The Cruise Itinerary Schedule Design (CISD) problem determines the optimal sequence of a given set of ports of call (a port of call is an intermediate stop in a cruise itinerary) and the arrival and departure times at each port of call in order to maximize the monetary value of the utility at ports of call minus the fuel cost. To solve this problem, in view of the practical observations that most cruise itineraries do not have many ports of call, we first enumerate all sequences of ports of call and then optimize the arrival and departure times at each port of call by developing a dynamic programming approach. To improve the computational efficiency,we propose effective bounds on the monetary value of each sequence of ports of call, eliminating non-optimal sequences without invoking the dynamic programming algorithm. Extensive computational experiments are conducted and the results showthat, first, using the bounds on the profit of each sequence of ports of call considerably improves the computational efficiency; second, the total profit of the cruise itinerary is sensitive to the fuel price and hence an accurate estimation of the fuel price is highly desirable; third, the optimal sequence of ports of call is not necessarily the sequencewith the shortest voyage distance, especially when the ports do not have a natural geographic sequence.