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.

Abstract Machines at customers have to be provided with spare parts upon failure. Consider a number of groups of machines, for each of which a target aggregate fill rate or target average response time (waiting time) should be met. Between groups, commonality exists, i.e., some parts occur in the material breakdown structure of machines in multiple groups. Instead of using separate stocks per group of machines, we study the potential benefits of exploiting commonality by using a shared stock for all groups together. For this purpose, we formulate a multi-item single-site spare parts inventory model, with the objective to minimize the spare parts provisioning costs, i.e., inventory holding and transportation costs, under the condition that all service level constraints are met. We develop a heuristic solution procedure using a decomposition approach as in Dantzig-Wolfe decomposition, in order to obtain both a heuristic solution and a lower bound for the optimal costs. In a case study and a numerical experiment, we show that significant reductions in spare parts provisioning costs can be obtained by using shared stocks. Furthermore, we show how the size of the potential benefits behaves as a function of the number of groups, the percentage of commonality and the occurrence of commonality in cheap or expensive items.