Lean buffering in production systems: A quantitative approach.

Abstract

This thesis addresses the problem of buffer capacity allocation in serial production lines. Both in-process and finished goods buffers are considered. The goal is to develop methods to calculate the smallest, i.e., lean, buffer capacities necessary to ensure the desired production rate or customer satisfaction level. In the case of in-process buffering, a new dimensionless parameter, referred to as the level of buffering, is introduced in order to measure the buffer capacity in terms of machine downtime and to show that the level of buffering may be estimated without knowledge of the distributions of the uptime and downtime, but based only on their coefficient of variation (<italic>CV</italic>). This implies that the level of buffering is practically the same for all uptime and downtime distributions, as long as their coefficients of variation are equal. Based on this observation, an empirical law is formulated and verified according to which the level of buffering can be upper bounded by a piece-wise linear function. Specifically, for <italic>CV</italic> &ge; 0.25, this upper bound is the product of the level of buffering for exponential machines kexpE</fen> and the <italic>CV</italic> of the machines in question; and, for <italic> CV</italic> < 0.25, it is a constant equal to 0.25 kexpE . Since kexpE can be evaluated and <italic>CV</italic> can be identified on the factory floor, the method developed provides a simple and practical tool for designing lean buffering in serial production lines. For finished goods buffers, an analytical method for evaluating due-time performance (<italic>DTP</italic>), i.e., the probability of producing a certain number of parts during a given shipping period, in production-inventory-customer systems with exponential machines, finite inventory, and random demand is provided. Using this method, the degradation of <italic>DTP</italic> as a function of demand variability is quantified. In addition, it is shown that <italic> DTP</italic> is practically independent of a particular type of demand distribution, as long as its coefficient of variation (<italic>CV</italic>) remains fixed. The results presented in this dissertation are for serial production lines with unreliable machines having identical efficiency, identical cycle time and time-dependent failures. The future work will extend these results to non-identical machines and buffers, machines with non-identical cycle time, machines with random processing time, and assembly lines.