A basic study on a limit-cycle problem with multi periods and the optimal assignment problem

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  • 多期間制約サイクル問題と最適配置に関する基礎的研究
  • タキカン セイヤク サイクル モンダイ ト サイテキ ハイチ ニ カンスル キソテキ ケンキュウ

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We consider the following situation. There exists an object with some constraints (e.g., processing time with a target), these constraints produce a risk and the object occurs repeatedly for multiple periods. In this paper, the problem of minimizing the expected risk in such a situation called a "limit-cycle problem with multiple periods", and we consider how to resolve it. First, we classify the limit-cycle problem with multiple periods into some classes and propose, as this type of problem, "a limit-cycle problem with dependent multiple periods", in which the occurrence of an object in a period depends on the occurrences of other objects in the other periods. Next, we propose a mathematical model for the limit-cycle problem with dependent multiple periods, and an efficient algorithm for expected risk (cost) is obtained by using some constraints. Finally, we conduct some numerical experiments to research the optimal assignments aimed at the minimum expected risk. Our proposed algorithm is based on recursive formulas, and the order of computing time is polynomial for the number of periods. From the results of the numerical experiments, it is found out that there exists a similar property to the "Bowl phenomenon" in a series manufacturing line, with simple assumptions. The results obtained in this paper are useful for the design of a production seat system.

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