The opportunistic replacement problem with individual component lives

We consider an extension of the opportunistic replacement problem, which has been studied by Dickman, Epstein and Wilamowsky [3], Andréasson [2], and Andréasson et al. [1], that allows the individuals of the same component to have nonidentical lives. Formulating and solving this problem defines a first step towards solving the opportunistic replacement problems with uncertain component lives. We show that the problem is NP-hard even with time independent costs, and present two mixed integer linear programming models for the problem. We show that in model I the binary requirement on the majority of the variables can be relaxed; this is in contrast to model II and Andréasson’s [2] model. We remove all superfluous variables and constraints in model I and show that the remaining constraints are facet inducing. We also utilize a linear transformation of model I to obtain a stronger version of model II, model II+, that inherits the polyhedral properties of model I. Numerical experiments show that the solution time of model I is significantly lower than the solution times of both model II and Andréasson’s model. It is also somewhat lower than the solution time of model II+