Lot streaming in no-wait flowshops with one machine never idle

We consider the problem of minimizing makespan in a no-wait flow-shop with an arbitrary number of machines, when one of the machines has to remain always active. A lot consists of many identical items of the same product. Lot streaming (lot sizing) is the process of creating sublots to move the completed portion of a production sublot to downstream machines so that operations will be overlapped. We consider the number of sublots as given. Some general results are proved for the general no-wait flow-shop with an arbitrary number of machines. A closed form formula is then proposed for the case where one machine never remain idle between the processing of two lots