In this work, a class of model predictive control problems with mixed real-valued and binary control signals is considered. The optimization problem to be solved is a constrained Mixed Integer Quadratic Programming (MIQP) problem. The main objective is to derive a distributed algorithm for limiting the search space in branch and bound approaches by tightening the lower and upper bounds of objective function. To this aim, a distributed algorithm is proposed for the convex relaxation of the MIQP problem via dual decomposition. The effectiveness of the approach is illustrated with a case study.