A modelling approach for the dynamic scheduling problem of manufacturing systems with non negligible setup times and finite buffers

In this paper we study optimal scheduling for two part-type, symmetric manufacturing systems subject to non negligible setup times, and characterized by finite buffer capacities. The modelling approach proposed is based on a two step transformation: the original fluid approximation is converted to a sampled model, according to the necessary condition of optimality of the transient policies, and then such a two-dimensional sampled model is mapped onto an equivalent scalar one. Based on the scalar model, the optimal solution of the original scheduling problem is proved, whenever a threshold condition holds for demand loss cost parameter.