  We propose a dual dynamic integer programming (DDIP) framework for solving
multi-scale mixed-integer model predictive control (MPC) problems. Such
problems arise in applications that involve long horizons and/or fine temporal
discretizations as well as mixed-integer states and controls (e.g., scheduling
logic and discrete actuators). The approach uses a nested cutting-plane scheme
that performs forward and backward sweeps along the time horizon to adaptively
approximate cost-to-go functions. The DDIP scheme proposed can handle general
MPC formulations with mixed-integer controls and states and can perform
forward-backward sweeps over block time partitions. We demonstrate the
performance of the proposed scheme by solving mixed-integer MPC problems that
arise in the scheduling of central heating, ventilation, and air-conditioning
(HVAC) plants. We show that the proposed scheme is scalable and dramatically
outperforms state-of-the-art mixed-integer solvers.
