This paper presents a neural network approach with successful implementation for the robot task-sequencing problem. The problem addresses the sequencing of tasks comprising loading and unloading of parts into and from the machines by a material-handling robot. The performance criterion is to minimize a weighted objective of the total robot travel time for a set of tasks and the tardiness of the tasks being sequenced. A three-phased parallel implementation of the neural network algorithm on Thinking Machine's CM-5 parallel computer is also presented which resulted in a dramatic increase in the speed of finding solutions. To evaluate the performance of the neural network approach, a branch-and-bound method and a heuristic procedure have been developed for the problem. The neural network method is shown to give good results and is especially useful for solving large problems on a parallel-computing platform. 2000 Elsevier Science Ltd. All rights reserved.