LQ Optimal Sliding Mode Supply Policy for Periodic Review Inventory Systems

• Published in: IEEE transactions on automatic control Vol. 55; no. 1; pp. 269 - 274
• Main Authors: Ignaciuk, P., Bartoszewicz, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automatic control; Computer science; control theory; systems; Control systems; Control theory; Control theory. Systems; Cost function; Delay; Exact sciences and technology; Inventories; Inventory control, production control. Distribution; Inventory management; Logistics; Marketing; Operational research and scientific management; Operational research. Management science; Optimal control; Optimization; Policies; Raw materials; Samarium; Sliding mode control; Stockpiling; Suppliers; Supply chains; System theory; sliding-mode control; Warehouse; Probabilistic approach; Variable structure control; Sliding mode; Variable structure system; Optimal policy; Periodicity; Review; Dynamical system; Delay; Time varying system; Sales; Optimal control; Inventory management; Inventory control; Supplier; Quadratic cost; Control theory; Transport; Quadratic functional; Periodic system; Logistics
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2036305

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.