The Cross-Docking Assignment Problem (CDAP) is a challenging optimization problem in supply chain management with important practical applications in the trucking industry. The goal is to assign incoming trucks (outgoing trucks) to inbound (outbound) doors to minimize the material handling cost within a cross-docking platform while respecting the capacity and assignment constraints. A capacity constraint is imposed on each inbound/outbound door and an associated assignment constraint is imposed on each incoming/outgoing truck requiring it to be assigned to only one inbound/outbound door. To solve this NP-hard optimization problem, we develop two novel heuristics based on Probabilistic Tabu Search utilizing a new neighborhood structure applicable both to CDAP and related problems. The proposed heuristics are evaluated on 99 benchmark instances from the literature, disclosing that our approaches outperform recent state-of-the-art approaches by reaching 45 previous best-known solutions and discovering 53 new best-known solutions while consuming significantly less CPU time.