COMPLEXITY REDUCTION FOR OPTIMIZATION OF DETERMINISTIC TIMED PETRI-NET SCHEDULING BY TRUNCATION

Methods of applying Petri nets to model and analyze scheduling problems, with constraints such as precedence relationships and multiple resource allocation, have been available in the literature. Searching for an optimum schedule can be implemented by combining the branch-and-bound technique with the execution of the timed Petri net. The resulting complexity problem in a large Petri net is handled by a truncation technique such that the original large Petri net is divided into several smaller subnets. The complexity involved in the analysis of each subnet individually is greatly reduced. However, as illustrated in this paper, the schedules for the subnets obtained by treating them separately may not lead to an optimal overall schedule for the original Petri net. To circumvent this problem, algorithms are developed that can be used to search for a proper schedule for each subnet such that the combination of these schedules yields an overall optimum schedule for the original timed Petri net. These algorithm...

[1]  Marshall L. Fisher,et al.  Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I , 1973, Oper. Res..

[2]  Edward G. Coffman,et al.  Computer and job-shop scheduling theory , 1976 .

[3]  Eduardo B. Fernández,et al.  Bounds on the Number of Processors and Time for Multiprocessor Optimal Schedules , 1973, IEEE Transactions on Computers.

[4]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[5]  Giuseppe Menga,et al.  Hybrid hierarchical scheduling and control systems in manufacturing , 1990, IEEE Trans. Robotics Autom..

[6]  Rachid Alami,et al.  Repetitive sequencing: from workcell tasks to workcell cycles , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[7]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[8]  C. L. Philip Chen.  Time lower bound for manufacturing aggregate scheduling problems , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[9]  Andrew Kusiak,et al.  Intelligent Manufacturing Systems , 1990 .

[10]  Philippe Chrétienne,et al.  Timed Petri net schedules , 1987, European Workshop on Applications and Theory of Petri Nets.

[11]  Oded Maimon,et al.  The robot task-sequencing planning problem , 1990, IEEE Trans. Robotics Autom..

[12]  Paul Freedman,et al.  The analysis and optimization of repetition within robot workcell sequencing problems , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.