Journal of Applied Mathematics
Volume 2013 (2013), Article ID 294835, 11 pages
Research Article

Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

1Department of Avionic Engineering, Air Force Academy, Taiwan
2Department of Electronic Engineering, National Ilan University, Taiwan
3Department of Electronic Engineering, Army Academy, Taiwan
4State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China
5Department of Electronic Engineering, National Taiwan Ocean University, Taiwan

Received 20 January 2013; Accepted 27 May 2013

Academic Editor: J. Liang

Copyright © 2013 Yen-Liang Pan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.