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This paper deals with the problem of cruise itinerary planning which plays a central role in worldwide cruise ship tourism. In particular, the Day-by-day Cruise Itinerary Optimization (DCIO) problem is considered. Assuming that a cruise has been planned in terms of homeports and journey duration, the DCIO problem consists in determining the daily schedule of each itinerary so that some Key Performance Indicators are optimized. The schedule of an itinerary, i.e. the sequence of visited ports, the arrival and departure time at each port, greatly affect cruise operative costs and attractiveness. We propose a Mixed Integer Linear Programming (MILP) formulation of the problem with the objective of minimizing the itinerary cost due to fuel and port costs, while maximizing an itinerary attractiveness index. This latter is strongly related to the ports visited as well as to the overall schedule of the itinerary. Therefore the problem turns out to be a bi-objective optimization problem. We provide its solution in terms of Pareto optimal solution points. Each single objective MILP problem which arises is solved by using an exact algorithm, implemented in a commercial solver. We consider the day-by-day itineraries of a major luxury cruise company in many geographical areas all over the world. Here we report, as illustrative examples, the results obtained on some of these real instances.

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. Here we report, as illustrative examples, the results obtained on some of these real instances to show the computational viability of the proposed approach.

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