This paper considers a multistage, serial production system using pull control for discrete parts manufacturing. A model is developed to locate inventory control points, i.e. where in the multistage sequence to locate the output buffers. 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. 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.