مدل سازی و برنامه ریزی از FMS مبتنی بر نسبت با استفاده از شبکه های پتری که همزمان با هم اتفاق می افتند

In this paper, we focus on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of the Work in Process (WIP for short). Especially, this paper deals with product ratio-driven FMS cyclic scheduling problem with each other products and ratios using Timed Petri nets unfolding (TPN for short). TPN slicing and unfolding are applied to analyze this FMS model. We can divide original system into subsystem using TPN slices and change iterated cycle module into acyclic module without any loss of other behavior properties.

In recent, many consumers want more kinds of products according to their desires. They also want to be distinguished from others. This new trend leads the industrial manufacturing systems to produce a large diversity of products in small quantities. The techniques of automatic transport system, new methods of production management and control are obtained by using flexible manufacturing systems (FMS for short) which are discrete-event systems. An FMS is composed of a set of versatile machines, zig and fixture, and automatic transport system for moving parts between each job. In FMS, an important subject is to formulate the general cyclic state scheduling problem to maximize the throughput and/or minimize the Work in Process (WIP) to satisfy economical constraints. Various scheduling methods have been proposed by researchers (Hillion, Julia et al., 1995, Korbaa et al., 1997, Lee and DiCesare, 1995, Ohl et al., 1995, Richard, 1998, Valentin, 1994 and Zuberek and Kubiah, 1993).

In this paper, we focused on the analysis of cyclic scheduling for the determination of the optimal cycle time and minimization of Work in Process. The analysis of the schedule for the determination of the optimal cycle time using the unfolding Petri nets after slicing BUC based on the transitive matrix has been studied. The scheduling problem in the resource shared system was strong NP-hard. That meant that if the original net was complex and large, then it would be difficult to analyze. To solve this problem, we have proposed an algorithm to analyze the scheduling problem after divide into some BUCs used transitive matrix based on the behavioral properties in the net. After applying to a system with 2 machines and 2 jobs some of the best solutions including another type with Camus have been identified. The calculation of the feasibility time was simple. These results indicated that our method was easy to understand to find good schedule, compute feasibility time, and combine the operation schedules also. Finally a simple example for guaranty about to get the good solution has been identified.