The stowage planning and block relocation problem (SPBRP) consider the relations between stowage planning and block relocation comprehensively, in which the retrieval sequence of containers in yard and the stowage plan of a ship are concerned. In this paper, an integer programming formulation called SPBRP-I is presented for the proposed problem in inland container liner shipping to minimize the total number of relocations in yard and re-handles in ship. To deal with the utilization preference in inland shipping, the minimization of ship stack occupancy number is introduced into SPBRP-I to develop a new model called SPBRP-II. In view of the complexity of problem-solving, a heuristic algorithm (HA) based on priority sorting, retrieval and local search strategies is proposed to achieve the efficient optimization. The algorithm consists of three parts including the yard container retrieving, yard container relocation and ship stowage planning. Finally, the container liner shipping on the Yangtze River is chosen with some typical ships for the case study. Numerical results show that SPBRP-II performs better than the original SPBRP-I, and it’s more suitable for solving the small-sized cases. Compared with the models, the algorithm with retrieval strategy RS1 (HA_RS1) can achieve the efficient problem solving with high-quantity solutions and very short computational time.

中文翻译：

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优化内河集装箱运输配载规划与分块搬迁问题

配载计划和块重定位问题（SPBRP）综合考虑了配载计划和块重定位之间的关系，其中涉及堆场集装箱的取回顺序和船舶的配载计划。在本文中，针对内陆集装箱班轮运输中提出的问题，提出了一种称为 SPBRP-I 的整数规划公式，以最小化堆场搬迁和船舶重新处理的总数。为应对内河航运的利用偏好，在SPBRP-I中引入船堆占用数最小化，开发了一种新的模型，称为SPBRP-II。针对问题求解的复杂性，提出了一种基于优先排序、检索和局部搜索策略的启发式算法(HA)来实现高效优化。该算法由堆场集装箱取回、堆场集装箱搬迁和船舶配载规划三部分组成。最后，选择长江集装箱班轮运输，并结合部分典型船舶进行案例研究。数值结果表明，SPBRP-II的性能优于原SPBRP-I，更适合解决小规模案件。与模型相比，具有检索策略RS1（HA_RS1）的算法可以实现高效的问题求解，解决方案数量多，计算时间极短。更适合解决小型案件。与模型相比，具有检索策略RS1（HA_RS1）的算法可以实现高效的问题求解，解决方案数量多，计算时间极短。更适合解决小型案件。与模型相比，具有检索策略RS1（HA_RS1）的算法可以实现高效的问题求解，解决方案数量多，计算时间极短。