Search results for: partitioning problem

Authors: Mohsen Ziaee

Abstract:

Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Cagri Memis, Muzaffer Kapanoglu

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The school bus routing problem (SBRP) is a variant of the Vehicle Routing Problem (VRP) classified as a location-allocation-routing problem. In this study, the SBRP is decomposed into two sub-problems: (1) bus route generation and (2) bus stop selection to solve large instances of the SBRP in reasonable computational times. To solve the first sub-problem, we propose a genetic algorithm to generate bus routes. Once the routes have been fixed, a sub-problem remains of allocating students to stops considering the capacity of the buses and the walkability constraints of the students. While the exact method solves small-scale problems, treating large-scale problems with the exact method becomes complex due to computational problems, a deficiency that the genetic algorithm can overcome. Results obtained from the proposed approach on 150 instances up to 250 stops show that the matheuristic algorithm provides better solutions in reasonable computational times with respect to benchmark algorithms.

Keywords: genetic algorithm, matheuristic, school bus routing problem, vehicle routing problem

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: binary cat swarm optimization, binarization methods, metaheuristic, set covering problem

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Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: S. Nasri, H. Bouziri

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Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: dynamic network flow, load dependent transit time, evacuation strategy, earliest arrival flow problem, tabu search metaheuristic

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

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Authors: Chaghoub Soraya, Zhang Xiaoyan

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This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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Authors: Abubakar Sa’adatu Mohammed

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This paper reports on a study of problem solving differences between expert and novice Problem solvers for effective physics teaching. Significant differences were found both at the conceptual level and at the level of critical thinking, creative thinking and reasoning. It is suggested for a successful solution of a problem, conceptual knowledge alone may not be sufficient. There is the need of the knowledge of how the conceptual knowledge should be applied (problem solving skills). It is hoped that this research might contribute to efforts of exploring ways for students to acquire a powerful conceptual toolkit based on experts like problem solvers approach for effective teaching delivery.

Keywords: conceptual knowledge, procedural knowledge, critical thinking, creative thinking, reasoning ability

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Authors: Mahnaz Hosseinzadeh, Mohammad Reza Mehregan

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In this paper, we have developed a morphological field to assist multi- methodology (combining methodologies together in whole or part) in Operations Research (OR) for the problem contexts in Iranian organizations. So, we have attempted to identify some dimensions for problem context according to Iranian organizational problems. Then, a general morphological program is designed which helps the OR practitioner to determine the suitable OR methodology as output for any configuration of conditions in a problem context as input and to reveal the fields necessary to be improved in OR. Applying such a program would have interesting results for OR practitioners.

Keywords: hard, soft and emancipatory operations research, General Morphological Analysis (GMA), multi-methodology, problem context

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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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-Ito 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-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Sarwat Sultan, Shahzad Gul

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This study was carried out to see the mediating role of problem solving styles (sensing, intuitive, feeling, and thinking) in the predictive relationship of gratitude with subjective well-being. A sample of 454 college students aged 20-26 years old participated in this study and provided data on the measures of gratitude, problem solving styles, and subjective well-being. Results indicated the significant relationships of gratitude with subjective well-being and problem solving styles of intuitive and thinking. Results further indicated the positive link of intuitive and thinking styles with subjective well-being. Findings also provided the evidence for the significant mediating role of problem solving styles in the relationship of gratitude with subjective well-being. The implication for this study is likely to enhance the medium to long term effects of gratitude on subjective well-being among students and as well as assessing its value in promoting psychological health and problem solving strategies among students.

Keywords: gratitude, subjective well-being, problem solving styles, college students

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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

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

Keywords: bus scheduling problem, decision support system, genetic algorithm, shortest path

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Authors: Fernanda M. Assef, Maria Teresinha A. Steiner, David Gabriel F. Barros

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Review researches are useful in terms of analysis of research problems. Between the types of review documents, we commonly find bibliometric studies. This type of application often helps the global visualization of a research problem and helps academics worldwide to understand the context of a research area better. In this document, a bibliometric view surrounding clustering techniques and sustainability problems is presented. The authors aimed at which issues mostly use clustering techniques, and, even which sustainability issue would be more impactful on today’s moment of research. During the bibliometric analysis, we found ten different groups of research in clustering applications for sustainability issues: Energy; Environmental; Non-urban planning; Sustainable Development; Sustainable Supply Chain; Transport; Urban Planning; Water; Waste Disposal; and, Others. And, by analyzing the citations of each group, we discovered that the Environmental group could be classified as the most impactful research cluster in the area mentioned. Now, after the content analysis of each paper classified in the environmental group, we found that the k-means technique is preferred for solving sustainability problems with clustering methods since it appeared the most amongst the documents. The authors finally conclude that a bibliometric assessment could help indicate a gap of researches on waste disposal – which was the group with the least amount of publications – and the most impactful research on environmental problems.

Keywords: bibliometric assessment, clustering, sustainability, territorial partitioning

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Authors: Hollie Ashworth, Sarah Heath, Nick Bryan, Liam Abrahamsen, Simon Kellet

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Sellafield has a number of fuel storage ponds, some of which have been open to the air for a number of decades. This has caused corrosion of the fuel resulting in a release of some activity into solution, reduced water clarity, and accumulation of sludge at the bottom of the pond consisting of brucite (Mg(OH)2) and other uranium corrosion products. Both of these phases are also present as colloidal material. 90Sr and 137Cs are known to constitute a small volume of the radionuclides present in the pond, but a large fraction of the activity, thus they are most at risk of challenging effluent discharge limits. Organic molecules are known to be present also, due to the ponds being open to the air, with occasional algal blooms restricting visibility further. The contents of the pond need to be retrieved and safely stored, but dealing with such a complex, undefined inventory poses a unique challenge. This work aims to determine and understand the sorption-desorption interactions of 90Sr and 137Cs to brucite and uranium phases, with and without the presence of organic molecules from chemical degradation and bio-organisms. The influence of organics on these interactions has not been widely studied. Partitioning of these radionuclides and organic molecules has been determined through LSC, ICP-AES/MS, and UV-vis spectrophotometry coupled with ultrafiltration in both binary and ternary systems. Further detailed analysis into the surface and bonding environment of these components is being investigated through XAS techniques and PHREEQC modelling. Experiments were conducted in CO2-free or N2 atmosphere across a high pH range in order to best simulate conditions in the pond. Humic acid used in brucite systems demonstrated strong competition against 90Sr for the brucite surface regardless of the order of addition of components. Variance of pH did have a small effect, however this range (10.5-11.5) is close to the pHpzc of brucite, causing the surface to buffer the solution pH towards that value over the course of the experiment. Sorption of 90Sr to UO2 obeyed Ho’s rate equation and demonstrated a slow second-order reaction with respect to the sharing of valence electrons from the strontium atom, with the initial rate clearly dependent on pH, with the equilibrium concentration calculated at close to 100% sorption. There was no influence of humic acid seen when introduced to these systems. Sorption of 137Cs to UO3 was significant, with more than 95% sorbed in just over 24 hours. Again, humic acid showed no influence when introduced into this system. Both brucite and uranium based systems will be studied with the incorporation of cyanobacterial cultures harvested at different stages of growth. Investigation of these systems provides insight into, and understanding of, the effect of organics on radionuclide partitioning to brucite and uranium phases at high pH. The majority of sorption-desorption work for radionuclides has been conducted at neutral to acidic pH values, and mostly without organics. These studies are particularly important for the characterisation of legacy wastes at Sellafield, with a view to their safe retrieval and storage.

Keywords: caesium, legacy wastes, organics, sorption-desorption, strontium, uranium

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Authors: M. Erol Genevois, D. Celik, H. Z. Ulukan

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Automated teller machines (ATMs) can be considered among one of the most important service facilities in the banking industry. The investment in ATMs and the impact on the banking industry is growing steadily in every part of the world. The banks take into consideration many factors like safety, convenience, visibility, cost in order to determine the optimum locations of ATMs. Today, ATMs are not only available in bank branches but also at retail locations. Another important factor is the cash management in ATMs. A cash demand model for every ATM is needed in order to have an efficient cash management system. This forecasting model is based on historical cash demand data which is highly related to the ATMs location. So, the location and the cash management problem should be considered together. Although the literature survey on facility location models is quite large, it is surprising that there are only few studies which handle together ATMs location and cash management problem. In order to fulfill the gap, this paper provides a general review on studies, efforts and development in ATMs location and cash management problem.

Keywords: ATM location problem, cash management problem, ATM cash replenishment problem, literature review in ATMs

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Authors: Md. Zahidul Islam

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Illegal immigrants’ problem is a big problem all over the world including America. Malaysia is also facing this problem. Nowadays, it is turned into a major problem for Malaysia. Many illegal immigrants are staying in Malaysia from different countries such as Bangladesh, Myanmar, India, Pakistan, Indonesia, Vietnam, Thailand, Philippine, Nigeria. This article is only focusing on the present situation of illegal immigrants of Bangladesh. The aim of this article is to highlight how the Bangladeshi nationals are becoming an illegal immigrant in Malaysia. In the same time, this article also tries to identify the present situation of Bangladeshi illegal immigrants in Malaysia. The research will adopt qualitative methods of research. Both countries have to find a solution to solve this problem.

Keywords: illegal immigrants, present situation, Bangladesh, Malaysia

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Authors: E. Eroglu, S. Semsit, E. Sener, U.S. Sener

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In Electromagnetics, there are three canonical boundary value problem with given initial conditions for the electromagnetic field sought, namely: Cavity Problem, Waveguide Problem, and External Problem. The Cavity Problem and Waveguide Problem were rigorously studied and new results were arised at original works in the past decades. In based on studies of an analytical time domain method Evolutionary Approach to Electromagnetics (EAE), electromagnetic field strength vectors produced by a time dependent source function are sought. The fields are took place in L2 Hilbert space. The source function that performs signal transferring, energy and surplus of energy has been demonstrated with all clarity. Depth of the method and ease of applications are emerged needs of gathering obtained results. Main discussion is about perfect electric conductor and hollow waveguide. Even if well studied time-domain modes problems are mentioned, specifically, the modes which have a hollow (i.e., medium-free) cross-section domain are considered.

Keywords: evolutionary approach to electromagnetics, time-domain waveguide mode, Neumann problem, Dirichlet boundary value problem, Klein-Gordon

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Hessam Mortezaei, Saeid Joudakian

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In this paper, the wear problem on rider rings of boil off gas compressor has been studied. This kind of oil free double acting compressor has free floating piston (FFP) technology and as a result of that it should have the lowest possible wear on its rider rings. But a design problem had caused a complete wear of rider rings after one month of continuous operation. In this case study, the source of this problem was recognized and solved.

Keywords: piston rider, rings, gas distribution, pressure wear

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: Filipe Cardoso de Oliveira, Lino Marcos da Silva, Ademar Nogueira do Nascimento, Cristiano Hora de Oliveira Fontes

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This article presents a mathematical formulation for the production Break-Even Point problem in a non-homogeneous system. The optimization problem aims to obtain the composition of the best product mix in a non-homogeneous industrial plant, with the lowest cost until the breakeven point is reached. The problem constraints represent real limitations of a generic non-homogeneous industrial plant for n different products. The proposed model is able to solve the equilibrium point problem simultaneously for all products, unlike the existing approaches that propose a resolution in a sequential way, considering each product in isolation and providing a sub-optimal solution to the problem. The results indicate that the product mix found through the proposed model has economical advantages over the traditional approach used.

Keywords: branch and bound, break-even point, non-homogeneous production system, integer linear programming, management accounting

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Authors: Khalil H. Al-Bayati, G. Nasma, Hussein Ban H. Adel

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The purpose of the present work is to calculate the expectation value of potential energy for different spin states (ααα ≡ βββ, αβα ≡ βαβ) and compare it with spin states (αββ, ααβ ) for lithium excited state (1s2s3s) and Li-like ions (Be+, B+2) using Hartree-Fock wave function by partitioning technique. The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ααα < ααβ < αββ < αβα.

Keywords: lithium excited state, potential energy, 1s2s3s, mathematical physics

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Authors: Tarek Aboueldahab, Hanan Farag

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

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

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Authors: Kayode A. Olaniyi, Tola. M. Osifeko, Adeola A. Ogunleye

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Text line segmentation is an important step in document image processing. It represents a labeling process that assigns the same label using distance metric probability to spatially aligned units. Text line detection techniques have successfully been implemented mainly in printed documents. However, processing of the handwritten texts especially unconstrained documents has remained a key problem. This is because the unconstrained hand-written text lines are often not uniformly skewed. The spaces between text lines may not be obvious, complicated by the nature of handwriting and, overlapping ascenders and/or descenders of some characters. Hence, text lines detection and segmentation represents a leading challenge in handwritten document image processing. Text line detection methods that rely on the traditional global projection profile of the text document cannot efficiently confront with the problem of variable skew angles between different text lines. Hence, the formulation of a horizontal line as a separator is often not efficient. This paper presents a technique to segment a handwritten document into distinct lines of text. The proposed algorithm starts, by partitioning the initial text image into columns, across its width into chunks of about 5% each. At each vertical strip of 5%, the histogram of horizontal runs is projected. We have worked with the assumption that text appearing in a single strip is almost parallel to each other. The algorithm developed provides a sliding window through the first vertical strip on the left side of the page. It runs through to identify the new minimum corresponding to a valley in the projection profile. Each valley would represent the starting point of the orientation line and the ending point is the minimum point on the projection profile of the next vertical strip. The derived text-lines traverse around any obstructing handwritten vertical strips of connected component by associating it to either the line above or below. A decision of associating such connected component is made by the probability obtained from a distance metric decision. The technique outperforms the global projection profile for text line segmentation and it is robust to handle skewed documents and those with lines running into each other.

Keywords: connected-component, projection-profile, segmentation, text-line

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Authors: Temitayo Ogunsanwo

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Problem-solving is an important way of learning way of learning because it propels children to use previous experiences to deal with new situations. The purpose of this study is to find out the attitude of pre-service teachers to problem-solving as a strategy for promoting early mathematics learning in children. This qualitative study employed a descriptive design to investigate the experiences of twenty second-year undergraduate early childhood education Pre-service teachers in a teaching practice and their attitude towards five-year-old children’s problem-solving strategies in mathematics. Pre-service teachers were exposed to different strategies for teaching children how to solve problems in mathematics. They were taken through a micro teaching in class using different strategies to teach problem-solving in different topics in the five-year-old mathematics curriculum. The students were then made to teach five-year-olds in neighbouring schools for three weeks, working in pairs, observing and recording children’s problem-solving activities and strategies. After the three weeks exercise, their experiences and attitude towards children’s problem-solving strategies were collected using open-ended questions and analysed in themes. Findings were discussed.

Keywords: attitude, early mathematics learning, experience, pre-service teachers, problem-solving, strategies

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Authors: Rachid Ziteuni, Selt Omar

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In this paper, we propose a new polynomial metaheuristic elaboration (tabu search) for solving scheduling problems. This method allows us to solve the scheduling problem of n tasks on m identical parallel machines with unavailability periods. This problem is NP-complete in the strong sens and finding an optimal solution appears unlikely. Note that all data in this problem are integer and deterministic. The performance criterion to optimize in this problem which we denote Pm/N-c/summs of (wjCj) is the weighted sum of the end dates of tasks.

Keywords: scheduling, parallel identical machines, unavailability periods, metaheuristic, tabu search

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Authors: Hans Tjio, Wee Meng Seng

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The interaction of contract and property has always been a concern in corporate and commercial law, where there are internal structures created that may not match the externally perceived image generated by the labels attached to those structures. We will focus, in particular, on the priority structures created by affirmative asset partitioning, which have increasingly come under challenge by those attempting to negotiate around them. The most prominent has been the AT1 bonds issued by Credit Suisse which were wiped out before its equity when the troubled bank was acquired by UBS. However, this should not have come as a surprise to those whose “bonds” had similarly been “redeemed” upon the occurrence of certain reference events in countries like Singapore, Hong Kong and Taiwan during their Minibond crisis linked to US sub-prime defaults. These were derivatives classified as debentures and sold as such. At the same time, we are again witnessing “liabilities” seemingly ranking higher up the balance sheet ladder, finding themselves lowered in events of default. We will examine the mechanisms holders of perpetual securities or preference shares have tried to use to protect themselves. This is happening against a backdrop that sees a rise in the strength of private credit and inter-creditor conflicts. The restructuring regime of the hybrid scheme in Singapore now, while adopting the absolute priority rule in Chapter 11 as the quid pro quo for creditor cramdown, does not apply to shareholders and so exempts them from cramdown. Complicating the picture further, shareholders are not exempted from cramdown in the Dutch scheme, but it adopts a relative priority rule. At the same time, the important UK Supreme Court decision in BTI 2014 LLC v Sequana [2022] UKSC 25 has held that directors’ duties to take account of creditor interests are activated only when a company is almost insolvent. All this has been complicated by digital assets created by businesses. Investors are quite happy to have them classified as property (like a thing) when it comes to their transferability, but then when the issuer defaults to have them seen as a claim on the business (as a choice in action), that puts them at the level of a creditor. But these hidden interests will not show themselves on an issuer’s balance sheet until it is too late to be considered and yet if accepted, may also prevent any meaningful restructuring.

Keywords: asset partitioning, creditor priority, restructuring, BTI v Sequana, digital assets

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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