A decomposition and coordination method for optimising ( Q , S ) policies in a two-echelon distribution system with joint replenishment

AbstractA continuous-review, two-echelon distribution system with one central distribution centre (CDC) and multiple regional distribution centres (RDCs) is studied. The CDC jointly replenishes its inventories of multiple items from an external supplier, while each RDC replenishes its inventories of the items from the CDC. Each RDC faces a Poisson demand for each item, and the inventories of each stock in the system are controlled by a (Q, S) policy. Under this policy, an order is placed by a stock whenever its aggregate demand since the last order reaches a given quantity, and the inventory position of each item is raised up to its order-up-to level after the order placement. The objective is to optimise these (Q, S) policies so that the expected total cost of this system is minimised. We propose a decomposition and coordination method for this optimisation after deriving analytically the cost function of the system. Our extensive numerical experiments demonstrate the effectiveness of the proposed method. Furthermore, a parameter sensitivity analysis is conducted to analyse the impacts of some key system parameters on the performance of the method, and managerial insights are provided for optimising distribution systems with joint replenishment and real applications of the method.KEYWORDS: Inventory managementjoint replenishmentdistribution systemdecomposition and coordinationoptimisation Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.Additional informationFundingThis work was supported by China Scholarship Council with [grant number 201806950117].Notes on contributorsLei WangLei Wang received his B.Eng. and M.Sc. degrees in logistics engineering from Wuhan University of Technology, China, in 2017 and 2019, respectively. He received his Ph.D. degree in system security and optimisation from University of Technology of Troyes, France, in 2023. He has published an article in the Computers & Operations Research. His current research interests include inventory management, supply chain optimisation, and operations research.Haoxun ChenHaoxun Chen received his B. S. degree in applied mathematics from Fudan University, China, in 1984, his Master and Ph.D. degree in systems engineering in 1987 and 1990, respectively, from Xi’an Jiaotong University, China. He was with Xi’an Jiaotong University as a Lecturer from 1990 to 1992 and as an Associate Professor from 1993 to 1996. He visited INRIA-Lorraine, France, as a Visiting Professor, in 1994, University of Magdeburg, Germany, as a Research Fellow of Alexander von Humboldt Foundation, in 1997 and 1998, and University of Connecticut as an Assistant Professor in 1999 and 2000. He joined University of Technology of Troyes, France, in 2001 and has been a Full Professor since 2004. His research interests include supply chain inventory management, collaborative logistics, combinatorial auctions, game theory, and data envelopment analysis. He has published more than 170 papers in international journals and conference proceedings. He received King-Sun Fu Memorial Best Transactions Paper Award from IEEE Robotics and Control Society in 1998 and National Natural Science Award (China) of Second-Class in 2005. He was responsible for more than ten academic and industrial research projects such as a French ANR (Agence Nationale de la Recherche) project on collaborative logistics and an AIR (Alibaba Innovative Research) project on inventory management.