Control of production-inventory systems with deteriorating stock and unreliable delayed supply channel

The paper considers the problem of establishing an efficient control strategy for production-inventory systems in which the stock replenishment process is unreliable. In the analyzed setting, the stock used to satisfy unknown, variable demand deteriorates with time. It is refilled with delay from a remote supply source. Due to information distortion, production, or transportation faults, the shipments may arrive damaged, or incomplete. The setting is modeled as a time-varying discrete-time system with delay. A new dead-time compensation mechanism, which provides smooth ordering pattern and ensures closed-loop stability for arbitrary delay, is proposed. The properties of the proposed control system are formally proved and illustrated in numerical experiments.