Modeling Methods Based on Discrete Algebraic Systems

Goto, Hiroyuki

doi:10.5772/46958

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…The MPL system is described in max-plus algebraic contexts; it is able to represent time structures of two types of systems: parallelizing a job and synchronizing multiple jobs. Several scheduling methods have been proposed using an MPL system [1,2].…”

Section: Introductionmentioning

confidence: 99%

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Two-level priority scheduling framework in a max-plus linear representation

Sagawa

Shimakawa

Goto

2021

SICE Journal of Control, Measurement, and System Integration

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A common type of scheduling policy includes first-in-first-out (FIFO) and earliest-outset bases. Among many approaches to this, max-plus linear representation is beneficial for event-driven discrete event systems (DESs). The earliest event occurrence times can be represented by linear relations in max-plus algebra, the resultant of which is analogous with the state equation in modern control theory. Methodologies in control theory such as evolution prediction and just-in-time scheduling can thus be utilized. Although useful, the description capability remains confined to FIFO contexts, for which the method would not be capable of producing an efficient solution for systems with two-level priorities. An entity, e.g. a task or token in scheduling contexts, with higher qualification would be prioritized over one with a lower qualification. A framework for overtaking tasks is necessary for this. Motivated by this need, this article is concerned with constructing a two-level priority scheduling methodology in a max-plus linear context. A numerical experiment applied to a simple manufacturing system highlights the significance of the constructed method.

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Section: Introductionmentioning

confidence: 99%

“…Even with an extended model, there has been an issue that the departure time of the overtaking cannot be calculated in a correct manner. This will be resolved by recasting the model in [2].…”

Section: Introductionmentioning

confidence: 99%

Two-level priority scheduling framework in a max-plus linear representation

Sagawa

Shimakawa

Goto

2021

SICE Journal of Control, Measurement, and System Integration

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“…On the other hand, the max-plus linear (MPL) representation is known as an efficient tool for describing a class of discrete event systems (DESs) (Heidergott et al, 2006;Goto, 2010). The typical and significant feature of DESs is that events occur at discrete time instants and the values of the internal states change non-continuously.…”

Section: Introductionmentioning

confidence: 99%

Buffer Management Method for Multiple Projects in the CCPM-MPL Representation

Truc¹,

Takei²,

Goto³

et al. 2012

Industrial Engineering and Management Systems

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This research proposes a framework of buffer management for multi-project systems in the critical chain project management (CCPM) method, expressed in the form of max-plus linear (MPL) representation. Since time buffers are inserted in the projects for absorbing uncertainties in task durations and protecting the completion times, the proposed method provides a procedure for frequently surveying the rates of consumed buffers and the rate of elapsed times. Their relation expresses the performance of the projects which is plotted on a chart through the completed processes. The chart presents the current performance of the projects and their interaction, which alerts managers to make necessary decisions at the right time for managing each project and the entire multi-project system. The proposed framework can analyze the complex system readily, and it enables managers to make an effective decision on scheduling. The effectiveness of the framework is demonstrated through a numerical example.

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Modeling Methods Based on Discrete Algebraic Systems

Cited by 2 publications

References 12 publications

Two-level priority scheduling framework in a max-plus linear representation

Two-level priority scheduling framework in a max-plus linear representation

Buffer Management Method for Multiple Projects in the CCPM-MPL Representation

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