Research on Multi-period Empty Container Repositioning Optimization under Free Detention Time and Shipping Company Cooperation

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Journal of Dalian Maritime University ›› 2026, Vol. 52 ›› Issue (1) : 40-51.

CAI Jia-xin¹，HUANG Ying²，JIN Zhi-hong^2*

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Abstract

In response to the industry pain point of high cost of ocean freight empty container repositioning, an innovative combination of shipping company cooperation mechanism and free detention time strategy is proposed. Taking into account four channels for obtaining empty containers, namely container repositioning, storage, rental, and exchange, a nonlinear programming model is constructed with the goal of minimizing the total cost of empty container repositioning. By designing an approximate dynamic programming algorithm based on greedy strategy, the multi-period decision-making and nonlinear coupling problems that traditional methods are difficult to handle have been solved, and the optimal decision for the length of free container period in different scenarios has been provided. Research has found that setting a reasonable free container detention period can reduce container rental costs and optimize container usage costs under cooperation with shipping companies. Sensitivity analysis shows that when the supply of empty containers exceeds the demand, the total cost of empty container management for shipping companies will reach its optimal level. For every 33% increase in inland container volume or 1 day extension in transportation time, the free detention period needs to be shortened by 1-2 days to achieve cost optimization. This collaborative decision-making framework helps improve the efficiency of empty container resource turnover in shipping companies and provides a basis for determining the length of free detention period for shipping companies.

Key words

free detention period / approximate dynamic programming / empty container repositioning / nonlinear programming / shipping company cooperation

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CAI Jia-xin, HUANG Ying, JIN Zhi-hong. Research on Multi-period Empty Container Repositioning Optimization under Free Detention Time and Shipping Company Cooperation[J]. Journal of Dalian Maritime University. 2026, 52(1): 40-51

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