Optimal buffer space size in two-stage machining systems with Markovian or non-Markovian tool life processes

This paper presents a model for obtaining the optimal buffer space size in two-stage machining systems. It is shown that the optimal buffer space size is the one necessary to keep the critical machine running even when there are tool failures and subsequent tool changes on the non-critical machine. An analytical expression for the optimal buffer space size is derived when tool failures follow a Markovian process and the objective function is the minimization of the unit cost. A simulation mode! is developed for obtaining the optimal buffer space size when tool failures follow a non-Markovian process. It is shown that the optimal buffer space size depends on the expected delay time per part due to tool failures on the non-critical machine (which depends on the probability of tool failure on the non-critical machine during machining on the critical machine), on the labour and the buffer space cost, and on the tool-change time. The model can be extended to cover the case of two or more identical parallel machines per stage and the case of multi-stage machining systems.