LQ optimal and time-varying sliding modes for inventory management systems

In this paper, the theory of discrete sliding-mode control is used to design new supply strategies for periodic-review inventory systems. The proposed strategies guarantee that the demand is always entirely satisfied from the on-hand stock (yielding the maximum service level), and the warehouse capacity is not exceeded (what eliminates the cost of emergency storage). In contrast to the classical, stochastic approaches, in this paper, we focus on optimizing the inventory system dynamics. The parameters of the first control strategy are selected by minimizing a quadratic cost functional. Next, it is shown how the system dynamical performance can be improved by applying the concept of reaching law and time-varying sliding modes. The stable, non-oscillatory behavior of the closed-loop system is demonstrated and the properties of the designed controllers are discussed and strictly proved.