In order to solve the problem of the combination of short-term task allocation and collision avoidance path planning, considering the correlation between automatic guided vehicles (AGVs) and tasks, this paper firstly introduced the task allocation mechanism (TA) , so that a variety of task allocation methods can be generated according to the order of the total cost of task allocation from low to high. For the AGV collision avoidance path planning problem under each task allocation method, it established the main problem model of the restriction and designed the improved branch-and-cut-and-price (BCP) algorithm to solve the model, then the collision avoidance path of all AGVs can be obtained and the sum of the path lengths can be shortest. It innovatively introduced the Fox rule method for the problem that the main problem model of the restriction generated by adding the cut plane and the branch constraint is not feasible. The process of solving a scenario that helps to restore the feasibility of the model is transformed into solving the problem of the shortest path on a 3D spatio-temporal map with special weights to quickly restore the feasibility of the model or prove that the model is not feasible. It designed an accurate algorithm BCP-TA to combine TA with BCP, and used the property that the sum of the shortest collision avoidance path lengths of all AGVs must be greater than or equal to the sum of the shortest obstacle avoidance path lengths under the same task allocation mode, which helps the algorithm to converge quickly, so that the sum of the collision avoidance path lengths of all AGVs can obtain the global minimum, that is, to obtain the optimal solution of the short-term combination problem. In the final experiment, the number of AGVs and the correlation strength between AGVs and tasks were adjusted under different map sizes, and the running speed and results of BCP-TA algorithm were compared with the existing accurate algorithms CBS-TA and two-stage method, which was used to solve the combined problem of short-term task assignment and collision avoidance path planning, and the results of the experiments showed that the more complicated the algorithm's running environment was, the more obvious the advantages of BCP-TA were in terms of computational efficiency and solving results.