Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model

Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and the maintenance workshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon. We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.