Zhou He

Optimization of Deterministic Timed Weighted Marked Graphs

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model systems with bulk services and arrivals. We consider two problems of practical importance for this class of nets. The marking optimization problem consists in finding an initial marking to minimize the weighted sum of tokens in places, while the average cycle time is less than or equal to a given value. The cycle time optimization problem consists in finding an initial marking to minimize the average cycle time, while the weighted sum of tokens in places is less than or equal to a given value. We propose two heuristic algorithms to solve these problems. Several simulation studies show that the proposed approach is significantly more efficient than existing ones.

Marking optimization of deterministic timed weighted marked graphs

For modelling and analysis of automated production systems as batch or high throughput systems, timed Petri nets are commonly used. In this paper, we deal with the marking optimization problem of a timed weighted marked graphs under infinite server semantics. The problem consists in finding an initial marking to minimize the weighted sum of tokens in places while the average cycle time is less than or equal to a given value. We propose two different heuristic approaches to solve the optimization problem.

Cycle Time Optimization of Deterministic Timed Weighted Marked Graphs by Transformation

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems such as robotic work cells or embedded systems. The main problem for designers is to find a trade off between minimizing the cost of the resources and maximizing the systems throughput. It is possible to apply analytical techniques for the average cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the average cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value.

Cycle time optimization of deterministic timed weighted marked graphs

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems, such as robotic work cells or embedded systems, and reduce the size of the model. The main problem for designers is to find a tradeoff between minimizing the cost of the resources and maximizing the system’s throughput (also called cycle time). It is possible to apply analytical techniques for the cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value. We transform a weighted marked graph into several equivalent marked graphs and formulate a mixed integer linear programming model to solve this problem. Moreover, several techniques are proposed to reduce the complexity of the proposed method. We show that the proposed method can always find an optimal solution.

Marking optimization of deterministic timed weighted marked graphs under infinite server semantics

For modelling and analysis of automated production systems as batch or high throughput systems, timed Petri nets are commonly used. In this paper, we deal with the marking optimization problem of a timed weighted marked graphs under infinite server semantics. The problem consists in finding an initial marking to minimize the weighted sum of tokens in places while the average cycle time is less than or equal to a given value. We propose two different heuristic approaches to solve the optimization problem.

Stationary behavior of manufacturing systems modeled by timed weighted marked graphs

Time Petri nets are commonly used for modelling and analyzing embedded systems, assembly lines, and streaming applications. In this paper, a sub class of time Petri net named timed weighted marked graphs (TWMGs) are studied. Stationary throughput analysis of these TWMGs is an important step for checking throughput requirements of concurrent real-time applications and finding the best schedules. We proposed some important properties of TWMGs which are useful for designers or engineers to study the stationary throughput and solve the scheduling problem for practical usage.

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.