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

✍ Scribed by Przemysław Ignaciuk; Andrzej Bartoszewicz

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 802 KB
• Volume: 46
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2010.09.010

✦ Synopsis

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.