Semi-liner and liner service synchronization with desulfurization strategies subject to emission control areas

Semi-liner services have been increasingly adopted by many shipping companies to capture high-value spot cargoes. However, their limited capacity, deviation cost, and restricted network coverage constrain the possibility to serve more profitable cargo demand. A promising way to overcome these limitations is to synchronize the operations of the semi-liner service with a fixed liner service by transshipment. Such synchronization is challenging because it requires joint decisions on ship routing, optional port selection, cargo allocation, sailing speed, and transshipment timing, all of which further interact with the current Emission Control Area (ECA) requirements in calling multi-calling ports. To address these challenges, this study proposes a semi-liner and liner service synchronization (S&LS2) problem with practical significance that determines the semi-liner’s operation and transshipment plan, as well as the liner’s acceptance of transshipment cargoes, under two desulfurization strategies: fuel switching and scrubber installation. We formulate a mixed-integer linear programming (MILP) model for the S&LS2 problem and develop an effective column generation based heuristic method capable of solving real-sized instances efficiently. Numerical experiments show that the proposed method outperforms the MILP solver for large instances and produces good solutions with an optimality gap below 0.2%. The results also indicate that ships with scrubbers can be more profitable than those with fuel-switching due to their higher speed flexibility and the price spread between fuels. These findings offer practical guidance for shipping companies when planning semi-liner operations and selecting suitable emission-control strategies.