We propose optimization methods to accept immediate tasks in automated warehouses. While Multi-Agent Pickup and Delivery (MAPD) problems for the automated warehouses suppose that all delivery tasks are given at planning phases, there are several situations where the system needs to accept immediate and emergent tasks in real-time in practical applications. We conducted four methods, Optimal Timing Search, Optimal Vertical Location Search, Optimal Horizontal Location Search, and Variance Minimization to assign an immediate task into already-planned schedules of MAPD. We demonstrate that the proposed methods can mitigate costs increases associated with accepting immediate tasks on the system.