The production control system for a shop can be viewed as consisting of three sequential stages, the order-promising stage, the order-release stage, and the dispatching (or shop floor) stage. The first stage, wherein a customer's job arrives and is assigned a due date, provides the focus for this research. In particular, the performance of six regression-based due-date assignment rules found in the literature is compared with due dates determined by a neural network. The purpose is to see whether neural networks hold any promise for application in this area. For the particular shop and the conditions studied, it is found that the neural network outperforms all six conventional rules according to mean-absolute-deviation (MAD) and standard-deviation-of-lateness (SDL) criteria, although for one rule on the latter criterion, the difference is not statistically significant. Further analysis indicates that this conclusion generally holds both when the amount of data available is varied and a second, more structured shop is studied. On a third shop with random routings, the neural network outperforms the best conventional method according to the MAD measure, but results are mixed for the SDL criterion. The superior performance of the neural network leads us also to evaluate a regression model nonlinear in its independent variables, a case not considered in the due-date literature. The nonlinear model generally outperforms the conventional rules on MAD and SDL. The neural network outperforms the nonlinear model on MAD, while the results for SDL are not as clear.