty

Abstract:

This paper investigates the effect of product substitution in the single-period 'newsboy-type' problem in a fuzzy environment. It is supposed that the single-period problem operates under uncertainty in customer demand, which is described by imprecise terms and modelled by fuzzy sets. To perform this analysis, we consider the fuzzy model for two-item with upward substitution. This upward substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. We show that the explicit consideration of this substitution opportunity increase the average expected profit. Computational study is performed to observe the benefits of product's substitution.

Keywords: Fuzzy demand, Newsboy, Single-period problem, Substitution.

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

Abstract:

The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: Job-shop scheduling, classification, constraints, objective functions.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Bita Tadayon, Nasser Salmasi

Abstract:

This research deals with a flexible flowshop scheduling problem with arrival and delivery of jobs in groups and processing them individually. Due to the special characteristics of each job, only a subset of machines in each stage is eligible to process that job. The objective function deals with minimization of sum of the completion time of groups on one hand and minimization of sum of the differences between completion time of jobs and delivery time of the group containing that job (waiting period) on the other hand. The problem can be stated as FFc / rj , Mj / irreg which has many applications in production and service industries. A mathematical model is proposed, the problem is proved to be NPcomplete, and an effective heuristic method is presented to schedule the jobs efficiently. This algorithm can then be used within the body of any metaheuristic algorithm for solving the problem.

Keywords: flexible flowshop scheduling, group processing, machine eligibility constraint, mathematical modeling.

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