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2013 Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems
Yen-Liang Pan, Yi-Sheng Huang, Yi-Shun Weng, Weimin Wu, MuDer Jeng
J. Appl. Math. 2013(SI17): 1-11 (2013). DOI: 10.1155/2013/294835

Abstract

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches.

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Yen-Liang Pan. Yi-Sheng Huang. Yi-Shun Weng. Weimin Wu. MuDer Jeng. "Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems." J. Appl. Math. 2013 (SI17) 1 - 11, 2013. https://doi.org/10.1155/2013/294835

Information

Published: 2013
First available in Project Euclid: 14 March 2014

MathSciNet: MR3068876
zbMATH: 1271.90004
Digital Object Identifier: 10.1155/2013/294835

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI17 • 2013
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