Robust selective maintenance optimization of series–parallel mission-critical systems subject to maintenance quality uncertainty

This paper studies the optimization of the joint selective maintenance and repairperson assignment problem when the quality of maintenance actions is uncertain, thus leading to uncertain post-maintenance reliability of system components. This situation is common in practice since maintenance actions are never perfect and are affected by several factors such as the qualification and the degree of expertise of the repairpersons, the maintenance methods and tools used, and naturally occurring operating environment variability. Using a robust optimization framework, the maintenance quality uncertainty is captured via non-symmetric budget uncertainty sets that enable the level of decision-maker conservatism to be controlled. Both the nominal (i.e., deterministic) and robust problems are reformulated as mixed-integer exponential conic programs that can be solved using currently available solvers. Extensive numerical experiments on benchmark instances show the favorable computational performance of the proposed reformulations and the value of considering maintenance quality uncertainty when developing selective maintenance plans.