Beyond Manual Planning: Seating Allocation for Large Organizations

TL;DR

This work addresses the challenge of seating large organizations with hierarchical structures by introducing HSAP, which seeks to seat closely related teams near one another on a floor plan. It advances distance estimation through a scalable PRM/RRT framework to capture traversable walking paths, and decomposes HSAP into SA subproblems solvable by IPSA, ICA, GSA, and LS, with a hierarchical extension via DF-HSA and Delayed Office Selection. The study shows IPSA generally yields the best average central-seat distances across multiple instance sizes, while ICA+LS offers favorable trade-offs between quality and time, and delaying office allocation improves alignment with leaf-team offices. Practically, the framework enables near-online reallocation of office space for large organizations, balancing distance-based objectives with hierarchical constraints and office-resource considerations.

Abstract

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.

Figures (5)

• Figure 1: Output of the PRM algorithm when applied to a synthetic floor plan. The hyper-parameters for $\delta_c$ and $\delta_s$ were manually tuned until the algorithm converged with a node limit of $K=2000$.
• Figure 2: An example organizational hierarchy. Each node corresponds to a team and each child node is a member of its own team and its parent team.
• Figure 3: Depicts the output of the HSA-DF algorithm with local search heuristics as applied to the organizational hierarchy as described in Figure \ref{['fig:hierarchy']} with the floor plan from Figure \ref{['fig:RRT']}. In total the population required 103 desks and 6 offices, leaving 3 vacant desks.
• Figure 4: Depicts the effect on total office distance per level of DF-HSA across all methods. Note how delaying the office decision enables higher level hierarchy teams to on average sit closer to their aligned offices. This is beneficial as the purpose of the HSA framework is to allocate leaf teams while considering their branch parent's team.
• Figure 5: Toy example allocation of 4 teams being allocated to a total of 42 seats which are physically separated by four gray-colored walls using IPSA framework with different seat distance estimation methods.

Theorems & Definitions (2)

• Definition 3.1: Seat Allocation (SA)
• Definition 3.2: Hierarchical Seat Allocation Problem (HSAP)