A multicast packet switching system can replicate a packet in the window of each input port to send out the copies from different output ports simultaneously. In order to maximize the throughput, a combinatorial optimization problem must be solved in real time of finding a switching configuration which does not only satisfy the constraints on the system, but also maximizes the number of copies under transmission demands. In this paper, we focus on the one-shot scheduling problem where all the copies of selected packets must be sent out simultaneously. We propose the neural network composed of W×N binary neurons for the problem in the W-window-N-input-port system. The motion equation is newly defined with three heuristic methods. We verify the performance through simulations in up to 3-window-1000-input-port systems, where our binary neural network provides the better performance than the existing methods so as to reduce the delay time under practical situations.