In the context of increasingly uncertain maritime logistics environments, container Demurrage and Detention (D&D) charges pose a significant challenge to both carriers and shippers. Traditional policies typically impose separate cost structures for container pickup (demurrage) and container return (detention), yet such separate impositions often fail to capture the interconnected nature of operational delays and the pervasive uncertainty present in hinterland container flows. This study addresses the problem of D&D decision-making under uncertainty by proposing a merged free time policy that integrates both D&D charges into a unified framework. By merging the free time allocated for both pickup and return processes, the proposed policy aims to enhance operational flexibility, reduce overall logistics costs, and provide a more predictable cost structure for carriers while improving service quality for shippers. To achieve these objectives, we develop a mathematical optimization model that incorporates stochastic pickup and return scenarios, thereby reflecting the uncertainties in container availability and transportation delays. The model embeds a strategic decision-making process between carriers and shippers through a hierarchical framework to jointly optimize free time allocations and penalty structures. Numerical experiments based on simulated data demonstrate that the merged free time policy outperforms traditional separate policies by improving container turnover efficiency and mitigating the negative impact of uncertainty on operational performance. Our findings offer valuable insights into cost management and risk reduction in maritime logistics and contribute to the literature by providing a comprehensive strategy for D&D management that supports more collaborative hinterland container operations and enhances overall supply chain resilience.

1. 서 론
2. Literature Review
    2.1 D&D 정책 관련 연구
    2.2 해운물류 불확실성 및 최적화 모델 연구
    2.3 연구의 차별성
3. Mathematical Model
    3.1 문제정의
    3.2 Stackelberg 게임 모델 적용 방식
    3.3 주요 파라미터 및 결정변수
    3.4 선사 이익 함수
    3.5 화주 이익 함수
4. Experiments
    4.1 Validation
    4.2 Sensitivity Analysis
5. Conclusion
Acknowledgement
References
Appendix

• Yoonjea Jeong(Division of Systems Management and Safety Engineering, Pukyong National University) | 정윤제 (부경대학교 시스템경영, 안전공학부) Corresponding author
• HaeKyeong Jung(Department of Data Engineering, Pukyong National University) | 정해경 (부경대학교 데이터공학과)