LQ Optimal and Nonlinear Supply Policies for Periodic-Review Inventory Systems with Time-Varying Lead-Time Delay

In this paper we consider an inventory system where the stock at a distribution center, used to fulfill the demand imposed by customers and retailers, is replenished with delay from a supplier. In contrast to the typical, stochastic approaches, which operate mainly on average or static quantities, the emphasis is placed on optimizing the dynamics of the goods flow process in the presence of the time-varying delay between placing of an order and shipment arrival at the center. The designed policy ensures that the demand is always entirely satisfied from the on-hand stock (yielding zero lost-sales cost) and the warehouse capacity is not exceeded (what eliminates the risk of high-cost emergency storage). It is shown how the linear-quadratic (LQ) optimal controller with saturation achieves robustness with respect to the time-varying lead-time delay and unknown demand fluctuations.