A multi-zone vapor compression system (MZ-VCS) includes a compressor connected to a set of heat exchangers controlling environments in a set of zones. A supervisory controller includes a processor configured for optimizing a cost function subject to constraints on an operation of the MZ-VCS to produce a set of values of the thermal capacity requested for the set of heat exchangers to achieve setpoint temperatures in the corresponding zones. The supervisory controller is a model predictive controller for determining the set of control inputs using a model of the MZ-VCS including a linear relationship between the thermal capacity of each heat exchanger and the temperature in a corresponding zone controlled by the heat exchanger. A set of capacity controllers, wherein there is one capacity controller for each heat exchanger, such that each capacity controller is configured for controlling the corresponding heat exchanger to achieve the requested thermal capacity.