Robust Spare Parts Inventory Management

Abstract

We study spare parts inventory management. Most conventional spare parts inventory control models assume that the demand follows a Poisson process with a known rate. However, this assumption may not hold, particularly when limited data is available for estimating the demand process. Thus, this paper delves into how to deal with demand process uncertainty in the context of spare parts inventory management.

We propose an adaptive robust optimization (ARO) approach for multi-item, single-location spare parts inventory control with lost sales. We show how the ARO problem can be reformulated as a deterministic integer programming problem with an exponential number of constraints. Based on insight obtained from the reformulation, we subsequently introduce the iterative projection in descending order (IPDO) algorithm, which is efficient and finds, under some conditions, an optimal solution. Since only a few constraints are active in an optimal solution, we propose a more time-efficient algorithm, called the constraint generation algorithm (ConGA). We perform comprehensive simulation-based experiments with non-Poissonian demand to demonstrate that our ARO model outperforms the conventional model in achieving a higher fill rate at a lower investment cost.

Our robust spare parts inventory control model has huge potential to deliver value to maintenance service providers of expensive equipment. To demonstrate the applicability of our model, we conduct a case study at ASML, a lithography machine manufacturer. This study confirms our experimental findings that our model is reliable and cost-effective in achieving the target service performance, making it attractive for ASML and other companies.

Keywords: robust optimization, inventory control, spare parts, demand uncertainty