Petri net models for automated assembly systems.

摘要

Modern automated assembly systems are classified into two classes. One is dedicated assembly lines which are appropriate for high volumes of products, whereas the other is flexible assembly systems which are suitable for small volumes of a wide variety of products. Assembly process planning includes various fundamental areas, such as optimal sequencing, scheduling, layout and location of assembly cells, and performance analysis of the process. Two of these areas, optimal sequencing and performance analysis, have attracted the attention of several researchers for the past two decades.; This research is concerned with these two areas and presents a series of new procedures encompassing (1) the determination of optimal sequences, including generation and evaluation of feasible assembly sequences, and (2) performance analysis of an automated assembly system by virtue of Petri net models which characterize the dynamic behavior of system operation. These procedures are addressed through four associated problems.; The first problem consists of finding optimal assembly sequences in an automated assembly system. The selection of an assembly sequence of a product has a great effect on the efficiency of the assembly process. A dynamic programming algorithm is developed to find all optimal sequences from a Petri net model. Two assembly products are provided to validate the algorithm.; The second problem is to find tight bounds on optimal assembly sequences where assembly operation constraints, such as ease of component handling, ease of component joining, and tool changes, are considered. A Petri net can be formulated as a 0-1 integer linear program which minimizes the total assembly time or cost while satisfying the operation constraints. A Lagrangian relaxation approach with subgradient optimization is proposed to obtain tight bounds from the Petri net model. Two assembly products are provided for validation of the solution procedure.; In the third problem, as an incorporation of non-exponentially distributed transitions, a Petri net for flexible assembly systems with phase type distributions is considered. A Petri net reduction procedure is proposed to decrease the size of the reachability set of a large Petri net by employing commonly used subnets and the closure properties of phase type distributions. An example of an automated assembly system is provided to illustrate the phase type representations of basic subnets and the reduction algorithm.; The fourth problem is to find transient and steady state probabilities when the stochastic Petri net model for a flexible assembly system has arbitrarily distributed transitions and allows multiple non-exponentially distributed transitions to be enabled in a particular system state. Since it is practically impossible to find an analytical method for performance analysis of this class of stochastic Petri nets, a phase type approximation method is presented to provide accurate solutions.