Like many other service organizations, drop-in peer tutoring centers often struggle to determine the required number of qualified tutors necessary to meet learner expectations. Service work is largely a response to probabilistic calls for staff action and therefore difficult to forecast with precision. Moreover, forecasting models under long planning horizons often lack the complexity or specificity necessary to accurately predict flexible labor demand due to sparse availability of influential model inputs. This study builds upon the flexible demand literature by exploring the use of neural networks for labor demand forecasting for a drop-in peer tutoring center of a large university. Specifically, this study employs a neural network solution that includes a genetic algorithm to search for optimal solutions using evolutional processes. The proposed forecasting model outperforms traditional smoothing and extrapolation forecasting methods.