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Article

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

1
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
2
Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(15), 8582; https://doi.org/10.3390/app15158582 (registering DOI)
Submission received: 25 June 2025 / Revised: 23 July 2025 / Accepted: 30 July 2025 / Published: 1 August 2025
(This article belongs to the Special Issue Risk and Safety of Maritime Transportation)

Abstract

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.
Keywords: container liner shipping; bi-objective mixed-integer programming model; totally unimodular; Pareto frontier; operational surcharges; risk management container liner shipping; bi-objective mixed-integer programming model; totally unimodular; Pareto frontier; operational surcharges; risk management

Share and Cite

MDPI and ACS Style

Tao, Y.; Yang, Y.; Wang, S. Managing Surcharge Risk in Strategic Fleet Deployment: A Partial Relaxed MIP Model Framework with a Case Study on China-Built Ships. Appl. Sci. 2025, 15, 8582. https://doi.org/10.3390/app15158582

AMA Style

Tao Y, Yang Y, Wang S. Managing Surcharge Risk in Strategic Fleet Deployment: A Partial Relaxed MIP Model Framework with a Case Study on China-Built Ships. Applied Sciences. 2025; 15(15):8582. https://doi.org/10.3390/app15158582

Chicago/Turabian Style

Tao, Yanmeng, Ying Yang, and Shuaian Wang. 2025. "Managing Surcharge Risk in Strategic Fleet Deployment: A Partial Relaxed MIP Model Framework with a Case Study on China-Built Ships" Applied Sciences 15, no. 15: 8582. https://doi.org/10.3390/app15158582

APA Style

Tao, Y., Yang, Y., & Wang, S. (2025). Managing Surcharge Risk in Strategic Fleet Deployment: A Partial Relaxed MIP Model Framework with a Case Study on China-Built Ships. Applied Sciences, 15(15), 8582. https://doi.org/10.3390/app15158582

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