Science/Balancing of Multibody Systems

In general terms, the world of nature is physically compatible to a cyclic type, while the world of artifacts is restricted to that of a limited cycle because of limited resources (material, space, and time). In this environment, the sustainable recirculation and balancing problem could be regarded as the cooperative and synergistic use of limited resources (cycle). There are two types of deterministic and stochastic scheduling/balancing methods described in Sects. 3.1 and 3.2, respectively. In Sect. 3.1, we present the dual relation of a job shop (JS) and a line system (OE) by using the flow time approach in order to identify the scheme of Matsui’s equation. This would elicit an optimal/balancing condition beyond Johnson’s rule “bowl effect ”. Furthermore, in Sect. 3.2, we consider an optimal arrangement to minimize the total expected risk on limited-cycle scheduling, in accordance with the stochastic type. A recursive formula for the total expected risk is presented next, and its algorithm is proposed based on the Branch and Bound method. Finally, the so-called “bowl effect ” is also refounded as the balancing property by introducing a theorem and conducting numerical experiments.

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