This paper presents a heuristic algorithm to implement a model predictive controller for systems with binary inputs in which the effect of the control signal on the response partially vanishes before reaching steady state, for example systems that exhibit both fast and slow stable dynamics. The proposed algorithm is based on an iterative procedure that constructs a reduced set of suboptimal solutions. The size of this set can be set accordingly to the computing capabilities and the sample time. The iterative procedure rejects possible solutions profiting from the partial fading memory property of the system and an approximation of the optimal cost-to-go function. The properties of the proposed controller are illustrated with a simulated example of a photobioreactor. (C) 2018 Elsevier Ltd. All rights reserved.