OPTIMIZATION OF THE SELECTIVE MAINTENANCE PROBLEM FOR LARGE-SCALE SYSTEMS UNDER UNCERTAINTY

Abstract

As complex engineering systems have become more prevalent in recent years, the importance of reliability and maintenance has become increasingly apparent. Maintenance is essential to keep systems functioning properly and ensure that they perform their intended functions. However, limited resources such as budget, time, and repairperson availability can make it challenging to perform all necessary maintenance. In these situations, it is crucial to optimally allocate available maintenance resources to carefully selected components within a system and perform the necessary maintenance actions in order to ensure satisfactory performance after maintenance. Such a maintenance policy is called selective maintenance (SM). When tasks are assigned to multiple repairpersons, potentially with different skill levels and costs, it is referred to as the joint selective maintenance and repairperson assignment problem (JSM--RAP).

This dissertation explores four themes dealing with the optimization of JSM--RAP for large-scale systems under uncertainty. The dissertation starts with the first theme which provides a critical review of SM literature, identifying challenges and potential areas for future research. The second theme introduces four column-generation-based algorithms to effectively address the JSM--RAP for large-scale systems. The third theme presents a piecewise-linear-approximation-based approach PLA and a distributionally robust chance-constrained program with a Wasserstein ambiguity set (DRC-W) to handle uncertain maintenance duration in large-scale instances of the JSM--RAP. The fourth theme reformulates the JSM--RAP as a mixed-integer exponential conic program before a robust optimization framework is used to capture the maintenance quality uncertainty through non-symmetric budget uncertainty sets allowing the level of decision-maker conservatism to be controlled.

The proposed JSM--RAP models are applied to several illustrative examples. The results demonstrate the effectiveness and advantages of the proposed models.