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This paper presents a set covering model based on route representation to solve the green ship routing and scheduling problem (GSRSP) with berth time-window constraints for multiple bulk ports. A bi-objective set covering model is constructed with features based on the minimization of the total CO2 equivalent emissions and the total travel time subject to a limited number of berths in each port, berthing time windows, and the time window for each job. The solutions are obtained using the ε-constraint method, after which a Pareto frontier is plotted. This problem is motivated by the operations of feeder barges and terminals, where the logistics control tower is used to coordinate the routing and berthing time of its barges. We show that the proposed method outperforms the weighted sum method in terms of the number of Pareto solutions and the value of the hypervolume indicator.

A Set Covering Model for a Green Ship Routing and Scheduling Problem with Berth Time-Window Constraints for Use in the Bulk Cargo Industry