Geodesic
Multiple-warehouse sliding mode control with a predefined demand trajectory profile
International Journal of Applied Mathematics and Computer Science, Tome 34 (2024) no. 3, pp. 375-389.

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The paper discusses the inventory management problem with a single product stored in two warehouses, where each has its unique suppliers with certain lead times. Moreover, one of the warehouses may act as a backup supplier for the other. In other words, product exchange between two different warehouses within one company is allowed. The first warehouse operates under an a priori known time-variant contractual demand and a bounded random one. Its secondary goal is to accumulate emergency stock that can be delivered to the second warehouse within one time period. For this warehouse we use a desired trajectory generator to shape the required stock level and then utilize a trajectory following control law. The demand in the second warehouse is unknown but bounded, and its suppliers have limited delivery capacity. The challenge is to fulfill the customers’ needs, although they might exceed the order limit. Therefore, occasional backup supplies from the first warehouse are necessary. For the control of the second warehouse, a simple sliding mode (SM) scheme is applied. The paper proves that, with appropriate compensation of the emergency deliveries in the first warehouse, our proposed control scheme ensures full demand satisfaction in both warehouses despite the second one’s control limit.
Keywords: control design, discrete time system, inventory control, model reference control, sliding mode control
Mots-clés : projekt sterowania, układ dyskretny, sterowanie trybem ślizgowym 
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Adamiak, Katarzyna; Zwierzchowski, Tymoteusz. Multiple-warehouse sliding mode control with a predefined demand trajectory profile. International Journal of Applied Mathematics and Computer Science, Tome 34 (2024) no. 3, pp. 375-389. http://geodesic.mathdoc.fr/item/IJAMCS_2024_34_3_a3/

[1] Alessandri, A., Gaggero, M. and Tonelli, F. (2011). Min-max and predictive control for the management of distribution in supply chains, IEEE Transactions on Control Systems Technology 19(5): 1075-1089.

[2] Bartoszewicz, A. (1998). Discrete-time quasi-sliding-mode control strategies, IEEE Transactions on Industrial Electronics 45(4): 633-637.

[3] Bartoszewicz, A. and Adamiak, K. (2018). Model reference discrete-time variable structure control, International Journal of Adaptive Control and Signal Processing 32(10): 1440-1452.

[4] Bartoszewicz, A. and Adamiak, K. (2020). Discrete-time sliding-mode control with a desired switching variable generator, IEEE Transactions on Automatic Control 65(4): 1807-1814.

[5] Bartoszewicz, A. and Leśniewski, P. (2014). Reaching law approach to the sliding mode control of periodic review inventory systems, IEEE Transactions on Automation Science and Engineering 11(3): 810-817.

[6] Boccadoro, M., Martinelli, F. and Valigi, P. (2008). Supply chain management by H-infinity control, IEEE Transactions on Automation Science and Engineering 5(4): 703-707.

[7] Boiko, I., Fridman, L., Pisano, A. and Usai, E. (2008). A Comprehensive Analysis of Chattering in Second Order Sliding Mode Control Systems, Springer, Berlin/Heidelberg, pp. 23-49.

[8] Cao, P. and Xie, J. (2016). Optimal control of an inventory system with joint production and pricing decisions, IEEE Transactions on Automatic Control 61(12): 4235-4240.

[9] Chołodowicz, E. and Orłowski, P. (2023). Switching robust neural network control of perishable inventory with fixed shelf life products under time-varying uncertain demand, Journal of Computational Science 70(1): 102035.

[10] Drakunov, S. and Utkin, V. (1989). On discrete-time sliding modes, IFAC Proceedings Volumes 22(3): 273-278.

[11] Drakunov, S. and Utkin, V. (1992). Sliding mode control in dynamic systems, International Journal of Control 55(4): 1029-1037.

[12] Draženović, B. (1969). The invariance conditions in variable structure systems, Automatica 5(1): 287-295.

[13] Edwards, C. and Spurgeon, S. (1998). Sliding Mode Control: Theory And Applications, Taylor & Francis, London.

[14] Framinan, J.M. (2022). Modelling Supply Chain Dynamics, Springer, Cham.

[15] Gao, W., Wang, Y. and Homaifa, A. (1995). Discrete-time variable structure control systems, IEEE Transactions on Industrial Electronics 42(2): 117-122.

[16] Golo, G. and Milosavljević, Č. (2000). Robust discrete-time chattering free sliding mode control, Systems & Control Letters 41(1): 19-28.

[17] Hamdi, H., Rodrigues, M., Rabaoui, B. and Benhadj Braiek, N. (2021). A fault estimation and fault-tolerant control based sliding mode observer for LPV descriptor systems with time delay, International Journal of Applied Mathematics and Computer Science 31(2): 247-258, DOI: 10.34768/amcs-2021-0017.

[18] Hung, J., Gao, W. and Hung, J. (1993). Variable structure control: A survey, IEEE Transactions on Industrial Electronics 40(1): 2-22.

[19] Ignaciuk, P. and Bartoszewicz, A. (2010a). Linear-quadratic optimal control strategy for periodic-review inventory systems, Automatica 46(12): 1982-1993.

[20] Ignaciuk, P. and Bartoszewicz, A. (2010b). LQ optimal sliding mode supply policy for periodic review inventory systems, IEEE Transactions on Automatic Control 55(1): 269-274.

[21] Kaynak, O. and Denker, A. (1993). Discrete-time sliding mode control in the presence of system uncertainty, International Journal of Control 57(5): 1177-1189.

[22] Liu, J. and Wang, X. (2011). Advanced Sliding Mode Control for Mechanical Systems: Design, Analysis and MATLAB Simulation, Springer, Berlin/Heidelberg.

[23] Ordaz, P., Romero-Trejo, H., Cuvas, C. and Sandre, O. (2024). Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation, International Journal of Applied Mathematics and Computer Science 34(1): 29-43, DOI: 10.61822/amcs-2024-0003.

[24] Steinberger, M., Horn, M. and Fridman, L. (Eds) (2020). Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice, Springer, Cham.

[25] Utkin, V. (1984). Variable structure systems: Present and future, Automation and Remote Control 44(9): 1105-1220.

[26] Utkin, V. (1992). Sliding Modes in Control and Optimization, Springer, Berlin.

[27] Utkin, V., Guldner, J. and Shi, J. (1999). Sliding Mode Control in Electromechanical Systems, Taylor & Francis, London.

[28] Utkin, V. and Lee, H. (2006). Chattering problem in sliding mode control systems, International Workshop on Variable Structure Systems, VSS’06, Alghero, Italy, pp. 346-350.

[29] White, A. S. (1999). Management of inventory using control theory, International Journal of Technology Management 17(1): 847.

[30] Zipkin, P. (2000). Foundations of Inventory Management, McGraw-Hill, New York.