Siddiqui presented a mixed-integer bi-objective optimization program to solve routing and scheduling of crude oil tankers from a cost and risk perspective. A two-phase heuristic was proposed to determine routing and scheduling for the shipping company and showed the influence of benefits obtainable through VMI. Otherwise, a vendor managed inventory (VMI) service in tramp shipping was considered by Hemmati. They proposed an adaptive large neighborhood search (ALNS) for solving the problem, which was used to provide best known results for the benchmark instances. presented a benchmark suite for ship routing and scheduling problems from industrial and tramp shipping. An adaptive large neighborhood search-based heuristic was proposed. They considered owner ships and tramp ships for industrial ship routing problem. Lee solved an industrial ship routing problem of heterogeneous ships. One characteristic of the problem was that, in contrast to the problem discussed above, each ship was capable to carry several different products simultaneously in separate cargo tanks. The arbitrary split model provides better results but cannot solve large instances. The discrete split model provides quicker results but lower quality solutions. Hennig considered the crude oil tanker routing and scheduling problem with split pickup and split delivery and proposed two approaches to solve this problem. Armas focused on the ship routing and scheduling problem with discretized time windows and proposed a hybridization of a greedy randomized adaptive search procedure and a variable neighborhood search (GRASP–VNS). Here, service quality was a key consideration by them. Thai proposed and validated a service quality (SQ) model for tramp shipping. In recent years, scholars have conducted an in-depth exploration of the problem of tramp ship routing and scheduling. Research results can not only deepen the study of the theory of tramp scheduling but also to effectively solve the tramp shipping schedule considering carbon emissions problems faced by companies to provide theoretical guidance. The effectiveness of the proposed model and algorithm is verified by an example, which also confirms that ship scheduling and sailing speed joint optimization can reduce costs and carbon emissions. Then the route is generated according to the time constraint, and finally, the neighborhood search strategy is adopted to improve the solution quality. Firstly, the ship type is matched with the cargo. A genetic simulated annealing algorithm based on a variable neighborhood search is proposed to solve the problem. In view of the tramp ship scheduling with speed optimization problem, considering carbon emissions, the configuration of owner ships and charter ships, and the impact of sailing speed on ship scheduling with the target of minimizing the total costs of shipping companies, multi-type tramp ship scheduling and speed optimization considering carbon emissions is established. Therefore, shipping companies need to consider environmental impacts while pursuing benefits. The International Maritime Organization (IMO) proposed to reduce the total CO 2 emissions of the maritime sector by 50% by 2050, and strive to gradually achieve the zero-carbon target.
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