LQR Control of Multiple Product Inventory Systems for Profit and Warehouse Capacity Maximization

This paper describes the management of inventory systems with multiple products. Linear Quadratic Regulator (LQR) strategy is used for optimizing the profit on the sale and managing the warehouse capacity. While the warehouse capacity is always maintained the customer demand for the products, are also satisfied most of the times. The system model of the considered inventory system includes the supply states in it. The control law is designed to keep the warehouse capacity at the desired level and at the same time it takes into account profit maximization from the sale of the products in the inventory. Numerical example of an inventory system with two products is presented to validate the effectiveness of the designed control law.

[1]  Christos D. Tarantilis,et al.  Dynamic modeling and control of supply chain systems: A review , 2008, Comput. Oper. Res..

[2]  Herbert J. Vassian.  Application of Discrete Variable Servo Theory to Inventory Control , 1955, Oper. Res..

[3]  Przemyslaw Ignaciuk.  LQ Optimal and Robust Control of Perishable Inventory Systems With Multiple Supply Options , 2013, IEEE Transactions on Automatic Control.

[4]  Joakim Wikner,et al.  Inventory trigger control policies developed in terms of control theory , 1996 .

[5]  S. Janardhanan,et al.  Management of periodically reviewed inventory systems with discrete variable structure control , 2016, 2016 11th International Conference on Industrial and Information Systems (ICIIS).

[6]  A. S. White.  Management of inventory using control theory , 1999 .

[7]  Przemyslaw Ignaciuk,et al.  Linear-Quadratic Optimal Control of Periodic-Review Perishable Inventory Systems , 2012, IEEE Transactions on Control Systems Technology.

[8]  Sven Axsäter,et al.  Control theory concepts in production and inventory control , 1985 .

[9]  Reinhard Neck,et al.  Stochastic control theory and operational research , 1984 .

[10]  H. Simon,et al.  On the Application of Servomechanism Theory in the Study of Production Control , 1952 .

[11]  M. Ortega,et al.  Control theory applications to the production–inventory problem: a review , 2004 .

[12]  S. Janardhanan,et al.  Inventory control for nonperishable and perishable goods based on model predictive control , 2020 .

[13]  Przemyslaw Ignaciuk,et al.  Linear-quadratic optimal control strategy for periodic-review inventory systems , 2010, Autom..

[14]  Przemyslaw Ignaciuk,et al.  Sliding Mode Dead-Beat Control of Perishable Inventory Systems With Multiple Suppliers , 2012, IEEE Transactions on Automation Science and Engineering.

[15]  Przemyslaw Ignaciuk,et al.  Nonlinear Inventory Control With Discrete Sliding Modes in Systems With Uncertain Delay , 2014, IEEE Transactions on Industrial Informatics.

[16]  S. Janardhanan,et al.  Management of Inventory for Periodically Reviewed Goods Using Discrete Higher Order Sliding Mode , 2017 .

[17]  Przemyslaw Ignaciuk,et al.  LQ optimal sliding-mode supply policy for periodic-review perishable inventory systems , 2012, J. Frankl. Inst..

[18]  Przemyslaw Ignaciuk,et al.  LQ optimal and reaching law-based sliding modes for inventory management systems , 2012, Int. J. Syst. Sci..

[19]  Przemyslaw Ignaciuk,et al.  Discrete-Time Control of Production-Inventory Systems With Deteriorating Stock and Unreliable Supplies , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[20]  El Kebir Boukas,et al.  Piecewise-linear Hinfinity controller synthesis with applications to inventory control of switched production systems , 2006, Autom..