Dynamic models of closed-loop supply chain and robust H∞ control strategies

To meet the current environmental challenges and sustainable development, closed-loop supply chain (CLSC) management has become increasingly important and urgent. In this paper, we mainly consider three uncertainties: (1) uncertainty of time-delay in re-manufacturing and returns, (2) uncertainty of system cost parameters, (3) uncertainty of customers’ demand disturbances. Using control theories we dynamically analyse and establish a class of dynamic closed-loop supply chain models of linear discrete time system, including the product return model, the re-manufacturing model and the third party reverse logistic providers (3PRLP) collecting model. Furthermore, we analyse the robust operations in the closed-loop supply chains and bring forward relative strategies with robust H∞ control methods. Finally, according to the practical operations of scrap supply chain in the Chinese steel industry, we carry out some simulation calculations to prove how our proposed robust H∞ control strategies can restrain all uncertainties of our closed-loop supply chain system. Our analyses and results may be helpful for further insight into closed-loop supply chain uncertain operations and production control, for both theoretical researchers and practitioners, especially for those in the Chinese steel manufacturing industry.