Branch-and-price algorithms for large-scale mission-oriented maintenance planning problems

This paper presents a novel column-generation-based approach for solving large-scale instances of the joint selective maintenance and repairperson assignment problem (JSM-RAP) for mission-oriented systems in industrial settings. Such systems perform consecutive missions separated by scheduled finite-duration breaks during which some of their components are imperfectly maintained by repairpersons, aiming to maximize system reliability in subsequent missions. The resulting mathematical model is computationally expensive, even for problems of moderate size. The proposed approach decomposes the JSM-RAP into a master problem and multiple subproblems that are solved to generate maintenance patterns, i.e., columns. Two methods are developed to handle the mixed-integer nonlinear subproblems: a piecewise-linear approximation and an exact reformulation into mixed-integer exponential conic programs. Branch-and-price algorithms are developed by embedding the column-generation method into a branch-and-bound tree to restore solution integrality and guarantee its optimality. Furthermore, we use a stabilization scheme to accelerate convergence. Numerical experiments validate the proposed approach and demonstrate its added value in terms of computation time and solution quality. Problem instances of very-large size, similar to real-life industrial production plants, are solved efficiently. Results also show that increasing the number of maintenance levels grants more flexibility to the optimizer to find combinations of components and maintenance actions that better use the limited resources.