Simultaneous Optimization of the Liner Shipping Route and Ship Schedule Designs with Time Windows

Abstract

This paper proposes to address the problem of the simultaneous optimization of the liner shipping route and ship schedule designs by incorporating port time windows. A mathematical programming model was developed to minimize the carrier’s total operating cost by simultaneously optimizing the port call sequence, ship arrival time per port of call, and sailing speed per shipping leg under port time window constraints. In view of its structure, the nonlinear nonconvex optimization model is further transformed into a mixed-integer linear programming model that can be efficiently solved by extant solvers to provide a global optimal solution. The results of the numerical experiments performed using a real-world case study indicated that the proposed model performs significantly better than the models that handle the design problems separately. The results also showed that different time windows will affect the optimal port call sequence. Moreover, port time windows, bunker price, and port efficiency all affect the total operating cost of the designed shipping route.

The System Research and Implementation for Autorecognition of the Ship Draft via the UAV

“…ere are a variety of existing draft detection methods [2], mainly including (1) artificial observation, which is vulnerable to interference from subjective factors and objective condition [3]. e observation results have a large deviation from the actual real value and need a large amount of manpower and time consumption.…”

Integrated Planning of Feeder Route Selection, Schedule Design, and Fleet Allocation with Multimodal Transport Path Selection Considered

“…To solve the route-selection model with the nonlinear functions of sailing time and fuel consumption, the common method is to first linearize the nonlinear functions and then use CPLEX to solve the linear model [12,25,32,47]. However, there is currently no effective method to linearize the nested Logit model used in this study.…”

“…The relaxed model is still a mix-integer nonlinear programming model, but it can be linearized completely [8,27,46,47,49]. The linearization process is as follows:…”

A goal-programming based optimal port docking scheme under COVID-19

“… De et al (2020) studied a ship routing problem considering the concept of time window and fuel management, established a mixed integer linear programming model, and proposed a new particle swarm optimization algorithm (called BVNS-PSO) to solve it, so as to realize reasonable arrangements of ship berthing. Jiang et al, 2020a , Jiang et al, 2020b proposed the need to optimize the shift route and shipping schedule design at the same time. Under the constraint of port time window, a mathematical programming model is established to minimize the total operation cost, which considers the optimization of port docking sequence, ship arrival time and speed of each leg at the same time, and is transformed into a mixed integer programming model to obtain the optimal solution.…”

“…It is found that different time windows will affect the call order of the optimal port. Jiang et al, 2020a , Jiang et al, 2020b also proposed a soft time window considering customer preferences, constructed a mixed integer nonlinear nonconvex model comprehensively considering how to balance the total operating cost of ships and the penalty cost for violating the weekly soft time window, and transformed it into a mixed integer linear optimization model for solution, and determined the optimal ship arrival time and alleviated port congestion.…”