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 piecewise 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 with a conventional simulator, the model is superior in speed and very accurate. An alternative model is developed for non-acyclic production networks where each machine provides service to different parts repetitively. The model is employed to simulate a re-entrant production line under a class of heuristic scheduling policies. The optimal policy is the one that meets demand while maintaining small buffer sizes and short delays of parts.