With the advent of "Industry 4.0", more matrix manufacturing workshops have adopted automated guided vehicle (AGV) for material handling. AGV transportation has become a key link in manufacturing production. Traditional AGVs scheduling problem (AGVSP) is studied in depth. However, most research overlooks an important problem, in production with limited resources, the number of AGVs is insufficient. Therefore, the wait time of workstations is longer than expected. The service time of the task is delayed and the cost is increased. To solve above problem, this paper proposes the binary discrete enhanced Jaya (BDE-Jaya) algorithm. The main goal is to minimize transportation cost, including AGV traveling cost, service early penalty, and total tardiness (TTD). A key-task shift method is proposed to reduce TTD and task service early penalty. Two heuristics based on the problem features are designed to generate the initial solution. In the evolutionary stage, three offspring generation methods are used to improve the algorithm exploitation capability and exploration capability. Then, an insertion-based repair method is designed to prevent the exploitation process falling into local optimum. Furthermore, three parameters are proposed to improve the performance of the algorithm. Finally, simulation experiment shows that the proposed BDE-Jaya algorithm has significant advantages compared with other algorithms.