Search results for: travel salesman problem

Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

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Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design

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Authors: Sabri Sulaiman, Siti Hajar Abu Bakar Ah, Haris Abd Wahab

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Street children is a global phenomenon and declared as a social problem by social researcher and scholars across the world. The insecure street environment exposes street children into various risk factors. One of them is the health and psychological problem. The objective of this study is to assess the health problem and psychological wellbeing of street children in Kuala Lumpur, Malaysia. The cross-sectional study involved 303 street children in Chow Kit, Kuala Lumpur. The study confirmed that the majority (95.7%) of street children who participated in the study have a health problem. The findings also demonstrated that the majority of them have issues related to their psychological wellbeing. The inputs from this study are instrumental for the suggestion of specific intervention to improve the health and psychology wellbeing of street children in Malaysia. Agencies which are responsible for the street children well-being can utilise the inputs to framing and improving the social care programmes for the children.

Keywords: street children, health status, psychology wellbeing, homeless

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Authors: Abdulaziz Alageel, Martino Luis, Shuya Zhong

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The main focus of this research study is on the challenges faced in decision-making in a supply chain network regarding the facility location while considering carbon emissions. The study aims (i) to locate facilities (i.e., distribution centeres) in a continuous space considering limitations of capacity and the costs associated with opening and (ii) to reduce the cost of carbon emissions by selecting the mode of transportation. The problem is formulated as mixed-integer linear programming. This study hybridised a greedy randomised adaptive search (GRASP) and variable neighborhood search (VNS) to deal with the problem. Well-known datasets from the literature (Brimberg et al. 2001) are used and adapted in order to assess the performance of the proposed method. The proposed hybrid method produces encouraging results based on computational analysis. The study also highlights some research avenues for future recommendations.

Keywords: supply chain, facility location, weber problem, sustainability

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Authors: Yangyang Zhang

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In The Valley of the Moon, Jack London implicitly presents the connection between the city and the male, the country and the female, constructing a gender space where the city and the countryside are opposed. But meanwhile, London is constantly dismantling the gender space through the reversed travel map so as to highlight the fluidity and productivity of female space. Under such circumstance, the original gender space has to be reorganized. Through the construction of gendered urban and rural spaces, Jack London presents the national crisis in the process of urbanization of the American West in the late 19th century, while the female-led reversed travel map reproduces the original contribution of the American West to the construction of nationality. In the end, the reorganized neutral space “valley of the moon” reflects the “garden” motif in American national imagination and plays an important role in rebuilding national identity. This research studies the feminist geography and cartography in Jack London's novel The Valley of the Moon and analyzes the gender-politics attribution in the literary geography writing in London's novel on this basis. The research returns to the American historical context at the end of the 19th century, focusing on how London’s feminist geography embodies his sense of nationality and investigating how female-dominated literary cartography reconstructs American identity. This paper takes Literary Cartography, and feminist geography as the ideological guide combines with the discourse of gender politics. comprehensively uses various literary criticism methods such as deconstructionist literary criticism, and new historicism literary criticism, etc., Through the study of Jack London's work, the paper aims to analyse how London constructs a national image by literary geography.

Keywords: American identity, American west, feminist geography, garden motif, the valley of the moon

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Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

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The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

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Authors: Sutanto, Alexander Christy, N. Sutrisno

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The demand of a product is linearly dependent on the price and quality of the product. It is analog to the demand of the employee in job-seeker problem. This paper address a closed-loop supply chain (CLSC) where a university plays role as manufacturer that produce graduates as job-seeker according to the demand and promote them to a certain corporation through a trial. Unemployed occurs when the job-seeker failed the trial or dismissed. A third party accomodates the unemployed and sends them back to the university to increase their quality through training.

Keywords: CLSC, price, quality, job-seeker problem

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Nejah Ben Mabrouk, Bassem Jarboui, Habib Chabchoub

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Production and distribution planning is the most important part in supply chain management. In this paper, a NP-hard production-distribution problem for one product over a multi-period horizon is investigated. The aim is to minimize the sum of costs of three items: production setups, inventories and distribution, while determining, for each period, the amount produced, the inventory levels and the delivery trips. To solve this difficult problem, we propose a bi-phase approach based on a Variable Neighbourhood Search (VNS). This heuristic is tested on 90 randomly generated instances from the literature, with 20 periods and 50, 100, 200 customers. Computational results show that our approach outperforms existing solution procedures available in the literature

Keywords: logistic, production, distribution, variable neighbourhood search

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Authors: Siddhartha Chauhan, Nitin Kumar Kotania

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Traditional Wireless Sensor Networks (WSNs) generally use static sinks to collect data from the sensor nodes via multiple forwarding. Therefore, network suffers with some problems like long message relay time, bottle neck problem which reduces the performance of the network. Many approaches have been proposed to prevent this problem with the help of mobile sink to collect the data from the sensor nodes, but these approaches still suffer from the buffer overflow problem due to limited memory size of sensor nodes. This paper proposes an energy efficient scheme for data gathering which overcomes the buffer overflow problem. The proposed scheme creates virtual grid structure of heterogeneous nodes. Scheme has been designed for sensor nodes having variable sensing rate. Every node finds out its buffer overflow time and on the basis of this cluster heads are elected. A controlled traversing approach is used by the proposed scheme in order to transmit data to sink. The effectiveness of the proposed scheme is verified by simulation.

Keywords: buffer overflow problem, mobile sink, virtual grid, wireless sensor networks

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Authors: Anna Sikharulidze, Gia Sirbiladze

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For the evaluation of unreliability levels of movement on the closed routes in the vehicle routing problem, the fuzzy operators family is constructed. The interactions between routing factors in extreme conditions on the roads are considered. A multi-criteria decision-making model (MCDM) is constructed. Constructed aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are proved. Connections between the operators and the compositions of dual triangular norms are described. The conjugate connections between the constructed operators are shown. Operators reflect interactions among all the combinations of the factors in the fuzzy MCDM process. Several variants of constructed operators are used in the decision-making problem regarding the assessment of unreliability and possibility levels of movement on closed routes.

Keywords: vehicle routing problem, associated probabilities of a fuzzy measure, choquet integral, fuzzy aggregation operator

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Authors: Wen-Tsung Ho, Ku-Kuang Chang, Hsin-Yuan Chang

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In this study, we consider an economic lot-size batch-shipment scheduling problem (ELBSP) with extended basic period (EBP) and power-of-two (PoT) policies. In this problem, the supplier using a single facility to manufacture multiple products and equally sized batches are then delivered by the supplier to buyers over an infinite planning horizon. Further, the extended basic period (EBP) and power-of-two (PoT) policy are utilized. Relaxing the production schedule converts the ELBSP to an economic lot-size batch-shipment problem (ELBP) with EBP and PoT policies, and a nonlinear integer programming model of the ELBP is constructed. Using the replenishment cycle division and recursive tightening methods, optimal solutions are then solved separately for each product. The sum of these optimal solutions is the lower bound of the ELBSP. A proposed heuristic method with polynomial complexity is then applied to figure out the near-optimal solutions of the ELBSP. Numerical example is presented to confirm the efficacy of the proposed method.

Keywords: economic lot-size scheduling problem, extended basic period, replenishment cycle division, recursive tightening, power-of-two

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Authors: Mohammad Idrees Yusofzai, Hirobata Yasuhiro, Matsuo Kojiro

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Kabul is the capital of Afghanistan. It is the focal point of educational, industrial, etc. of Afghanistan. Additionally, the population of Kabul has grown recently and will increase because of return of refugees and shifting of people from other province to Kabul city. However, this increase in population, the issues of urban congestion and other related problems of urban transportation in Kabul city arises. One of the problems is public transport (large buses) service and needs to be modified and enhanced especially large bus routes that are operating in each zone of the 22 zone of Kabul City. To achieve the above mentioned goal of improving public transport, Spatial Accessibility Analysis is one of the important attributes to assess the effectiveness of transportation system and urban transport policy of a city, because accessibility indicator as an alternative tool to support public policy that aims the reinforcement of sustainable urban space. The case study of this research compares the present model (present bus route) and the modified model of public transport. Furthermore, present model, the bus routes in most of the zones are active, however, with having low frequency and unpublished schedule, and accessibility result is analyzed in four cases, based on the variables of accessibility. Whereas in modified model all zones in Kabul is taken into consideration with having specified origin and high frequency. Indeed the number of frequencies is kept high; however, this number is based on the number of buses Millie Bus Enterprise Authority (MBEA) owns. The same approach of cases is applied in modified model to figure out the best accessibility for the modified model. Indeed, the modified model is having a positive impact in congestion level in Kabul city. Besides, analyses of person trip and trip distribution have been also analyzed because how people move in the study area by each mode of transportation. So, the general aims of this research are to assess the present movement of people, identify zones in need of public transport and assess equity level of accessibility in Kabul city. The framework of methodology used in this research is based on gravity analysis model of accessibility; besides, generalized cost (time) of travel and travel mode is calculated. The main data come from person trip survey, socio-economic characteristics, demographic data by Japan International Cooperation Agency, 2008, study of Kabul city and also from the previous researches on travel pattern and the remaining data regarding present bus line and routes have been from MBEA. In conclusion, this research explores zones where public transport accessibility level is high and where it is low. It was found that both models the downtown area or central zones of Kabul city is having high level accessibility. Besides, the present model is the most unfavorable compared with the modified model based on the accessibility analysis.

Keywords: accessibility, bus generalized cost, gravity model, public transportation network

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Authors: Sunday Nanosi Ndovi, Patrick Albert Chikumba

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In Malawi, smallholder dairy farmers transport unprocessed milk to sell at Milk Bulking Groups (MBGs). MBGs store and chill the milk while awaiting collection by processors. The farmers deliver milk using various modes of transportation such as foot, bicycle, and motorcycle. As a perishable food, milk requires timely transportation to avoid deterioration. In other instances, some farmers bypass the nearest MBGs for facilities located further away. Untimely delivery worsens quality and results in rejection at MBG. Subsequently, these rejections lead to revenue losses for dairy farmers. Therefore, the objective of this study was to optimize routes when transporting milk by selecting the shortest route using time as a cost attribute in Geographic Information Systems (GIS). A spatially organized transport system impedes milk deterioration while promoting profitability for dairy farmers. A transportation system was modeled using Route Analysis and Closest Facility network extensions. The final output was to find the quickest routes and identify the nearest milk facilities from incidents. Face-to-face interviews targeted leaders from all 48 MBGs in the study area and 50 farmers from Namahoya MBG. During field interviews, coordinates were captured in order to create maps. Subsequently, maps supported the selection of optimal routes based on the least travel times. The questionnaire targeted 200 respondents. Out of the total, 182 respondents were available. Findings showed that out of the 50 sampled farmers that supplied milk to Namahoya, only 8% were nearest to the facility, while 92% were closest to 9 different MBGs. Delivering milk to the nearest MBGs would minimize travel time and distance by 14.67 hours and 73.37 km, respectively.

Keywords: closest facility, milk, route analysis, spatial transport

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Authors: Ashwani Kumar

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Use of NIR light for imaging the biological tissue and to quantify its optical properties is a good choice over other invasive methods. Optical tomography involves two steps. One is the forward problem and the other is the reconstruction problem. The forward problem consists of finding the measurements of transmitted light through the tissue from source to detector, given the spatial distribution of absorption and scattering properties. The second step is the reconstruction problem. In X-ray tomography, there is standard method for reconstruction called filtered back projection method or the algebraic reconstruction methods. But this method cannot be applied as such, in optical tomography due to highly scattering nature of biological tissue. A hybrid algorithm for reconstruction has been implemented in this work which takes into account the highly scattered path taken by photons while back projecting the forward data obtained during Monte Carlo simulation. The reconstructed image suffers from blurring due to point spread function.

Keywords: NIR light, tissue, blurring, Monte Carlo simulation

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Authors: Srushti Bhatt, M. B. Kiran

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Two-sided assembly line balancing problem is yet to be addressed simply to compete for the global market for manufacturers. The task assigned in an ordered sequence to get optimum performance of the system is known as assembly line balancing problem mainly classified as single and two sided. It is very challenging in manufacturing industries to balance two-sided assembly line, wherein the set of sequential workstations the task operations are performed in two sides of the line. The conflicting major objective in two-sided assembly line balancing problem is either to maximize /minimize the performance parameters. The present study emphases on combining different evolutionary algorithm; ant colony, Tabu search and petri net method; and compares their results of an algorithm for solving two-sided assembly line balancing problem. The concept of multi objective optimization of performance parameters is now a day adopted to make a decision involving more than one objective function to be simultaneously optimized. The optimum result can be expected among the selected methods using multi-objective optimization. The performance parameters considered in the present study are a number of workstation, slickness and smoothness index. The simulation of the assembly line balancing problem provides optimal results of classical and practical problems.

Keywords: Ant colony, petri net, tabu search, two sided ALBP

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Authors: Gopi Ram, Durbadal Mandal, Rajib Kar, Sakti Prasad Ghoshal

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A design problem of non-uniform circular antenna arrays for maximum reduction of both the side lobe level (SLL) and first null beam width (FNBW) is dealt with. This problem is modeled as a simple optimization problem. The method of Firefly algorithm (FFA) is used to determine an optimal set of current excitation weights and antenna inter-element separations that provide radiation pattern with maximum SLL reduction and much improvement on FNBW as well. Circular array antenna laid on x-y plane is assumed. FFA is applied on circular arrays of 8-, 10-, and 12- elements. Various simulation results are presented and hence performances of side lobe and FNBW are analyzed. Experimental results show considerable reductions of both the SLL and FNBW with respect to those of the uniform case and some standard algorithms GA, PSO, and SA applied to the same problem.

Keywords: circular arrays, first null beam width, side lobe level, FFA

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Authors: Halil Ibrahim Demir, Caner Erden, Abdullah Hulusi Kokcam, Mumtaz Ipek

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Process planning, scheduling, and due date assignment are three important manufacturing functions which are studied independently in literature. There are hundreds of works on IPPS and SWDDA problems but a few works on IPPSDDA problem. Integrating these three functions is very crucial due to the high relationship between them. Since the scheduling problem is in the NP-Hard problem class without any integration, an integrated problem is even harder to solve. This study focuses on the integration of these functions. Sum of weighted tardiness, earliness, and due date related costs are used as a penalty function. Random search and hybrid metaheuristics are used to solve the integrated problem. Marginal improvement in random search is very high in the early iterations and reduces enormously in later iterations. At that point directed search contribute to marginal improvement more than random search. In this study, random and genetic search methods are combined to find better solutions. Results show that overall performance becomes better as the integration level increases.

Keywords: process planning, genetic algorithm, hybrid search, random search, weighted due-date assignment, weighted scheduling

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Authors: Maatoug Hassine, Mourad Hrizi

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In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: geometric inverse source problem, heat equation, topological optimization, topological sensitivity, Kohn-Vogelius formulation

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Authors: Muhammad Umair, Syed Qasim Gilani

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A technique using Independent Component Analysis (ICA) for blind receiver signal processing is investigated. The problem of the receiver signal processing is viewed as of signal equalization and implementation imperfections compensation. Based on this, a model similar to a general ICA problem is developed for the received signal. Then, the use of ICA technique for blind signal equalization in the time domain is presented. The equalization is regarded as a signal separation problem, since the desired signal is separated from interference terms. This problem is addressed in the paper by over-sampling of the received signal. By using ICA for equalization, besides channel equalization, other transmission imperfections such as Direct current (DC) bias offset, carrier phase and In phase Quadrature phase imbalance will also be corrected. Simulation results for a system using 16-Quadraure Amplitude Modulation(QAM) are presented to show the performance of the proposed scheme.

Keywords: blind equalization, blind signal separation, equalization, independent component analysis, transmission impairments, QAM receiver

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: engineering education, errors, limits, mathematics competences, problem solving

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

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Concurrent planning of project scheduling and material ordering has been increasingly addressed within last decades as an approach to improve the project execution costs. Therefore, we have taken the problem into consideration in this paper, aiming to maximize schedules quality robustness, in addition to minimize the relevant costs. In this regard, a bi-objective mathematical model is developed to formulate the problem. Moreover, it is possible to utilize the all-unit discount for materials purchasing. The problem is then solved by the constraint method, and the Pareto front is obtained for a variety of robustness values. The applicability and efficiency of the proposed model is tested by different numerical instances, finally.

Keywords: e-constraint method, material ordering, project management, project scheduling

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Authors: M. Bouinoun, M. Bouhadef

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The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime).

Keywords: free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime

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Authors: Vesna Kirandziska, Nevena Ackovska, Ana Madevska Bogdanova

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The problem of emotion recognition is a challenging problem. It is still an open problem from the aspect of both intelligent systems and psychology. In this paper, both voice features and facial features are used for building an emotion recognition system. A Support Vector Machine classifiers are built by using raw data from video recordings. In this paper, the results obtained for the emotion recognition are given, and a discussion about the validity and the expressiveness of different emotions is presented. A comparison between the classifiers build from facial data only, voice data only and from the combination of both data is made here. The need for a better combination of the information from facial expression and voice data is argued.

Keywords: emotion recognition, facial recognition, signal processing, machine learning

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Authors: H. Mashhady, H. A. Manzoori, M. Doosti, M. Fatollahi

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This study reports a descriptive research in the form of a genre analysis of postgraduates' theses and dissertations at three Iranian universities, including Ferdowsi, Tehran, and Tarbiat Moddares universities. The researchers sought to depict the generic structure of “statement of the problem” section of PhD dissertations and MA theses. Moreover, researchers desired to find any probable variety based on the year the dissertations belonged, to see weather genre-consciousness developed among Iranian postgraduates. To obtain data, “statement of the problem” section of 90 Ph.D. dissertations and MA theses from 2001 to 2013 in Teaching English as a Foreign Language (TEFL) at above-mentioned universities was selected. Frequency counts was employed for the quantitative method of data analysis, while genre analysis was used as the qualitative method. Inter-rater reliability was found to be about 0.93. Results revealed that students in different degrees at each of these universities used various generic structures for writing “statement of the problem”. Moreover, comparison of different time periods (2001-2006, and 2007-2013) revealed that postgraduates in the second time period, regardless of their degree and university, employed more similar generic structures which can be optimistically attributed to a general raise in genre awareness.

Keywords: genre, genre analysis, Ph.D. and MA dissertations, statement of the problem, generic structure

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Authors: Eylem Koç, Hasan Arda Burhan

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Location selection presents a crucial decision problem in today’s business world where strategic decision making processes have critical importance. Thus, location selection has strategic importance for companies in boosting their strength regarding competition, increasing corporate performances and efficiency in addition to lowering production and transportation costs. A right choice in location selection has a direct impact on companies’ commercial success. In this study, a store location selection problem of Carglass Turkey which operates in vehicle glass branch is handled. As this problem includes both tangible and intangible criteria, Analytic Network Process (ANP) was accepted as the main methodology. The model consists of control hierarchy and BOCR subnetworks which include clusters of actors, alternatives and criteria. In accordance with the management’s choices, five different locations were selected. In addition to the literature review, a strict cooperation with the actor group was ensured and maintained while determining the criteria and during whole process. Obtained results were presented to the management as a report and its feasibility was confirmed accordingly.

Keywords: analytic network process (ANP), BOCR, multi-actor decision making, multi-criteria decision making, real-life problem, location selection

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Authors: Mintu Philip, Renumol V. G.

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An introductory programming course is a major challenge faced in Computing Education. Many of the introductory programming courses fail because student concentrate mainly on writing programs using a programming language rather than involving in problem solving. Computational thinking is a general approach to solve problems. This paper proposes a new preliminary course that aims to develop computational thinking skills in students, which may help them to become good programmers. The proposed course is designed based on the four basic components of computational thinking - abstract thinking, logical thinking, modeling thinking and constructive thinking. In this course, students are engaged in hands-on problem solving activities using a new problem solving model proposed in this paper.

Keywords: computational thinking, computing education, abstraction, constructive thinking, modelling thinking

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Authors: Adelaide Rethabile Motshabi Pitso-Mbili

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Higher education institutions (HEIs) are under pressure in producing PhD graduates so that they can position themselves higher in terms of rankings. However, hospitality and tourism higher degree enrolment numbers are very low within South African universities. Furthermore, hospitality and tourism students choose these fields of study because they want to travel, be social, and have fun. Students in higher education are anxious about their future after studies as they are particularly worried about the job conditions in the hospitality and tourism sector, the remuneration, and the status perceptions of many jobs in the sector. Hence, there is a need for a continuous increase in the level of education with the formation of professional aptitudes and personnel quality. In order to understand the reasons for low enrolments, this study aims to explore the perceptions of the final year in tourism and hospitality diploma students towards enrolling for higher degree qualifications after their graduation. This paper utilised a quantitative research method, and data was gathered through questionnaires. In addition, the Linkert scale design was used for questionnaires. The questionnaires were distributed to 137 hospitality and tourism students who are on their exit level at Walter Sisulu University. SPSS was used to analyse data. The findings revealed that students do not wish to continue studying for higher degrees as they believe higher degrees are not important for the industry. Furthermore, families already have financial expectations as they think one qualification is enough. In addition, some students mentioned that they would love to study further, but lack of funding is a problem since NSFAS only funds the first qualification. Thus, it is recommended that students are made aware of the benefits and opportunities available after obtaining higher degrees.

Keywords: hospitality and tourism education, higher degrees, higher education, student’s perceptions, hospitality and tourism sector

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Aquil Ahmed, Srikant Gupta, Irfan Ali

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In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem, multi objective linear programming, multi-objective fractional programming, fuzzy goal programming, fuzzy sets, trapezoidal fuzzy number

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