Hoist scheduling problem in a real time context

An electroplating, or chemical treatment, line is composed of (see fig 1) : tanks containing each a chemical reagent, an input and an output buffer, hoists transporting the products from tank to tank. Therefore, a treatment results from the successive immersion of a product in several tanks. Tanks and hoists can only process one job at a time. Specific chemical constraints exist : • once a product finishes its processing in a tank, it must go as fast as possible to the next tank. This means there is no in-process inventory. • the soaktime, as it corresponds to the time needed to complete a chemical reaction, is not precisely given. But, in order to ensure the quality of the reactions (and, then, of the whole treatment) chemists give minimum and maximum limits. Those quality constraints are considered absolute in printed circuit boards or airplane parts production. As no inventories are allowed, this soaktime tolerance is the only source of flexibility. The control of the hoist's movements with respect to those constraints is known as the Hoist Scheduling Problem (HSP).