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国际学术期刊
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国际学术期刊
Liner ship route schedule design with port time windows
发布时间:2014-3-219:0:45来源:作者:Shuaian Wang, Abdurahim Alharbi, Pam Davy   

Shuaian Wang
Abdurahim Alharbi
Pam Davy


Highlights


•Liner ship route schedule design considering port availability.
•Holistic solution approach that obtains global optimal solution.
•Extensive experiments based on real-case liner ship routes.



Keywords
Container liner shipping; Schedule design; Containership scheduling; Port time windows; Mixed-integer nonlinear programming



Abstract

This paper examines a practical tactical liner ship route schedule design problem, which is the determination of the arrival and departure time at each port of call on the ship route. When designing the schedule, the availability of each port in a week, i.e., port time window, is incorporated. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear nonconvex optimization model. In view of the problem structure, an efficient holistic solution approach is proposed to obtain global optimal solution. The proposed solution method is applied to a trans-Atlantic ship route. The results demonstrate that the port time windows, port handling efficiency, bunker price and unit inventory cost all affect the total cost of a ship route, the optimal number of ships to deploy, and the optimal schedule.



Article Outline

1. Introduction
1.1. Literature review
1.2. Objectives and contributions

2. Problem description
2.1. Ship cost, bunker cost and inventory cost
2.2. Liner ship route schedule
2.3. Port time windows
2.3.1. Berth time windows
2.3.2. Feasible arrival days at ports and berths


3. Mathematical model
4. Solution method
4.1. Relaxed models
4.1.1. Relaxing port time window constraints
4.1.2. An equivalent mixed-integer linear programming model

4.2. Global optimization method
4.2.1. Reformulation
4.2.2. Linear constraints excluding infeasible solutions
4.2.3. Overall algorithm


5. Case study
5.1. Performance of the solution algorithm
5.2. Impact of port time windows
5.3. Consequence of port efficiency
5.4. Result of bunker prices
5.5. Effect of inventory cost

6. Conclusions and future work
Acknowledgment
References


Figures

   

Fig. 1.

AGM service provided by OOCL (2013).


Fig. 2.

Linerization.


Fig. 3.

Number of ships and total cost in each iteration.


Fig. 4.

Impact of port time windows.


Fig. 5.

Impact of port time at Miami on the total cost.


Fig. 6.

Impact of port time at Miami on the number of ships.


Fig. 7.

Result of bunker prices on the total cost and the number of ships.


Fig. 8.

Effect of unit inventory cost on the total cost and the number of ships.



Tables


Table 1. Available time at each port.

Table 2. Parameters in the case study.

Table 3. Different cases of available time at Miami.

Table 4. Impact of port time window on the optimal schedule.

Table 5. The scenarios of port times of the two calls at Miami.

Table 6. Optimal schedules of the 4 scenarios under berth availability case 2.

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