We introduce the Hierarchical Seating Allocation Problem (HSAP) which addresses the optimal assignment of hierarchically structured organizational teams to physical seating arrangements on a floor plan. This problem is driven by the necessity for large organizations with large hierarchies to ensure that teams with close hierarchical relationships are seated in proximity to one another, such as ensuring a research group occupies a contiguous area. Currently, this problem is managed manually leading to infrequent and suboptimal replanning efforts. To alleviate this manual process, we propose an end-to-end framework to solve the HSAP. A scalable approach to calculate the distance between any pair of seats using a probabilistic road map (PRM) and rapidly-exploring random trees (RRT) which is combined with heuristic search and dynamic programming approach to solve the HSAP using integer programming. We demonstrate our approach under different sized instances by evaluating the PRM framework and subsequent allocations both quantitatively and qualitatively.

翻译：本文提出了层次化座位分配问题（HSAP），旨在解决具有层级结构的组织团队在平面布局中的最优物理座位分配。该问题的现实背景在于，具有复杂层级体系的大型组织需要确保具有紧密层级关系的团队（例如一个研究小组）在空间上相邻分布，以占据连续区域。目前，该问题主要通过人工方式处理，导致重新规划频率低且效果欠佳。为减轻人工负担，我们提出了一种端到端的HSAP求解框架。该框架采用概率路图（PRM）与快速探索随机树（RRT）相结合的方法，可扩展地计算任意座位对之间的距离，并融合启发式搜索与动态规划方法，通过整数规划求解HSAP。我们通过定量与定性评估，在不同规模实例中验证了PRM框架及其后续分配方案的有效性。