Most scheduling problems have been demonstrated to be NP-complete problems. The Hop"eld neural network is commonly applied to obtain an optimal solution in various di!erent scheduling applications, such as the traveling salesman problem (TSP), a typical discrete combinatorial problem. Hop"eld neural networks, although providing rapid convergence to the solution, require extensive e!ort to determine coe$cients. A competitive learning rule provides a highly e!ective means of attaining a sound solution and can reduce the e!ort of obtaining coe$cients. Restated, the competitive mechanism reduces the network complexity. This important feature is applied to the Hop"eld neural network to derive a new technique, i.e. the competitive Hop"eld neural network technique. This investigation employs the competitive Hop"eld neural network to resolve a multiprocessor problem with no process migration, time constraints (execution time and deadline), and limited resources. Simulation results demonstrate that the competitive Hop"eld neural network imposed on the proposed energy function ensures an appropriate approach to solving this class of scheduling problems.