A Multi-Item Spare Parts Inventory Model with Customer Differentiation

We consider a single warehouse where spare parts of multiple stock-keeping units are kept on stock to serve customers with (close-to-)identical machines. Customers are divided into multiple customer classes, and a target aggregate fill rate is set per class. In order to get differentiated service levels, critical level policies are assumed. We formulate a multi-item, single-stage spare parts inventory model for this problem, with the objective to minimize the inventory investment under the condition that all target aggregate fill rates are met. We develop a solution procedure based on Lagrange relaxation, in order to obtain both a heuristic solution and a lower bound for the optimal costs. Underlying subproblems are solved by applying product-form solutions for closed queueing networks, an exact optimization procedure for a single-item spare parts inventory problem, and linear programming theory. An extensive computational experiment shows that the gap between the costs of the heuristic solution and the lower bound is small in general (on average 1.5%), and that computation times are limited (e.g., 3 minutes for instances with 20-100 items and 5 customer classes). The solution procedure is also applied to a case at ASML, a manufacturer of so-called step and scan systems, which are used for the production of integrated circuits. For their situation, applying critical level policies gives 10-20% reduction in inventory investment in comparison to simply using basestock policies (without critical levels) and providing the highest target aggregate fill rate to all customer classes. Although the focus of this paper is on the customer differentiation problem, our approach is described in general terms and seems applicable to several other multi-item spare parts problems.