Reentrant Flow Shops

We introduce flow shops that revisit certain processors, and define the common patterns of flow: cyclic, chain, hub, and V-shaped. We show that even the simplest case, the (1,2,1)-reentrant shop, is NPhard, establish properties that facilitate a branch-and-bound algorithm, and present two simple but very effective heuristics. With m machines, we give for chain-reentrance simplifying properties, for hub-reentrance a DP based on simplifying assumptions that yet performs well, for Vreentrance a solvable special case. For cyclic production of a single product in the general m-machine reentrant shop, we give an algorithm for finding the efficient frontier between cycle time and flow time, and a heuristic for larger instances. For the hybrid reentrant system, if all jobs require the same time for each production step but have different due dates, dispatching rules are recommended and compared.