Defining inventory control points in multiproduct stochastic pull systems

Multistage pull production systems have been widely implemented in recent years and constitute a significant aspect of lean manufacturing. One of the important considerations in such systems is identifying the 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 yet the issue of optimal location has not been widely addressed. This paper considers a multiproduct pull setting where part types compete with each other for common production resources. In this environment it is important to consider factors such as lead time variability and to include the corresponding queuing aspects into the model. Each workstation is modeled as a GI/G/1 queue. Waiting times spent by parts at workstations are approximated using a decomposition/recomposition algorithm. Necessary and sufficient conditions are provided for the optimality of a single control point. Conditions under which multiple control points are optimal are investigated along with the impact of product mix and utilization parameters on the number of control points. Analytical model results are validated by simulation.