Selection Of Inventory Control Points In Multi-Stage Pull Production Systems

Abstract

We consider multistage, stochastic production systems using pull control for production authorization in discrete parts manufacturing. These systems have been widely implemented in recent years and constitute a significant aspect of lean manufacturing. Extensive research has appeared on the optimal sizing of buffer inventory levels in such systems. However the issue of control points, i.e. where in the multistage sequence to locate the output buffers, has not been addressed for pull systems. Allowable container/batch sizes, optimal inventory levels, and ability of systems to automatically adjust to stochastic demand depend on the location of these control points.We begin by examining a serial production system producing a single part type. Two models are examined in this regard. In the first, container size is independent of the control section, while in the second, container sizes are section dependent. Additionally, a nesting policy is introduced which introduces the additional constraint that the container size in a section is related to the container size in any other section by a power of two.Necessary and sufficient conditions are derived for ensuring that a single, end-of-line accumulation point is optimal. When this is not the case, an algorithm is provided to determine the optimal control points. Effects of factors such as value added structure, fixed location cost, setup and material handling cost, kanban collection time, and material transportation time on the control structure are investigated. Results are extended to determine the optimal container size when lead time at a stage is a concave function of container size.The study is then extended to a multi-product case. Queuing aspects are introduced to account for the interaction between the different part types. The queuing model used is a modification of the Decomposition/Recomposition model described in Shantikumar and Buzacott (1981). The models in the chapter do not assume a serial structure any longer. Additionally, general interarrival and service time distributions are considered. The effect of number of products, demand arrival distribution, value added structure, and number of stages on the control structure and system cost is investigated.Finally, a simulation model is developed in Chapter 5 to verify and validate the mathematical models described in Chapters 3 and 4.