Markovian Analysis of a Push-Pull Merge System with Two Suppliers, An Intermediate Buffer, and Two Retailers

Literature Review

There is a rich body of literature on the analysis of push serial flow lines with linear flow of material (Gershwin, 1994; Papadopoulos, Heavey, & Browne, 1993). The amount of research devoted to the analysis of push-pull systems is relatively small. Moreover, the number of papers in the literature addressing the analysis of push-pull systems with merge operations is really small.

Considering the literature of push merge systems, a push model with two merging stations and two buffers, which was analysed through decomposition using as a decomposition block virtual two-machine one buffer lines was presented by (Helber, 1999). Three machine one buffer systems with machine specific processing times, exponentially distributed failure and repair times examined by (Helber & Mehrtens, 2003). Additionally, continuous flow of material was assumed. An exact analysis of this model was presented using differential equations to derive the transition probabilities. An exact algorithm to compute the throughput of a more general system that allows arbitrary deterministic processing times and exponentially distributed failure and repair times was developed by (Helber & Jusic, 2004). A discrete material push merge system with three unreliable machines and one buffer of limited capacity was examined by (Diamantidis, Papadopoulos, & Vidalis, 2004). Processing times were assumed to be deterministic and identical for all machines and were taken as the time unit. The operation dependent failures at the machines were also assumed to be Geometrically distributed.