Browsing by Subject "Mathematical formulation"

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    An efficient grouping genetic algorithm for U-shaped assembly line balancing problems with maximizing production rate
    (Springer Verlag, 2017) Şahin M.; Kellegöz T.
    U-type assembly line is one of the important tools that may increase companies’ production efficiency. In this study, two different modeling approaches proposed for the assembly line balancing problems have been used in modeling type-II U-line balancing problems, and the performances of these models have been compared with each other. It has been shown that using mathematical formulations to solve medium and large size problem instances is impractical since the problem is NP-hard. Therefore, a grouping genetic and simulated annealing algorithms have been developed, and a particle swarm optimization algorithm is adapted to compare with the proposed methods. A special crossover operator that always obtains feasible offspring has been suggested for the proposed grouping genetic algorithm. Furthermore, a local search procedure based on problem-specific knowledge was applied to increase the intensification of the algorithm. A set of well-known benchmark instances was solved to evaluate the effectiveness of the proposed and existing methods. Results showed that while the mathematical formulations can only be used to solve small size instances, metaheuristics can obtain high quality solutions for all size problem instances within acceptable CPU times. Moreover, grouping genetic algorithm has been found to be superior to the other methods according to the number of optimal solutions, or deviations from the lower bound values. © 2017, Springer-Verlag GmbH Germany.
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    Disassembly line balancing with sequencing decisions: A mixed integer linear programming model and extensions
    (Elsevier Ltd, 2019) Edis E.B.; Ilgin M.A.; Edis R.S.
    Due to the acceleration of technological developments and shortening of product life cycles, product recovery has gained great importance in recent years. Disassembly line balancing (DLB) problem is one of the most important problems encountered during disassembly operations in product recovery. In this study, a single model and complete DLB problem with balancing issues, hazardousness of parts, demand quantities and direction changes is considered. Majority of DLB studies in the literature solve this problem using heuristics or metaheuristics which do not guarantee the optimality. Although a few studies present mathematical formulations for some variants of this problem, they prefer to solve the problem by using heuristics or metaheuristics due to the non-linear structure and combinatorial nature of the problem. In this study, a generic mixed integer linear programming (MILP) model is developed for the investigated problem and its performance is tested through a series of benchmark instances. The computational results demonstrate that the proposed MILP model is able to solve test instances with up to 30 tasks. Hence, it can effectively be utilized to evaluate the optimality performance of DLB approaches. Moreover, several extensions on the MILP model regarding to line balancing, hazardousness and demand of parts and direction changes are proposed and their effects are analyzed through computational studies. © 2019 Elsevier Ltd
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    Balancing Multi-Manned Assembly Lines With Walking Workers: Problem Definition, Mathematical Formulation, and an Electromagnetic Field Optimisation Algorithm
    (Taylor and Francis Ltd., 2019) Şahin M.; Kellegöz T.
    Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
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    A directly convergent numerical method based on orthoexponential polynomials for solving integro-differential-delay equations with variable coefficients and infinite boundary on half-line
    (Elsevier B.V., 2021) Kürkçü Ö.K.; Sezer M.
    In this study, main concern is focused on numerically solving the integro-differential-delay equations with variable coefficients and infinite boundary on half-line, proposing a matrix-collocation method based on the orthoexponential polynomials. The method is equipped with the collocation points and the hybridized matrix relations between the orthoexponential and Taylor polynomials, which enable us to convert an integral form with infinite boundary into a mathematical formulation. The method also directly establishes the verification of the existence and uniqueness of this integral form through a convergent result. In order to observe the validity of the method versus its computation limit, an error bound analysis is performed by using the upper bound of the orthoexponential polynomials. A computer module containing main infrastructure of the method is specifically designed and run for providing highly precise results. Thus, the numerical and graphical implementations are completely monitored in table and figures, respectively. Based on the comparisons and findings, one can state that the method is remarkable, dependable, and accurate for approaching the aforementioned equations. © 2020 Elsevier B.V.