Three-tank hoist scheduling problem with unbounded or zero-width processing windows

On surface treatment lines, the products are transferred in successive tanks by a hoist. Moreover, each processing time is nested between a minimal and a maximal duration. This constraint is called the processing window constraint. An interesting problem is to find the hoist moves which maximise productivity. This paper deals with the production of identical parts in a balanced three-tank line. We prove that for zero-width or unbounded processing windows, production cycles of one or two parts are optimal.