Solving a multi-echelon inventory-location problem utilising an efficient Lagrangian relaxation-based heuristic

This paper considers an integrated inventory-location problem in which a single product is supplied and distributed through a multi-echelon supply chain including a number of suppliers, distribution centres (DCs), and retailers. It adopts the well-known periodic review inventory control policy (R, S) at DCs. The problem is formulated as a mixed integer nonlinear programming problem and is solved utilising a Lagrangian relaxation-based heuristic. One of its main focuses is to reduce processing time, particularly when dealing with large-size problems. This is achieved via an additional step which converts the lower bound of the Lagrangian relaxation algorithm to an appropriate upper bound. Furthermore, we examine all the combinations of the constraints of the model when selecting constraints to be relaxed. The computational results confirm the efficiency of the proposed approach (i.e., an obtained average time of around 8 minutes with an optimality distance of less than 3%).