A heuristic approach for multi-echelon inventory optimisation in a closed-loop supply chain

This study deals with a closed-loop supply chain where inventory levels are controlled by an order-up-to inventory policy. The system under consideration is the cylinder-packaged gas supply chain of Air Liquide company, where empty cylinders used by customers are returned to be filled again by company plants. First, we examine the goodness of fit for demand distributions based on company real data. This enables us to better characterise demands pertaining to different classes of products. Then, we formulate the multi-echelon serial inventory model to be optimised and propose a heuristic to compute the target inventory levels that helps in achieving the desired customer service level while minimising the total inventory cost. The proposed heuristic is easy to implement in the field and gives results close those obtained using a simulation-optimisation approach that is more time-consuming. Finally, we perform a numerical analysis based on company real data and compare several methods that can be used to compute the target inventory levels by varying mainly two assumptions: parameters regarding demand distributions and metrics used to assess customer service levels.