Motivated by reliability/availability concerns in chemical plants, this paper proposes MINLP models to determine the optimal selection of parallel units considering the trade-off between availability and cost. Assuming an underlying serial structure for availability, we consider first a case where the system transitions between available and unavailable states, and second the case with an intermediate state at half capacity. Two non-convex MINLP models maximizing net profit are introduced for the two cases. In addition, a bi-criterion MINLP model is proposed to maximize availability and to minimize cost for the first case. It is shown that the corresponding epsilon-constrained model, where the availability is maximized subject to parametrically varying upper bound of the cost, can be reformulated as a convex MINLP. Availability is also incorporated in the superstructure optimization of process flowsheets. The performances of the proposed models are illustrated with a methanol synthesis and a toluene hydrodealkylation process. (C) 2017 Elsevier Ltd. All rights reserved.