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A decomposition method for assembly/disassembly systems with blocking and general distributions

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Abstract

A modelling methodology is presented for assembly/disassembly systems with general processing time distributions and finite buffers. The approach combines the distributions discretization and a decomposition technique to analyze large manufacturing systems in a reasonable computational time and with good accuracy. In the decomposition technique, the system is decomposed into two station subsystems and the processing time distributions of the virtual stations are iteratively modified to approximate the impact of the rest of the network, adding estimations of the blocking and starving distributions. To analyze each subsystem, the general processing time distributions are discretized by aggregation of the probability masses, and the subsystem is then analytically modeled using a discrete Markov chain. We first show that this approach allows an accurate estimation of the subsystems cycle time distributions, which is crucial in the decomposition technique. Using computational experiments, we show that our decomposition method leads to accurate performance evaluation for large manufacturing systems (relative error on the order of 1%) and that the fine distribution estimation indeed seems to bring an improvement. Furthermore, we show on examples that, using decomposition, the cycle time distributions can be approximated reliably for large systems.

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Notes

  1. If \(S_3\) is starved by two preceding stations, the starving ends when each station has ended its job. The starvation time to be added to \(S_u(3)\) is thus the maximum of the starvation times computed on \(S_d(1)\) and \(S_d(2)\).

  2. If \(S_2\) is blocked by two successors, the blocking ends when each of them has ended its job. The blocking time to be added to \(S_d(1)\) is thus the maximum of the blocking times computed on \(S_u(2)\) and \(S_u(3)\).

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  1. Université catholique de Louvain, CORE, Louvain School of Management, Chaussée de Binche, 151, 7000, Mons, Belgium

    Jean-Sébastien Tancrez

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Tancrez, JS. A decomposition method for assembly/disassembly systems with blocking and general distributions. Flex Serv Manuf J 32, 272–296 (2020). https://doi.org/10.1007/s10696-019-09332-z

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