Scheduling problems are considered as combinatorial optimization problems. Hopfield and Tank (1985) showed that some combinatorial optimization problems can be solved using artificial neural network systems. However, their network model for solving the combinatorial optimization problems often attains a local optimum solution depending on the initial state of the network. Recently, some stochastic neural network models have been proposed for the purpose of avoiding convergence to a local optimum solution. In this paper a scheduling problem for minimizing the total actual flow time is solved by using the Gaussian machine model which is one of the stochastic neural network models.