Closed-Loop Supply Chain Inventory-Location Problem With Spare Parts in A Multi-Modal Repair Condition

In this paper, a closed-loop location-inventory problem for spare parts is presented. the proposed supply chain network includes two echelons, namely (1) distribution centers (dcs) and repairing centers (rcs) and (2) operational bases. multiple types of spare part are distributed among operational bases from distribution centers in the forward supply chain and failed spare parts from operational bases are sent back to the repairing centers to receive multi-modal repair services in the reverse supply chain. the rcs have no limitation to repair failed items and all of them should be repaired by minimizing total repairing cost. the main purpose of the proposed model is to minimize the total cost of inventory and location-allocation decisions in the proposed network in order to deal with the uncertainty nature of demand in both forward and reverse supply chains. thus, a mixed-integer nonlinear programming model is formulated for the location-allocation problem that tries to choose which dcs and rcs to be opened and to determine the repair service mode of each failed items with objective function of minimizing the total cost. furthermore, the validation of the model is tested by gams software for small-sized problem, and particle swarm optimization (pso) is proposed to solve large-sized problems in a reasonable time. finally, several sensitivity analyses are presented to evaluate the proposed model. furthermore, according to computational results, the proposed heuristic algorithm is more efficient in both cpu-time and quality of solution for medium and large size problems.