Search results for: mathematical programming problem

Authors: Rouhallah Bagheri, Morteza Mahmoudi, Hadi Moheb-Alizadeh

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In this paper, we develop a supplier selection and order allocation multi-objective model in stochastic environment in which purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. To do so, we use dependent chance programming (DCP) that maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. After transforming the above mentioned stochastic multi-objective programming problem into a stochastic single objective problem using minimum deviation method, we apply a genetic algorithm to get the later single objective problem solved. The employed genetic algorithm performs a simulation process in order to calculate the stochastic objective function as its fitness function. At the end, we explore the impact of stochastic parameters on the given solution via a sensitivity analysis exploiting coefficient of variation. The results show that as stochastic parameters have greater coefficients of variation, the value of objective function in the stochastic single objective programming problem is worsened.

Keywords: dependent chance programming, genetic algorithm, minimum deviation method, order allocation, supplier selection

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Authors: Tlou J. Ramabu

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Programming is one of the challenging subjects in the field of computing. In the higher education sphere, some programming novices’ performance, retention rate, and success rate are not improving. Most of the time, the problem is caused by the slow pace of learning, difficulty in grasping the syntax of the programming language and poor logical skills. More importantly, programming forms part of major subjects within the field of computing. As a result, specialized pedagogical methods and innovation are highly recommended. Little research has been done on the potential productivity of the WhatsApp platform as part of a blended learning model. In this article, the authors discuss the WhatsApp group as a part of blended learning model incorporated for a group of programming novices. We discuss possible administrative activities for productive utilisation of the WhatsApp group on the blended learning overview. The aim is to take advantage of the popularity of WhatsApp and the time students spend on it for their educational purpose. We believe that blended learning featuring a WhatsApp group may ease novices’ cognitive load and strengthen their foundational programming knowledge and skills. This is a work in progress as the proposed blended learning model with WhatsApp incorporated is yet to be implemented.

Keywords: blended learning, higher education, WhatsApp, programming, novices, lecturers

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Authors: Nur Aidya Hanum Aizam, Vikneswary Uvaraja

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The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming model to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describe about creating a general model which solve different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling

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Authors: Mustafa Ekici, Sacide Güzin Mazman

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Programming is the one of ability in computer science fields which is generally perceived difficult by students and various individual differences have been implicated in that ability success. Although several factors that affect programming ability have been identified over the years, there is not still a full understanding of why some students learn to program easily and quickly while others find it complex and difficult. Programming self-efficacy and mathematic success are two of those essential individual differences which are handled as having important effect on the programming success. This study aimed to identify the relationship between programming performance, programming self efficacy and mathematics success. The study group is consisted of 96 undergraduates from Department of Econometrics of Uşak University. 38 (39,58%) of the participants are female while 58 (60,41%) of them are male. Study was conducted in the programming-I course during 2014-2015 fall term. Data collection tools are comprised of programming course final grades, programming self efficacy scale and a mathematics achievement test. Data was analyzed through correlation analysis. The result of study will be reported in the full text of the study.

Keywords: programming performance, self efficacy, mathematic success, computer science

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: Nurul Liyana Abdul Aziz, Nur Aidya Hanum Aizam

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Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.

Keywords: university course timetabling problem, integer programming, preferences, constraints

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Z. Babic, I. Veza, A. Balic, M. Crnjac

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The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Keywords: business process, De Novo programming, optimizing, production

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

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The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering or collecting products to or from customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from a depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity for the goods that are delivered or collected. In the present work, we present a specific capacitated stochastic vehicle routing problem which has many realistic applications. We develop and analyze a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot and visits N customers according to a particular sequence in order to collect from them two similar but not identical products. We name these products, product 1 and product 2. Each customer possesses items either of product 1 or product 2 with known probabilities. The number of the items of product 1 or product 2 that each customer possesses is a discrete random variable with known distribution. The actual quantity and the actual type of product that each customer possesses are revealed only when the vehicle arrives at the customer’s site. It is assumed that the vehicle has two compartments. We name these compartments, compartment 1 and compartment 2. It is assumed that compartment 1 is suitable for loading product 1 and compartment 2 is suitable for loading product 2. However, it is permitted to load items of product 1 into compartment 2 and items of product 2 into compartment 1. These actions cause costs that are due to extra labor. The vehicle is allowed during its route to return to the depot to unload the items of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. It is possible to develop a suitable dynamic programming algorithm for the determination of the optimal routing strategy. It is also possible to prove that the optimal routing strategy has a specific threshold-type strategy. Specifically, it is shown that for each customer the optimal actions are characterized by some critical integers. This structural result enables us to design a special-purpose dynamic programming algorithm that operates only over these strategies having this structural property. Extensive numerical results provide strong evidence that the special-purpose dynamic programming algorithm is considerably more efficient than the initial dynamic programming algorithm. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed if N is smaller or equal to eight.

Keywords: dynamic programming, similar products, stochastic demands, stochastic preferences, vehicle routing problem

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Authors: Walid Moudani

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The Crew Reserve Assignment Problem (CRAP) considers the assignment of the crew members to a set of reserve activities covering all the scheduled flights in order to ensure a continuous plan so that operations costs are minimized while its solution must meet hard constraints resulting from the safety regulations of Civil Aviation as well as from the airlines internal agreements. The problem considered in this study is of highest interest for airlines and may have important consequences on the service quality and on the economic return of the operations. In this communication, a new mathematical formulation for the CRAP is proposed which takes into account the regulations and the internal agreements. While current solutions make use of Artificial Intelligence techniques run on main frame computers, a low cost approach is proposed to provide on-line efficient solutions to face perturbed operating conditions. The proposed solution method uses a dynamic programming approach for the duties scheduling problem and when applied to the case of a medium airline while providing efficient solutions, shows good potential acceptability by the operations staff. This optimization scheme can then be considered as the core of an on-line Decision Support System for crew reserve assignment operations management.

Keywords: airlines operations management, combinatorial optimization, dynamic programming, crew scheduling

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: Farzad Jafarpour Taher, Maghsud Solimanpur

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Production planning is one of the complex tasks in multi-product firms that produce a wide range of products. Since resources in mass production companies are limited and different products use common resources, there must be a careful plan so that firms can respond to customer needs efficiently. Azar-battery Company is a firm that provides twenty types of products for its customers. Therefore, careful planning must be performed in this company. In this research, the current conditions of Azar-battery Company were investigated to provide a mathematical programming model to determine the optimum production rate of the products in this company. The production system of this company is multi-stage, multi-product and multi-period. This system is studied in terms of a one-year planning horizon regarding the capacity of machines and warehouse space limitation. The problem has been modeled as a linear programming model with deterministic demand in which shortage is not allowed. The objective function of this model is to minimize costs (including raw materials, assembly stage, energy costs, packaging, and holding). Finally, this model has been solved by Lingo software using the branch and bound approach. Since the computation time was very long, the solver interrupted, and the obtained feasible solution was used for comparison. The proposed model's solution costs have been compared to the company’s real data. This non-optimal solution reduces the total production costs of the company by about %35.

Keywords: multi-period, multi-product production, multi-stage, production planning

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Authors: Wasif Mughees, Malik Al-Ahmad

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This research presents the graphical design analysis and mathematical programming technique to dig out the possible water allocation distribution to minimize water usage in process units. The study involves the mass and property integration in its core methodology. Tehran Oil Refinery is studied to implement the focused water pinch technology for regeneration, reuse and recycling of water streams. Process data is manipulated in terms of sources and sinks, which are given in terms of properties. Sources are the streams to be allocated. Sinks are the units which can accept the sources. Suspended Solids (SS) is taken as a single contaminant. The model minimizes the mount of freshwater from 340 to 275m3/h (19.1%). Redesigning and allocation of water streams was built. The graphical technique and mathematical programming shows the consistency of results which confirms mass transfer dependency of water streams.

Keywords: minimization, water pinch, process integration, pollution prevention

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Authors: Shunichi Ohmori, Sirawadee Arunyanart, Kazuho Yoshimoto

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We consider a periodic review inventory control problem of minimizing production cost, inventory cost, and lost-sales under demand uncertainty, in which product demands are not specified exactly and it is only known to belong to a given uncertainty set, yet the constraints must hold for possible values of the data from the uncertainty set. We propose a robust optimization formulation for obtaining lowest cost possible and guaranteeing the feasibility with respect to range of order quantity and inventory level under demand uncertainty. Our formulation is based on the adaptive robust counterpart, which suppose order quantity is affine function of past demands. We derive certainty equivalent problem via second-order cone programming, which gives 'not too pessimistic' worst-case.

Keywords: robust optimization, inventory control, supply chain managment, second-order programming

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Authors: Amir Azaron

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In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain.

Keywords: supply chain management, stochastic programming, multiobjective programming, inventory control

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Authors: Chaimongkol Limpianchob

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This work addresses the problem of production planning that arises in the production of aromatic coconuts from Samudsakhorn province in Thailand. The planning involves the forwarding of aromatic coconuts from the harvest areas to the factory, which is classified into two groups; self-owned areas and contracted areas, the decisions of aromatic coconuts flow in the plant, and addressing a question of which warehouse will be in use. The problem is formulated as a mixed-integer linear programming model within supply chain management framework. The objective function seeks to minimize the total cost including the harvesting, labor and inventory costs. Constraints on the system include the production activities in the company and demand requirements. Numerical results are presented to demonstrate the feasibility of coconuts supply chain model compared with base case.

Keywords: aromatic coconut, supply chain management, production planning, mixed-integer linear programming

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Authors: Ebrahim Asadi-Gangraj

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Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems.

Keywords: hybrid flow shop, mixed integer linear programming, Benders decomposition, makespan

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Authors: Omar Dib, Alexandre Caminada, Marie-Ange Manier

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The purpose of this study is to introduce a novel approach to solve the one-to-one shortest path problem. A directed connected graph is assumed in which all edges’ weights are positive. Our method is based on a memetic algorithm in which we combine a genetic algorithm (GA) and a variable neighborhood search method (VNS). We compare our approximate method with two exact algorithms Dijkstra and Integer Programming (IP). We made experimentations using random generated, complete and real graph instances. In most case studies, numerical results show that our method outperforms exact methods with 5% average gap to the optimality. Our algorithm’s average speed is 20-times faster than Dijkstra and more than 1000-times compared to IP. The details of the experimental results are also discussed and presented in the paper.

Keywords: shortest path problem, Dijkstra’s algorithm, integer programming, memetic algorithm

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Authors: N. Alias, W. Z. W. Muhammad, M. N. M. Ibrahim, M. Mohamed, H. F. S. Saipol, U. N. Z. Ariffin, N. A. Zakaria, M. S. Z. Suardi

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This paper presents the performance comparison of some computation software for solving the boundary element method (BEM). BEM formulation is the numerical technique and high potential for solving the advance mathematical modeling to predict the production of oil well in arbitrarily shaped based on multiple leases reservoir. The limitation of data validation for ensuring that a program meets the accuracy of the mathematical modeling is considered as the research motivation of this paper. Thus, based on this limitation, there are three steps involved to validate the accuracy of the oil production simulation process. In the first step, identify the mathematical modeling based on partial differential equation (PDE) with Poisson-elliptic type to perform the BEM discretization. In the second step, implement the simulation of the 2D BEM discretization using COMSOL Multiphysic and MATLAB programming languages. In the last step, analyze the numerical performance indicators for both programming languages by using the validation of Fortran programming. The performance comparisons of numerical analysis are investigated in terms of percentage error, comparison graph and 2D visualization of pressure on oil production of multiple leases reservoir. According to the performance comparison, the structured programming in Fortran programming is the alternative software for implementing the accurate numerical simulation of BEM. As a conclusion, high-level language for numerical computation and numerical performance evaluation are satisfied to prove that Fortran is well suited for capturing the visualization of the production of oil well in arbitrarily shaped.

Keywords: performance comparison, 2D visualization, COMSOL multiphysic, MATLAB, Fortran, modelling and simulation, boundary element method, reservoir pressure

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Authors: Nusrat T. Chowdhury, M. F. Baki, A. Azab

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The production planning problem is concerned with specifying the optimal quantities to produce in order to meet the demand for a prespecified planning horizon with the least possible expenditure. Making the right decisions in production planning will affect directly the performance and productivity of a manufacturing firm, which is important for its ability to compete in the market. Therefore, developing and improving solution procedures for production planning problems is very significant. In this paper, we develop a Dantzig-Wolfe decomposition of a multi-item hierarchical production planning problem with capacity constraint and present a column generation approach to solve the problem. The original Mixed Integer Linear Programming model of the problem is decomposed item by item into a master problem and a number of subproblems. The capacity constraint is considered as the linking constraint between the master problem and the subproblems. The subproblems are solved using the dynamic programming approach. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any kind of infeasibility that arises while solving the problem. We compare the computational performance of the developed solution approach against the state-of-the-art heuristic procedure available in the literature. The results show that the proposed heuristic-based decomposition approach improves the solution quality by 20% as compared to the literature.

Keywords: inventory, multi-level capacitated lot-sizing, emission control, setup carryover

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Authors: Bing Li

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The primitive code-level design patterns (PDP) are the rudimentary programming elements to develop any distributed systems in the generic distributed programming environment, GreatFree. The PDP works with the primitive distributed application programming interfaces (PDA), the distributed modeling, and the distributed concurrency for scaling-up. They not only hide developers from underlying technical details but also support sufficient adaptability to a variety of distributed computing environments. Programming with them, the simplest distributed system, the lightweight messaging two-node client/server (TNCS) system, is constructed rapidly with straightforward and repeatable behaviors, copy-paste-replace (CPR). As any distributed systems are made up of the simplest ones, those PDAs, as well as the PDP, are generic for distributed programming.

Keywords: primitive APIs, primitive code-level design patterns, generic distributed programming, distributed systems, highly patterned development environment, messaging

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Authors: Eashan Hatti

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In software development, programmers often must make a choice between high-level programming and high-performance programs. High-level programming encourages the use of complex, pervasive abstractions. However, the use of these abstractions degrades performance-high performance demands that programs be low-level. In a compiler, the optimizer attempts to let the user have both. The optimizer takes high-level, abstract code as an input and produces low-level, performant code as an output. However, there is a problem with having the optimizer be a built-in part of the compiler. Domain-specific abstractions implemented as libraries are common in high-level languages. As a language’s library ecosystem grows, so does the number of abstractions that programmers will use. If these abstractions are to be performant, the optimizer must be extended with new optimizations to target them, or these abstractions must rely on existing general-purpose optimizations. The latter is often not as effective as needed. The former presents too significant of an effort for the compiler developers, as they are the only ones who can extend the language with new optimizations. Thus, the language becomes more high-level, yet the optimizer – and, in turn, program performance – falls behind. Programmers are again confronted with a choice between high-level programming and high-performance programs. To investigate a potential solution to this problem, we developed Peridot, a prototype programming language. Peridot’s main contribution is that it enables library developers to easily extend the language with new optimizations themselves. This allows the optimization workload to be taken off the compiler developers’ hands and given to a much larger set of people who can specialize in each problem domain. Because of this, optimizations can be much more effective while also being much more numerous. To enable this, Peridot supports metaprogramming designed for implementing program transformations. The language is split into two fragments or “levels”, one for metaprogramming, the other for high-level general-purpose programming. The metaprogramming level supports logic programming. Peridot’s key idea is that optimizations are simply implemented as metaprograms. The meta level supports several specific features which make it particularly suited to implementing optimizers. For instance, metaprograms can automatically deduce equalities between the programs they are optimizing via unification, deal with variable binding declaratively via higher-order abstract syntax, and avoid the phase-ordering problem via non-determinism. We have found that this design centered around logic programming makes optimizers concise and easy to write compared to their equivalents in functional or imperative languages. Overall, implementing Peridot has shown that its design is a viable solution to the problem of writing code which is both high-level and performant.

Keywords: optimization, metaprogramming, logic programming, abstraction

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Authors: Birce Boga Bakirli

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In this paper, we investigate ideas on human capital development and management in industries. We structured a model to be able to gather the data from the interviews conducted with worker, specialists and owners of companies. Different aspects of the situation are found in these interviews, and we used the information to model the benefit of the business owners and workers perspectives. These are modelled as a bi-level programming problem. Several instances of the generic cases are solved. The results show the importance of education within and out of the company for workers, and it returns for the company.

Keywords: bi-level programming, corporate strategy, cost tradeoffs, human capital, mixed integer programming, Stackelberg game, supplier relations, strategic planning

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Authors: Geoffrey A. Wright

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In an attempt to address shortcomings revealed in international assessments and lamented in legislation, many schools are reducing or eliminating elective courses, applying the rationale that replacing "non-essential" subjects with core subjects, such as mathematics and language arts, will better position students in the global market. However, there is evidence that systematically pairing a core subject with another complementary subject may lead to greater overall learning in both subjects. In this paper, we outline the methods and preliminary findings from a study we conducted analyzing the influence learning programming has on student mathematical comprehension and ability. The purpose of this research is to demonstrate in what ways two subjects might complement each other, and to better understand the principles and conditions that encourage what we call lateral transfer, the synergistic effect that occurs when a learner studies two complementary subjects.

Keywords: programming, engineering, technology, complementary subjects

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Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Nadia Selene Molina-Moreno, Maria Susana Avila-Garcia, Marco Bianchetti, Marcelina Pantoja-Flores

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Visual Programming Tools available are a great tool for introducing children to programming and to develop a skill set for algorithmic thinking. On the other hand, collaborative learning and pair programming within the context of programming activities, has demonstrated to have social and learning benefits. However, some of the online tools available for programming for children are not designed to allow simultaneous and equitable participation of the team members since they allow only for a single control point. In this paper, a report the work conducted with children playing a user role is presented. A preliminary study to cull ideas, insights, and design considerations for a formal programming course for children aged 8-10 using collaborative learning as a pedagogical approach was conducted. Three setups were provided: 1) lo-fi prototype, 2) PC, 3) a 46' multi-touch single display groupware limited by the application to a single touch entry. Children were interviewed at the end of the sessions in order to know their opinions about teamwork and the different setups defined. Results are mixed regarding the setup, but they agree to like teamwork.

Keywords: children, collaborative programming, visual programming, multi-touch tabletop, lo-fi prototype

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Authors: Harshith Gowda K. S, Tejaskumar N, Shubhanga R. B, Gowtham N, Deekshith Gowda H. S

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Phasor measurement units (PMU) are playing an important role in the current power system for state estimation. It is necessary to have complete observability of the power system while minimizing the cost. For this purpose, the optimal location of the phasor measurement units in the power system is essential. In a bus system, zero injection buses need to be evaluated to minimize the number of PMUs. In this paper, the optimization problem is formulated using mixed integer programming to obtain the optimal location of the PMUs with increased observability. The formulation consists of with and without zero injection bus as constraints. The formulated problem is simulated using a CPLEX solver in the GAMS software package. The proposed method is tested on IEEE 30, IEEE 39, IEEE 57, and IEEE 118 bus systems. The results obtained show that the number of PMUs required is minimal with increased observability.

Keywords: PMU, observability, mixed integer programming (MIP), zero injection buses (ZIB)

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Authors: Geetha Baskaran, Andrzej Barjiela, Rong Qu

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Motivation: Nurse scheduling is a complex combinatorial optimization problem. It is also known as NP-hard. It needs an efficient re-scheduling to minimize some trade-off of the measures of violation by reducing selected constraints to soft constraints with measurements of their violations. Problem Statement: In this paper, we extend our novel approach to solve the nurse scheduling problem by transforming it through Information Granulation. Approach: This approach satisfies the rules of a typical hospital environment based on a standard benchmark problem. Generating good work schedules has a great influence on nurses' working conditions which are strongly related to the level of a quality health care. Domain transformation that combines the strengths of operation research and artificial intelligence was proposed for the solution of the problem. Compared to conventional methods, our approach involves judicious grouping (information granulation) of shifts types’ that transforms the original problem into a smaller solution domain. Later these schedules from the smaller problem domain are converted back into the original problem domain by taking into account the constraints that could not be represented in the smaller domain. An Integer Programming (IP) package is used to solve the transformed scheduling problem by expending the branch and bound algorithm. We have used the GNU Octave for Windows to solve this problem. Results: The scheduling problem has been solved in the proposed formalism resulting in a high quality schedule. Conclusion: Domain transformation represents departure from a conventional one-shift-at-a-time scheduling approach. It offers an advantage of efficient and easily understandable solutions as well as offering deterministic reproducibility of the results. We note, however, that it does not guarantee the global optimum.

Keywords: domain transformation, nurse scheduling, information granulation, artificial intelligence, simulation

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