Linear-quadratic optimal control strategy for periodic-review inventory systems

The paper addresses the problem of efficient Inventory management in production-inventory systems focusing on the dynamical nature of goods flow process In the considered systems the stock used to satisfy an unknown time-varying demand is replenished either from a single or from multiple supply sources The replenishment orders issued in each review period are realized with a delay which differs among the suppliers and transport alternatives For the analyzed setting modeled as a discrete-time nth-order deterministic system a new inventory policy is developed using a strict control-theoretic methodology In contrast to the classical stochastic approaches the proposed control law is obtained by minimizing a quadratic cost functional which guarantees the optimal dynamical performance of production-inventory systems with (possibly) different lead-time delays in the supply path 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 (which eliminates the risk of high-cost emergency storage) The closed-form solution of the linear-quadratic (LQ) optimization problem allows for a straightforward implementation of the developed control strategy in real systems (C) 2010 Elsevier Ltd All rights reserved