Integrated cruise fleet deployment and itinerary scheduling problem: An enhanced Benders decomposition approach

Abstract

With the growing popularity of cruise tourism, the issue of comprehensive and precise cruise management is emphasized by the industrial field, which demands effective strategies in both tactical-level cruise deployment and operational-level itinerary scheduling. This rising concern and the expectation of integrated decision, however, increase the complexity of the problem and the difficulty of optimization. This paper provides a cohesive framework and scalable algorithms for the integrated cruise fleet deployment and itinerary scheduling problem. First, to address this problem, we propose an integer programming model based on a time-expanded network that captures the movement dynamics of cruises over a planning horizon. Several problem-specific reformulations including cumulative-flow-based variables and route-based time-expanded network representation are introduced, based on which, we prove that the itinerary scheduling problem is totally unimodular and the integer variables can be relaxed. Second, we introduce a tailored Benders decomposition approach augmented by the simultaneous Magnanti–Wong method, where a valid and pre-obtainable Magnanti–Wong bound is designed, yielding Pareto-optimal cuts in small computation time in each iteration. Finally, we validate our approach using extensive numerical experiments on both simulation instances and a real case study. The results demonstrate the effectiveness of our integrated solving scheme and the practical applicability of our advanced decomposition method, marking a significant advancement in the field of cruise fleet management.