Single‐Stage and Serial Production Line Systems with Unreliable Machines and General Probability Distributions

Abstract

ABSTRACTThis paper presents stochastic models for analyzing production to stock and production on demand systems with arbitrary demand, production, machine breakdown and repair processes, and a finite buffer. Expressions are developed for the transition probabilities among the different states, the proportion of transitions that take the process to a particular state, the probabilities that the process is at a particular state, and the expected state residence times. Also, expressions are developed for some quantities of interest, like average inventory, percentage of lost sales, and expected waiting time. Applications are discussed for various demand, production, machine breakdown, and repair processes and numerical examples are presented. Guidelines are given for utilizing the models in evaluating the economic performance of production systems. Using an approximation procedure, the models are used for modeling multi‐stage serial production to stock and production on demand lines. Simulation results indicated that the quality of the approximation is very good. The multi‐stage models are useful in practical situations, because they allow the use of different probability distributions for the various processes (production, machine failure, etc.) of each stage.