Approximating the Pareto frontier for bi-objective preventive maintenance and workshop scheduling: A Lagrangean lower bounding methodology for evaluating contracting forms

Abstract Effective planning of preventive maintenance plays an important role in maximizing the operational readiness of any industrial system. We consider an operating system and a maintenance workshop governed by two stakeholders who collaborate based on a mutual contract: components of the operating system that need maintenance are sent to the maintenance workshop, where necessary maintenance activities are performed and after which the maintained components are returned to the operating systems and ready to be used again. While the maintenance activities must obey the workshop capacity, the components should be returned to the operating system within a contracted time frame. For this problem, we developed in a previous work a mixed-integer linear optimization model incorporating stocks of damaged as well as repaired components, workshop scheduling, and preventive maintenance planning for the operating system. We then investigated an availability contract between the stakeholders and which is in the paper at hand compared with a turn-around time contract type, which is more often used in reality. Since, for real instance sizes, the latter leads to a computationally demanding bi-objective optimization problem, we use Lagrangean relaxation and subgradient optimization to compute local lower bounds on the set of non-dominated points, complemented with math-heuristics to identify good feasible solutions (i.e., local upper bounds). Our suggested method thus provides a bounding of the set of non-dominated points for a turn–around time contract.