This paper introduces a robust mathematical formalism for the definition of deliberative agents implemented using a case-based reasoning system. The concept behind deliberative agents is introduced and the case-based reasoning model is described using this analytical formalism. Variational calculus is used during the reasoning process to identify the problem solution. The agent may use variational calculus to generate plans and modify them at execution time, so they can react to environmental changes in real time. Reflecting the continuous development in the tourism industry as it adapts to new technology, the paper includes the formalisation of an agent developed to assist potential tourists in the organisation of their holidays and to enable them to modify their schedules on the move using wireless communication systems.