Multi-Echelon Exchangeable-Item Repair System Optimization

We consider a multi-item, multi-echelon exchangeable-item repair system with ample repair servers. Customers arriving to the system with failed items will receive any available item whereas the failed item will be either repaired onsite or sent to higher echelons for repair. To decrease the average waiting time of a random customer, managers can invest in multiple ways: increasing the number of spares, reducing repair times, improving repair capabilities, and reducing shipping times. We provide an efficient algorithm for a suboptimal budget allocation at each location in the system and derive an upper bound for the distance of the solution from the optimal solution. We derive the waiting time distribution of a random customer and the distribution of the number of customers in the system. Finally, we provide a numerical example that is motivated by a real-life situation to demonstrate the results and intuitions learned from the model.