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No abstract

We consider a class of convex approximations for totally unimodular (TU) integer recourse models and derive a uniform error bound by exploiting properties of the total variation of the probability density functions involved. For simple integer recourse models this error bound is tight and improves the existing one by a factor 2, whereas for TU integer recourse models this is the first nontrivial error bound available. The bound ensures that the performance of the approximations is good as long as the total variations of the densities of all random variables in the model are small enough.

We consider the problem of scheduling time-based preventive maintenance under uncertainty in the lifetime distribution of a unit, with the understanding that every time a maintenance action is carried out, additional information on the lifetime distribution becomes available. Under such circumstances, typically either point estimates for the unknown parameters are used, or expected costs are minimized taking the uncertainty in the parameters into account. Both approaches, however, ignore that the uncertainty is reduced much faster if preventive maintenance actions are postponed. Although this initially leads to higher costs due to a higher risk of breakdowns, the obtained additional information can be exploited thereafter as it enables better maintenance decisions going forward. We assess the longterm benefits of initially postponing preventive maintenance, and perform a numerical study to identify under what circumstances these benefits are largest. This study is the first to recognize that the choice of a maintenance strategy influences the information that becomes available, and aims to initiate follow-up research in the area of maintenance planning.