Cycle time optimization for deterministic timed weighted marked graphs under infinite server semantics

Timed Petri nets are commonly used for modelling and analysis of automated manufacturing systems, including batch or high throughput systems. This paper consider the cycle optimization problem for a deterministic timed weighted marked graphs under infinite server semantics. The problem aims to find an initial marking to minimize the cycle time while the weighted sum of tokens in places is less than or equal to a desired value. We transform a timed weighted marked graph into several equivalent timed marked graphs and present a mixed integer linear programming method which can provide an optimal solution. Meanwhile, two suboptimal methods are proposed to reduce the computational cost.

[1]  Carla Seatzu,et al.  Control of Discrete-Event Systems , 2012, Lecture Notes in Control and Information Sciences.

[2]  Robert de Simone,et al.  Periodic scheduling of marked graphs using balanced binary words , 2012, Theor. Comput. Sci..

[3]  Manuel Silva,et al.  Cycle time computation in deterministically timed weighted marked graphs , 1999, 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No.99TH8467).

[4]  Alessandro Giua,et al.  Marking optimization of deterministic timed weighted marked graphs under infinite server semantics , 2016, 2016 International Conference on Control, Decision and Information Technologies (CoDIT).

[5]  Alessandro Giua,et al.  Cycle time optimization of deterministic timed weighted marked graphs , 2017, 2015 IEEE International Conference on Automation Science and Engineering (CASE).

[6]  Manuel Silva Suárez,et al.  On Weighted T-Systems , 1992, Application and Theory of Petri Nets.

[7]  Nathalie Sauer.  Marking Optimization of Weighted Marked Graphs , 2003, Discret. Event Dyn. Syst..

[8]  Olivier Marchetti,et al.  Periodic Schedules for Bounded Timed Weighted Event Graphs , 2012, IEEE Transactions on Automatic Control.

[9]  Alessandro Giua,et al.  Optimization of deterministic timed weighted marked graphs , 2017, 2017 13th IEEE Conference on Automation Science and Engineering (CASE).

[10]  Stéphane Gaubert.  An algebraic method for optimizing resources in timed event graphs , 1990 .

[11]  Giovanni Chiola,et al.  Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector , 1991, IEEE Trans. Software Eng..

[12]  Jan Magott,et al.  Performance Evaluation of Concurrent Systems Using Petri Nets , 1984, Inf. Process. Lett..

[13]  Zhiwu Li,et al.  Cycle Time Optimization of Deterministic Timed Weighted Marked Graphs by Transformation , 2015, IEEE Transactions on Control Systems Technology.

[14]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .