LQ optimal and reaching law-based sliding modes for inventory management systems

Abstract

In this article, the theory of discrete sliding-mode control is used to design new supply strategies for periodic-review inventory systems. In the considered systems, the stock used to fulfil an unknown, time-varying demand can be replenished from a single supply source or from multiple suppliers procuring orders with different delays. The proposed strategies guarantee that demand is always entirely satisfied from the on-hand stock (yielding the maximum service level), and the warehouse capacity is not exceeded (which eliminates the cost of emergency storage). In contrast to the classical, stochastic approaches, in this article, we focus on optimising the inventory system dynamics. The parameters of the first control strategy are selected by minimising a quadratic cost functional. Next, it is shown how the system dynamical performance can be improved by applying the concept of a reaching law with the appropriately adjusted reaching phase. The stable, nonoscillatory behaviour of the closed-loop system is demonstrated and the properties of the designed controllers are discussed and strictly proved.

Keywords:

• sliding-mode control
• inventory control
• discrete-time systems

Acknowledgements

This work has been financed by the Polish State budget in the years 2010–2012 as a research project N N514 108638 ‘Application of regulation theory methods to the control of logistic processes’. P. Ignaciuk gratefully acknowledges financial support provided by the Foundation for Polish Science (FNP). P. Ignaciuk is also a scholarship holder of the project entitled ‘Innovative Education without Limits – Integrated Progress of the Technical University of Łódź’ supported by the European Social Fund.