A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing

TLDR

Discrete‑event systems model processes as sequences of time‑consuming activities whose start and end events follow a prescribed order. The study develops an analogy between linear systems and a class of discrete‑event systems. Closed discrete‑event systems’ periodic behavior is characterized by solving an eigenvalue/eigenvector equation in the algebra, which is efficiently computed by a shortest‑path algorithm on a graph. The approach is shown to be useful for evaluating flexible manufacturing systems, with a detailed analysis of a flowshop‑like production process.

Abstract

A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e., involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized; the case of a flowshop-like production process is analyzed in detail.