LQ Optimal Sliding Mode Supply Policy for Periodic Review Inventory Systems

In this technical note, the problem of inventory management in supply chain is addressed from a control theory perspective. In the analyzed setting, the stock used to satisfy an unknown, time-varying demand can be replenished from several supply sources. The replenishment orders are realized with delay which differs among suppliers and transport alternatives. A novel sliding-mode inventory policy is proposed, which guarantees that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost), the warehouse capacity is not exceeded (what eliminates the risk of high-cost emergency storage) and ordered goods are not returned to the suppliers. As opposed to the classical, stochastic approaches, the parameters of the proposed controller are selected by minimizing a quadratic cost functional, which ensures an optimal dynamical performance of inventory systems with disparate lead times.