Solving integrated production and condition-based maintenance planning problems by MIP modeling

It has been demonstrated that integrating maintenance scheduling and production planning can lead to substantial savings. However in these works the associated optimization problems are solved by enumerating all (exponentially many) maintenance schedules. This has led these researchers to either solve instances of very small sizes, or consider cyclic maintenance schedules only to limit the possibilities to a small (polynomial) number. We show here how to formulate these problems as (strong) mixed-integer linear programs, and then solve them using off-the-shelve MIP solvers. We demonstrate the efficiency of the proposed approach to solve problems of up to 10 products and 24 time periods, sizes that were simply unreachable before. We also illustrate the value of using non-cyclic maintenance schedules when the demand varies over time, with savings of up to 41 % compared to cyclic schedules.