Motivated by a real-world case study in ceramic tile production, this paper addresses the problem of determining the minimum number of pallets required to load a given set of boxes. The problem must be solved quickly to give customers an expectation of the transportation cost of their orders. In addition, not all constraints and instance data can be easily determined in advance, and the items are loaded onto the pallets by operators who mostly rely on their personal experience. Therefore, traditional model-based solution methods do not apply well, and data-driven approaches are preferable. To solve the problem, we propose a hybrid algorithm in which a machine learning technique is trained over a company dataset comprising two years of customer orders, with the aim of predicting the number of pallets required by an order. The accuracy of the machine learning technique is largely improved by including additional features, such as lower and upper bounds, in the dataset, obtained using quick optimization algorithms. The resulting hybrid algorithm has been compared with the model-based software currently used at the company, consistently providing better-quality results in shorter computing times.