Feedback control of production-distribution systems with unknown demand and delays

A class of production-distribution problems with unknown-but-bounded uncertain demand is considered. At each time, the demand is unknown, but each of its components is assumed to belong to an assigned interval. Furthermore, the system has production, transportation, and storage capacity constraints. The paper extends previous results to the case in which transportation delays are present. We show that the problem of finding a strategy which keeps bounded the storage levels reduces to that of finding a strategy for the associated instantaneous network, which is the network obtained by setting all the delays to zero in the original system. The state variables of the associated instantaneous network are the "inventory positions," given by the goods actually present in the warehouses plus the goods already ordered and leading to them.