Managing Surcharge Risk in Strategic Fleet Deployment: A Partial Relaxed MIP Model Framework with a Case Study on China-Built Ships

Container liner shipping companies operate within a complex environment where they must balance profitability and service reliability. Meanwhile, evolving regulatory policies, such as surcharges imposed on ships of a particular origin or type on specific trade lanes, introduce new operational challe...

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Bibliographic Details
Published in:Applied sciences Vol. 15; no. 15; p. 8582
Main Authors: Tao, Yanmeng, Yang, Ying, Wang, Shuaian
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2025
Subjects:
bi-objective mixed-integer programming model
Case studies
Coal
container liner shipping
Costs
Decision making
Energy consumption
Integer programming
International trade
Linear programming
Mathematical programming
operational surcharges
Optimization
Pareto frontier
Ports
Profit maximization
Profits
risk management
Ships
totally unimodular
Trade restrictions
US exports
Variables
United States > US
China
ISSN:2076-3417, 2076-3417
Online Access:Get full text
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Summary:Container liner shipping companies operate within a complex environment where they must balance profitability and service reliability. Meanwhile, evolving regulatory policies, such as surcharges imposed on ships of a particular origin or type on specific trade lanes, introduce new operational challenges. This study addresses the heterogeneous ship routing and demand acceptance problem, aiming to maximize two conflicting objectives: weekly profit and total transport volume. We formulate the problem as a bi-objective mixed-integer programming model and prove that the ship chartering constraint matrix is totally unimodular, enabling the reformulation of the model into a partially relaxed MIP that preserves optimality while improving computational efficiency. We further analyze key mathematical properties showing that the Pareto frontier consists of a finite union of continuous, piecewise linear segments but is generally non-convex with discontinuities. A case study based on a realistic liner shipping network confirms the model’s effectiveness in capturing the trade-off between profit and transport volume. Sensitivity analyses show that increasing freight rates enables higher profits without large losses in volume. Notably, this paper provides a practical risk management framework for shipping companies to enhance their adaptability under shifting regulatory landscapes.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app15158582