Distributionally-robust chance-constrained optimization of selective maintenance under uncertain repair duration

Abstract

The joint selective maintenance and repairperson assignment problem with uncertain duration of maintenance actions is studied in this paper. This problem arises in mission-oriented assets that perform sequences of missions interspersed with scheduled pauses to allow maintenance activities. The goal is to find the optimal subset of components to maintain and the maintenance level to be carried out by each repairperson that maximizes system reliability for the following mission. We first reformulate the complex objective function via single-variable concave functions before applying piecewise-linear approximation. This tight approximation enables large instances of the problem to be solved efficiently. We also consider the commonly encountered case of probabilistic maintenance duration with their distributions estimated from limited historical data samples. Distributionally-robust chance constraints (DRCCs) are employed to ensure that the maintenance tasks assigned to each repairperson can be completed within the break for a set of distributions contained in a Wasserstein-1 ball around the empirical distribution of the field data. A CVaR-based tractable approximation is applied to the DRCCs such that the problem can be reformulated into a mixed integer linear program readily handled by standard solvers. Results from the numerical experiments conducted on large benchmark instances demonstrated the computational efficiency of the proposed models and the added value of considering distributional ambiguity when dealing with uncertain maintenance duration.