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.

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

This paper reviews recent work on the development of analytical models of Flexible Manufacturing Systems (FMSs). The contributions of each of the groups concerned with model development are summarized and an assessment is made of the strengths and weaknesses of its modelling approach. A number of directions in which models require extension are outlined, in particular the representation of such aspects of FMS operation as the tool delivery systems, the blocking phenomenon, the transient behavior and the differences between flexible machining systems and flexible assembly systems. Further work is also required on the structure of FMS control and the integration with plant production planning and control.

Flexible manufacturing systems: a review of analytical models

Modelling flexible manufacturing systems using mean-value analysis

Using a closed queueing network model, we explore the consequences of varying workloads among multiserver queues that may be of unequal size. In addition, we solve the problem of assigning servers of similar types to the queues in the network to maximize expected throughput.

We show that 1 unbalanced configurations of assigned servers are superior to balanced ones, and 2 unbalanced workloads are better than balanced ones. We find that there can be significant differences in system throughput from balanced versus unbalanced configurations/workloads. Finally, we discuss applications to planning problems of flexible manufacturing systems.

The Optimality of Unbalancing Both Workloads and Machine Group Sizes in Closed Queueing Networks of Multiserver Queues

Publisher Summary This chapter discusses different approaches to performance evaluation (PE) of discrete manufacturing systems that can be placed in three categories. These include static (allocation) models, aggregate dynamic models (ADMs), and detailed dynamic models. Except for the simplest of systems, ADMs usually provide estimates only of steady state performance measures (PMs), and often just average values are estimated (as opposed to say, entire distributions, or a 95% percentile). The PMs fall primarily into the category of physical PMs rather than financial PMs. The chapter also deals with physical PMs. Typical PMs estimated by an ADM include (all of these are steady state averages): utilization of each server; throughput (of production rate); flow time of a job through the system; queue length at a station; and work-in-process (WIP) in the system. These are among the primary physical PMs of interest to manufacturing personnel and, even though only steady state average values are estimated, they can be quite valuable in manufacturing decision making.

Chapter 5 Performance evaluation of production networks

The application of queuing network theory to the performance evaluation of flexible manufacturing systems (FMS) usually requires the assumption of exponential processing times on machines. It has resulted in pessimistic, although qualitatively robust, evaluation algorithms so far. A recent computational technique, named mean-value analysis, allows to depart from this unrealistic assumption and to derive approximate algorithms for networks with general servers and FIFO service rule. The case of deterministic service times is particularly relevant for FMS's, and the corresponding heuristic technique is described and validated by means of simulation. This technique is liable to extend to the case of unreliable deterministic servers, thus enabling to assess the overall effect of short incidents on machines, on the production rate of the system.

Jean-bernard Cavaille

Papers

Heuristic methods based on mean-value analysis for flexible manufacturing systems performance evaluation