## 2 Literature Review  
### Ship Routing and Scheduling Problems  
For many decades, ship routing and scheduling problems (SRSP) have been a broad topic of research. In fact, a review of the research concerning ship routing and scheduling complications has been published roughly every 10 years. In the early 1980s, [PERSON] [9] reviewed the work in this field and then delivered a revised summary of correlated work in the field of SRSP from the 1980s and the 1990s ten years later [10]. Unfortunately, there has been little change to the shortage of articles in this area. [PERSON] et al. [11] also examined research on ship scheduling and routing from a different perspective. Carrier collaboration, computer-aided decision support systems, software/hardware development, and supply chain management are a few of the trends that have emerged in recent decades. [PERSON] et al. [12] published material from 2002 to 2011, and this is detailed in a recent summary of the SRSP. Four basic models used in this field were critically reviewed, and SRSP research trends were identified. We found that several studies had proposed several approaches to solve the SRSP decades ago.  
[PERSON] and [PERSON] [13] presented a tabu search heuristic method to solve the ship routing and scheduling problem with the transport of bulk products. The objective function maximizes the revenue for all cargo using the route. [PERSON] et al. [14] proposed a large neighborhood search heuristic method for the ship routing and scheduling problem with split loads to maximize profit for bulk product transportation. [PERSON] et al. [15] presented a branch-price-and-cut algorithm to solve a maritime pickup and delivery problem with time windows and split loads. The objective was to maximize the total profit. [PERSON] and [PERSON] [16] presented a simulated annealing-based algorithm to solve the ship routing problem to minimize cost. [PERSON] and [PERSON] [17] proposed a heuristic algorithm based on the column generation method to solve the ship routing and scheduling problem with split deliveries to minimize the total distance and satisfy the capacity of tankers. [PERSON] and [PERSON] [18] formulated a mixed integer programming model for the industrial ship routing problem with split delivery to reduce the operation costs. An adaptive large neighborhood search-based heuristic model was proposed to solve the problem. [PERSON] et al. [PERSON] et al. (2018) formulated a mixed integer non-linear programming model to solve the sustainable integrated dynamic ship routing and scheduling problem to reduce carbon emissions. They used particle swarm optimization with composite particles to solve the problem. [PERSON] et al. [PERSON] et al. (2018) presented a fleet routing and scheduling problem with uncertain time window constraints. They solved the problem using the column generation optimization technique. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) proposed a Lagrangian relaxation-based decomposition algorithm to solve liner ship routing and freight assignment problems. [PERSON] et al. [PERSON] et al. (2018) proposed a multi-start heuristic method for ship routing and scheduling by an oil company to minimize transportation costs and the number of consecutive dockings at platforms and terminals. [PERSON] (2018) formulated a mixed integer programming model for a ship routing and scheduling problem for a steel plant cluster based alongside the Yangtze River. The proposed model was solved using an exact solution approach based on a dynamic programming algorithm.