A CONTINUOUS-FLOW MODEL FOR PRODUCTION NETWORKS WITH FINITE BUFFERS, UNRELIABLE MACHINES, AND MULTIPLE PRODUCTS

This paper presents a flow approximation of production networks with finite buffers and unreliable machines. Parts of various types compete for service before a machine, or they may be assembled before service to yield a composite part. Up times and down times of machines have arbitrary but known distributions and service times have gamma distributions, or may be constant quantities. Random service times are approximated by piece wise deterministic variables. Acyclic networks are considered first. The model is a combination of discrete-event simulation and analysis. The simulator keeps track of the buffer and machine states. Between two consecutive state transitions, flow rates remain constant and the model calculates the cumulative flow of each part type. Compared to a conventional simulator, the model is superior in speed and very accurate. An alternative model is developed for nonacyclic production networks where each machine provides service to different parts repetitively. The model is employed to si...