This paper proposes a non-centralized Model Predictive Control (MPC) scheme for a system comprised by several sub-systems. Operational constraints for each sub-system are considered as well as a single coupled constraint on the control inputs that models a limitation of the resource supplied by the controller. If the underlying optimization problem is of largescale nature, traditional MPC suffers from computational burden issues. A cause of this problem is the requirement of having centralized information to guarantee that the computed control actions satisfy the coupled constraint. In this work, a traditional MPC is made non-centralized by means of a strategy based on distributed population dynamics. The proposed methodology divides the problem into several local MPC controllers that coordinate their decisions by using a communication network without the need of a centralized scheme. It is proved that this methodology provides an optimal solution that satisfies both the operational constraints of each sub-system, and the coupled constraint of the control signals. Finally, the proposed method is compared with a traditional centralized MPC in an industrial problem that involves several continuously stirred tank reactors.