Analytical models of multi-stage make-to-stock systems

A new decomposition approach is presented for analyzing tandem configurations of multi-stage make-to-stock systems. An M-stage line is decomposed into M single stage lines. Each single stage line includes the corresponding stage in the multi-stage line and a delay node (except stage 1) which captures the upstream delay experienced by a backorder at the stage. The decomposition approach is explained by using a simple version of the system, where the demand process is Poisson, and the unit production times are exponentially distributed. The approximation scheme is tested by comparing the results obtained with published results. For all cases examined, the performance of the approximation scheme is equal to or better than that of a published method. Extensions of this procedure to general demand processes and general unit production time distributions are discussed briefly. The approach for solving the general case can be viewed as an extension of the popular parametric decomposition method for solving queueing network models.