In this paper we study a kind of transshipment problem，in which the flows through the crossdock are constrained by fixed transportation schedules with single release and single delivery，cargos can be delayed in crossdocks but any delay at the last time point of time horizon will incur inventory penalty cost，and the objective is to find a transshipment scheme with minimum cost． The problem is proved to be NP-hard in the strong sense in this paper． We therefore focus on developing efficient heuristics． Based on the problem structure， we propose a self-adaptive genetic algorithm with neighborhood search ( AGA with NS) to solve the problem efficiently． Computational experiments under different scenarios show that AGA with NS outperforms CPLEX solver，meanwhile，in order to further test the effectiveness of the adaptive scheme and neighborhood search，we also conduct computational experiments by different algorithms such as AGA without NS，GA with NS and PACO，and GA with NS and PUCO． Finally the results show that AGA with NS is the best one among these algorithms for this problem．