The stochastic opportunistic replacement problem: A two-stage solution approach

Preprint, 2011

In Almgren et al. 2009 we studied the opportunistic replacement problem, which is a multicomponent maintenance scheduling problem with deterministic component lives. The assumption of deterministic lives is a strong simplification, but valid in applications where critical components are assigned a technical life after which replacement is enforced. Here, we study the stochastic opportunistic replacement problem, which is a more general setting in which component lives are allowed to be stochastic. We consider a stochastic programming approach for the minimization of the expected cost over the remaining planning horizon. Further, we present a means to compute lower bounds on the recourse function. The lower bounds are used in the construction of a decomposition method which extends the integer L-shaped method to incorporate stronger optimality cuts. In order to obtain a computationally tractable model, a two-stage sample average approximation scheme is utilized. Numerical experiments on problem instances from the wind power and aviation industry as well as on two test instances are performed. The results show that the decomposition method is faster than solving the deterministic equivalent on the three more complex instances out of the four instances considered. Furthermore, the numerical experiments show that decisions based on the stochastic programming approach yield a lower average total maintenance cost compared to that of decisions based on simpler maintenance.