LQ optimal sliding mode stock replenishment strategy for inventory systems with multiple supply alternatives

In this paper, a new supply strategy for periodic-review inventory systems is developed using strict control-theoretic methodology. In the analyzed setting, the stock used to satisfy the unknown, time-varying demand can be replenished from several supply alternatives, characterized by different lead-time delays. A novel sliding-mode inventory policy is proposed, which guarantees that the demand is always entirely satisfied from the on-hand stock, and the warehouse capacity is not exceeded. As opposed to the classical, stochastic approaches, the parameters of the proposed controller are selected by minimizing a linear-quadratic (LQ) cost functional, which ensures the optimal dynamical performance of inventory systems with disparate lead-time delays.