An optimization model for determining cost-efficient maintenance policies for multi with economic and structural dependencies

In most multi-component systems, the cost-efficiency of maintenance policies depends on technical structural dependencies. Motivated by the recognition that these dependencies must be accounted for in the development of optimal maintenance policies, we develop an optimization model to determine cost-efficient maintenance schedules for multi-component systems. Our main contribution is twofold. First, we introduce directed graphs as an expressive tool to represent the economic and structural dependencies of the system, including situations in which the maintenance of a given component may require other components to be disassembled or maintained. Second, we formulate a Markov Decision Process model, which is solved through the modified policy-iteration algorithm to determine the most cost-efficient policy. This policy indicates which maintenance actions consisting of disassembly and component replacement decisions are optimal when mandatory replacements must be made whenever the system fails, or the reliability of the system falls below a predefined reliability threshold. To our knowledge, this is the first model that provides optimal maintenance policies that comply with reliability requirements in the presence of constraints arising from technical structural dependencies. We illustrate the model with a realistic case study on the development of cost-efficient maintenance policies and show that its results compare favorably with heuristic maintenance policies.