The stochastic opportunistic replacement problem, part II: a two-stage solution approach

In Almgren et al. (The opportunistic replacement problem: analysis and case studies, preprint, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Goteborg, Sweden, 2011) we studied the opportunistic replacement problem, which is a multi-component maintenance scheduling problem with deterministic component lives. The assumption of deterministic lives is a substantial 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 decomposition 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 all four instances considered. Furthermore, the numerical experiments show that decisions based on the stochastic programming approach compared with simpler maintenance policies yield maintenance decisions with a significantly lower expected total maintenance cost on two out of the four instances tested, and an equivalent maintenance cost compared to the best policy on the remaining two instances.