This work describes mathematical formulations for modeling aspects of partial shutdowns in multiunit plants. The specific type of partial shutdown considered is one that permits the decoupling of affected units from the rest of the plant, thus enabling continued plant operation, albeit in a more limited fashion. Parsimonious and computationally efficient mixed-integer formulations are presented for specific discontinuous phenomena that arise in partial shutdown modeling, such as shutdown thresholds, induced shutdowns, discontinuous costs, and minimum shutdown durations. It is demonstrated that induced shutdowns (secondary shutdowns triggered by the original shutdown) can be correctly penalized in the objective by capturing the shutdown's true discontinuous economic cost. The computed optimal solution is implemented in closed-loop by employing a multitiered model predictive shutdown controller, in which a discrete-time mixed-integer dynamic optimization (MIDO) problem is embedded. Both objectives of maximizing economics and minimizing restoration (shutdown recovery) time are considered. (C) 2016 Elsevier Ltd. All rights reserved.