Recently, Just-In-Time (JIT) production systems have much influence on the production fields. Miyazaki et al. propose a concept of actual flow time, which is a performance measure for scheduling in a JIT production environment. Scheduling problems are one of representative combinatorial optimization problems. Hopfield and Tank show that some combinatorial optimization problems can be solved by the artificial neural network system. Arizono et al. propose a neural solution for minimizing total actual flow time by the Gaussian machine. However, their method retains some problems which originate in the analog neurons. Then, we use interconnected neural networks which consist of the binary neurons whose output states take values either 0 or 1 unlike the Arizono's system. We call such a network the binary neural network. This paper deals with the scheduling problem for minimizing total actual flow time by the binary neural network.