Average flow constraints and stabilizability in uncertain production-distribution systems

Consider multi-inventory systems in presence of uncertain demand and assume that demand is unknown but bounded in an assigned compact set and the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we are interested in a control strategy that satisfies just one of the two requirements: i) meeting at each time all possible current demands (worst case stability) or ii) achieving a pre-defined nominal flow in the average (average flow constraints). We show that if we retain the average constraints and relax worst case stability requirement we can achieve stochastic stability. On the contrary, if we retain the worst case stability and relax the average flow constraints we can optimize the average linear flow cost. In the latter case we provide a tight bound for the cost.