A closed-loop location-inventory problem with spare parts consideration

A closed-loop location-inventory problem is considered. Forward supply chain consists of a single echelon where the distribution centers (DCs) have to distribute a single product to different retailers with random demands. Reverse supply chain also contains only one echelon where the remanufacturing centers (RCs) collect the returns from the retailers, remanufacture them as spare parts and then push them back to the retailers assigned to the DCs through the forward supply chain. The problem is to choose which DCs and RCs are to be opened and to associate the retailers with them. The problem is formulated using a mixed integer nonlinear location allocation model. An exact two-phase Lagrangian relaxation algorithm is developed to solve it. The computational results and sensitivity analysis are presented.