Data-driven joint optimization of maintenance and spare parts provisioning: A distributionally robust approach

Abstract: This paper investigates the joint optimization of condition-based maintenance and spare provisioning, incorporating insights obtained from sensor data. Prognostic models estimate components' remaining lifetime distributions (RLDs), which are integrated into an optimization model to coordinate maintenance and spare provisioning. The existing literature addressing this problem assumes that prognostic models provide accurate estimates of RLDs, thereby allowing a direct adoption of Stochastic Programming or Markov Decision Process methodologies. Nevertheless, this assumption often does not hold in practice since the estimated distributions can be inaccurate due to noisy sensors or scarcity of training data. To tackle this issue, we develop a Distributionally Robust Chance Constrained (DRCC) formulation considering general discrepancy-based ambiguity sets that capture potential distribution perturbations of the estimated RLDs. The proposed formulation admits a Mixed-Integer Linear Programming (MILP) reformulation, where explicit formulas are provided to simplify the general discrepancy-based ambiguity sets. Finally, for the numerical illustration, we test a type-$\infty$ Wasserstein ambiguity set and derive closed-form expressions for the parameters of the MILP reformulation. The efficacy of our methodology is showcased in a wind turbine case study, where the proposed DRCC formulation outperforms other benchmarks based on stochastic programming and robust optimization.