An accurate forecast of the electricity consumption is particularly important to both consumers and system operators. The purpose of this study is to develop a forecasting method that provides such an accurate forecast of the month-ahead hourly electricity consumption in the case of medium industrial consumers, therefore assuring an intelligent energy management and an efficient economic scheduling of their resources, having the possibility to negotiate in advance appropriate billing tariffs relying on accurate hourly forecasts, in the same time facilitating an optimal energy management for the dispatch operator. The forecasting method consists of developing first non-linear autoregressive, with exogenous inputs (NARX) artificial neural networks (ANNs) in order to forecast an initial daily electricity consumption, a forecast that is being further processed with custom developed long short-term memory (LSTM) neural networks with exogenous variables support in order to refine the daily forecast as to achieve an accurate hourly forecasted consumed electricity for the whole month-ahead. The obtained experimental results (highlighted also through a very good value of 0.0244 for the root mean square error performance metric, obtained when forecasting the month-ahead hourly electricity consumption and comparing it with the real consumption), the validation of the developed forecasting method, the comparison of the method with other forecasting approaches from the scientific literature substantiate the fact that the proposed approach manages to fill a gap in the current body of knowledge consisting of the need of a high-accuracy forecasting method for the month-ahead hourly electricity consumption in the case of medium industrial consumers. The developed forecasting method targets medium industrial consumers, but, due to its accuracy, it can also be a useful tool for promoting innovative business models with regard to industrial consumers willing to produce a part of their own electricity using renewable energy resources, benefiting from reduced production costs and reliable electricity prices.