Flow management in flexible manufacturing cells with pipeline operations

The problem of flow management for a class of flexible manufacturing cells is considered. The cell is designed for cyclic production of one product. This product is characterized by a sequence of operations of given length and each requiring a set of resources; the problem is therefore to allocate such resources and scheduling the operations in order to maximize the throughput. A general model is proposed and several special cases are discussed, corresponding to either polynomial or NP-complete problems. The cases analyzed differ from each other in the number of operating machines and in the number of product units present at the same time in the cell. The solution to the polynomial problems is given in terms of shortest path on particular networks.