• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.2
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• pp.105-116
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• 2018

In this study, we consider the assembly line balancing (ALB) problem which is known as an very important decision dealing with the optimal design of assembly lines. We consider ALB problems with soft constraints which are expected to be fulfilled, however they are not necessarily to be satisfied always and they are difficult to be presented in exact quantitative forms. In previous studies, most researches have dealt with hard constraints which should be satisfied at all time in ALB problems. In this study, we modify the mixed integer programming model of the problem introduced in the existing study where the problem was first considered. Based on the modified model, we propose a new algorithm using the genetic algorithm (GA). In the algorithm, new features like, a mixed initial population selection method composed of the random selection method and the elite solutions of the simple ALB problem, a fitness evaluation method based on achievement ratio are applied. In addition, we select the genetic operators and parameters which are appropriate for the soft assignment constraints through the preliminary tests. From the results of the computational experiments, it is shown that the proposed algorithm generated the solutions with the high achievement ratio of the soft constraints.