Multi-echelon inventory optimization in closed-loop supply chain

Abstract

In this paper, we are interested in the stock control in the closed-loop supply chain and its application to the cylinder packaged gas supply chains of Air Liquide company. Air Liquide is a multinational company producing and distributing industrial and medical gases. Firstly, we introduce a new classification of demand profile and perform a comprehensive study of the goodness of fit of demands sizes and time between successive demands based on real data. As well known in the literature (Boylan and Syntetos (2021)), we find that negative binomial distribution fits better demand sizes and intervals. Secondly, we explain how to use a single echelon model that is easy to implement on the field, to control inventory and compute the stock target in the observable part of the closed-loop supply chain. It is modeled as a multi-echelon serial inventory system. Finally, we perform numerical analysis and comparisons of methods to compute the stock target of the observable part of the closed-loop supply chain with real data. Those methods are derivated from the up-to-level periodic inventory review policy where we vary the statistical distribution of the demand and the measure of the service level. Using the Item Fill Rate (IFR) as a service level measure in the stock target calculation, reduce the stock target by more than 10% compared to the stock target obtained using the Cycle Service Level (CSL). We also investigate methods using compound Poisson distribution for demand models.