This paper deals with the inventory controller design for constrained production systems subject to uncertainties on the customer demands. The case study focuses on the inventory regulation problem in production systems where contain perishable finite products. Such systems are characterized by the presence of delays due to production processes, and constraints from the instantaneous inventory level, production level and the finite capacities of stocks. To do that, we propose a management strategy based on the inventory control, using either a linear control law or a bang-bang control. A design method is proposed to determine the parameters of an admissible control law. The design method is based on the invariance principle, and our proof is based on the exact identification of the admissible region on the space of the parameters of the system and the control specifications.