Multi-item spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of two-location inventory systems for repairable spare parts in which lateral and emergency shipments occur in response to stockouts. A continuous review basestock policy is assumed for the inventory control of the spare parts. The objective is to minimize the total costs for inventory holding, lateral transshipments and emergency shipments subject to a target level for the average waiting time at each of the two locations. A solution procedure based on Lagrangian relaxation is developed to obtain both a lower bound and an upper bound of the optimal total costs. The upper bound follows from a heuristic solution. An extensive numerical experiment shows an average gap of only 0.77% between the best obtained lower and upper bounds. It also gives insights into the relative improvement achieved when moving from a no-pooling policy to a pooling policy and when moving from an item approach to a system approach. We also applied the model to actual data from an air carrier company.