We study a dock assignment and truck scheduling problem arising within crossdocks. In the literature, variants of this problem are often modeled as big-M-like mixed integer programming formulations, which are known for their computational difficulties and often poor bound quality restricting their practical use. In this work, we propose a new integer programming (IP) formulation with O(n^4) variables. We then propose a Dantzig-Wolfe reformulation and an efficient branch-and-price as well as a VNS-like approach for solving real-life size instances of this model. Our extensive computational experiments confirms the efficiency of our exact method as well as that of the VNS-like approach.