A cruise company faces three decision problems: at a strategic level, to decide in which maritime area and in which season window to locate each ship of its fleet; at a tactical level, given a ship in a maritime area and in a season window, to decide which cruises to offer to the customers; at an operational level, to determine the day-by-day itinerary, in terms of transit ports, arrival and departure times and so on. This paper focuses on the tactical level, namely on the Cruise Itineraries Optimal Scheduling (CIOS), aiming at determining a scheduling of cruises with the objective to maximize the revenue provided by a given ship placed in a specified maritime area, in a selected season window, taking into account a number of constraints. In particular, we refer to luxury cruises, implying several additional considerations to be taken into account. We propose an Integer Linear Programming (ILP) model for such a CIOS problem. This model has been experimented by a major luxury cruise company to schedule the itineraries of its fleet in many geographical areas all over the world. A commercial solver has been used to solve the ILP problem.Herewe report, as illustrative examples, the results obtained on some of these real instances to showthe computational viability of the proposed approach.