Cargo airlines' Revenue Management (RM) departments oversee the acceptance/rejection process of incoming bookings. The overarching goal is to accept as many bookings as possible, hence maximizing profit, while avoiding overbooking and offloading of already accepted shipments, to ensure customer satisfaction. This whole process is characterized by great uncertainty, arising from the fact that the exact shipment dimensions and the available aircraft capacity are not always known beforehand. The decision process is further complicated by the fact that loading of shipments is generally performed by experience, resulting to inefficient use of the available space. These factors pose challenges to the acceptance/rejection of an incoming booking request, that can lead to loss of potential revenue for the airline. A novel combined forecasting and stochastic packing model is presented, that tackles the aforementioned issues. The forecasting block of our model, instead of providing point estimates, generates the probability distribution of the predicted capacity and shipment dimensions through the use of the Monte Carlo (MC) dropout technique in Long Short Term Memory (LSTM) and Multi-Layer Perceptron (MLP) network respectively. The stochastic packing block falls into the general category of Knapsack Problems and is solved using the Extreme Point (EP) heuristic within a user-defined confidence level. It uses the generated distributions to select the optimal ULD configuration and palletization strategy, and makes a decision to accept or decline an incoming booking request accordingly. For evaluation purposes, four case studies with real booking data provided by our partner airline are carried out. The results support the validity of the model as well as the efficiency and robustness of the solution method followed.