The problem of machine tools with real time ingot arrival

The Bellman - Johnson optimization problem for the speed of machining $n$ parts with the same sequence of machining at every tool is extended the case of real time arrival of ingots, or when at the time of machining a part the next one has not necessarily arrived at the system input. Speed optimization of a real time system reduces to solving a similar problem for a system in which ingots are machined lot-wise.