This paper presents a model for calculating optimal cutting speeds and tool replacement policies for both operations of a two-stage machining problem when the unit cost is minimized or the profit rate is maximized. The tool life is assumed to be a stochastic variable and penalty costs are imposed for tool failures during production. The optimal size of buffer space between the two machines is also calculated analytically. It is shown that the unit cost increases as the tool variability and/or the penalty cost increase. The cutting speeds and tool replacement policies on both operations depend strongly on the tool variability and the penalty cost. The cutting speeds differ from those determined independently for each operation. Finally, the optimal buffer space size is the one necessary to keep the critical machine running when there is a tool change on the non-critical machine, and its optimal size can be calculated analytically.